14 ms·

A Way to Detect Bias

282 points by bakztfuture 11y ago

urs2102 11y ago
I think the first footnote in this is extremely valid. It all depends on what performance metric the selection process is identifying compared to the performance metric you use to determine success. I would suspect the larger issue is that people are probably much worse at identifying what performance metrics for selection convert to their respective performance for success.
- newjersey 11y ago
  If students of Asian origin outperform the whole student body, can we conclude admissions folks are biased against students of Asian origin?
  - aceperry 11y ago
    That's possible. Without concrete data to give you, there are some suspicions that because of the much better performance of Asian students, they're being limited in the admissions process. Otherwise, Asian students would make up the vast majority of the students admitted. This would crowd out the non-Asian students accepted for admission. In this case, it would be more accurate to say that admissions officers limit the number of Asian students accepted instead of saying admissions folks are biased against Asian students.
    - pbhjpbhj 11y ago
      >admissions officers limit the number of Asian students accepted instead of saying admissions folks are biased against Asian students // The effect is the same isn't it? Less chance for a student with ancestors from a particular geographic locale getting a placement.
      - aceperry 11y ago
        The effect would result in the same situation, but the cause is much different.
  - cookiecaper 11y ago
    Alternately, you could conclude that instead of "mediocre" Asians being excluded by bias, Asians have an external advantage that makes them perform better. Maybe it's cultural, since most Asians are taught a very strong work ethic and heavy emphasis is placed on formal schooling, succeeding, and fitting in. Maybe Asians are physically better adapted to that type of work, with brains that retain information more easily or buttocks that don't get sore from sitting in a chair all day. The "high performance means there's a bias" theory only works if you assume that everyone is starting from the same social, cultural, and physical baseline. They aren't. Maybe a better metric would be if there were no mediocre data points among a certain group; that would be more evidence (but still not necessarily good evidence) that you have to exceptional to get attention and overcome the "bias barrier", not simply that most of a certain type of performer does better than a different type.
    - srtjstjsj 11y ago
      Even if Asians perform better for external reasons, the selection process should account for that before the selection is made, and the admitted class should be roughly equal performers, as a group. Unless Asians have a very lumpy shaped performance curve across the group
      - cookiecaper 11y ago
        This presupposes that we should not accept unequal representation among groups. I don't believe that, and I don't think it's an implicit Western value. People should be allowed to flourish according to their natural advantages. The value is to try not to make an early judgment and exclude people based on assumptions about their group's capability, whether that exclusion is based on the group's perceived disadvantage or advantage. The idea is that the individual shouldn't be held accountable for things he had nothing to do with, and shouldn't be assumed to be automatically compliant with stereotypes. I don't see a need to start throttling groups that are doing "too well".
        srtjstjsj 11y ago
        You misunderstood what I wrote. I didn't claim that a high performing subgroup should be throttled, I claimed that the Asians that pass an unbiased bar would be roughly as successful as the non-Asians that pass the same bar. I
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Phemist 11y ago
Footnote one should be put more generally, biases in the performance metrics (either appearance for women vs ability for men, or how many words of the US national anthem someone knows for US citizens vs rest of the world) will cause this method to fail. Unfortunately, unbiased performance metrics are quite hard on single dimensions, let alone when moving to multi-dimensional metrics
SeriousM 11y ago
Isn't every selection process based on experience, knowledge and/or mood and therefore baised?
- newjersey 11y ago
  He makes a few assumptions. But he is probably correct within those assumptions. We assume all candidate pools are homogeneous. If all members of a certain subset A of a global population P is simply better at a task than any member of another subset B of the global population, we will see that this holds true for members of our sample as well. Thus, members of A in our sample will consistently outperform members of B in our sample. Does this mean there is a bias against A? Well, yes because if there wasn't then there would be fewer members of B or perhaps no members of B in our sample based on this result alone. However, real life is not one-dimensional. Sometimes we need to consider other factors as well.
gizmo 11y ago
A related observation (which I've been making for a long time) is that the absence of mediocre women in positions of power is strong evidence of bias. Men can succeed when they're mediocre, but women have to be exceptional. Likewise for minorities.
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- cookiecaper 11y ago
  What's "exceptional"? I've known many women in my career and many of them were mediocre. Some were in positions of authority and some weren't. Another commenter lists several "mediocre" women in the corporate and political world (and leaves out some big ones, like Meg Whitman). If you're talking about becoming a CEO, you have to be an "exceptional" man to get there too, in absolute terms. I feel like the root erroneous assumption here is that an equal amount of people of all types are interested in the same things and that the only reason any group becomes more represented than another is that the others are getting alienated or funneled out somewhere along the way. That is a completely incorrect and invalid assumption. The fact that there are a lot more non-English-speakers in janitorial work in the US (when I worked as a janitor, I was 1 of 2 English speakers on the 12-person janitorial staff) doesn't necessarily mean the janitorial manager is biased against English speakers; it means that due to external considerations, like the fact that almost all other jobs require you to speak the native language, non-English-speakers are better suited for janitorial work, and therefore people do the logical thing, apply for work that they can do, and end up comprising a larger section of the application pool. People make decisions based on social, cultural, and physical expectations of them, and there's not anything wrong with that. By and large, women do not have an interest in computer sciencey or entrepreneurial work. It's OK if a woman does, but it's also OK to note that most women don't. There's nothing we need to fix about it. Most women don't want to do it, and there's no reason to force them. Why do you see fewer women becoming CEOs? Because fewer women want that kind of job and fewer women are qualified for that kind of job due to the biological realities of humanity that require women to take time out for pregnancy and child-rearing (sorry denialists, I didn't invent biology and choose that only women could bear and nurse children, so don't take it up with me), and the social and cultural expectations that have formed around these biological realities. In short, the serious applicant pool includes only a very small amount of women, so only a very small number of women obtain that position.
Mz 11y ago
Actual real world example (and application of an antidote) of this basic idea: https://en.wikipedia.org/wiki/Rooney_Rule https://en.wikipedia.org/wiki/Rooney_Rule
in3d 11y ago
Graham's statement about the possible bias of First Round is unfounded. This was not any sort of a real study like Graham thinks and First Round clearly notes that. When the returns are as skewed as they are in venture capital (http://www.sethlevine.com/archives/2014/08/venture-outcomes-are-even-more-skewed-than-you-think.html http://www.sethlevine.com/archives/2014/08/venture-outcomes-...), a small sample size and a simple analysis won't do. First Round even excluded their investment in Uber because it would skew the results too much.
- khed 11y ago
  Even if it were a statistically appropriate sample size and female founders still out performed male founders it still wouldn't exlcude other likely explanations other than bias. What if the culture in venture capital is more willing to assist and mentor female founders leading to greater success? In academia there is a women are selected over equally qualified men 2:1 for tenure positions now [1]. It is not unreasonable to wonder if a similiar hand up is being given to female founders in terms of training, social network inclusion, and mentorship leading to greater success. Alternatively, there may be a selection process in society that means only the most motivated women become entrepeneurs and so beat the average male entrepeneur. [1]. http://www.pnas.org/content/early/2015/04/08/1418878112.abstract http://www.pnas.org/content/early/2015/04/08/1418878112.abst...
  - TomGullen 11y ago
    > female founders still out performed male founders That's not what the study says, it says groups that have at least 1 female founder, not female founders.
eridius 11y ago
There's a few trivial ways to be biased that would not be detected in this way. The first is if you have multiple people accepting applicants and some of them are biased to the point of not accepting applicants of particular types. That means all the applicants that are discriminated against that did make it were simply selected by people who weren't biased, and therefore won't outperform anyone. The second is if the actual selection process is somewhat random instead of being based on pure performance. The ones who make it through that process won't necessarily perform any better, they'll just be luckier. The third is if the application process accepts everyone equally, and then randomly prunes out people according to a bias. This is similar to the second except the acceptance criteria is still performance-based, but because it randomly throws out people (instead of throwing out low-performers), the remaining people are still going to perform the same as those who were not pruned. The first footnote on the page also points out that if the selection criteria are different for the different groups then this process won't work, which seems like a pretty important caveat that I wish was in the article proper. One really common form of bias (especially in tech) is being biased against women, and that's also a situation where it's very common to (unconsciously or otherwise) use appearance in judging female applicants but ignore appearance for male applicants.
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- yummyfajitas 11y ago
  The second example adds statistical noise, but does not invalidate Graham's procedure. In the absence of noise, the distribution of accepted people will be H(x-C) f(x) for the main group, and H(x-C-K)g(x) for the other group (where H(x) is a step function, f(x) and g(x) are the distributions of quality of the two groups). If noise is present, then you get convolve(H(x-C)f(x), k(x)) instead, where k(x) is the pdf of the noise distribution. You'll need more samples to measure this, but it's completely measurable via Graham's method.
- lisper 11y ago
  A fourth is to deliberately select low-performing members of the discriminated-against group in order to game Graham's metric and justify the bias.
devalier 11y ago
Fortunately there's a way to measure bias that's much more reliable, when it can be used....A couple months ago, one VC firm (almost certainly unintentionally) published a study showing bias of this type. First Round Capital found that among its portfolio companies, startups with female founders outperformed those without by 63%. Except if you want to use statistics to measure bias, you need a statistically significant sample. And actually, if you are studying complex human affairs, with a hundred different variables, you need more than statistical significance, you need a sensitivity analysis. It is similar to nutrition studies. There are so many variables at play that something can always be found to increase or decrease your risk of cancer by 50%. You really only need to pay attention when statistics show an order-of-magnitude correlation, as with the link between smoking and lung cancer. With the First Round Capital data, they excluded Uber from their calculations, because it would skew everything. If a single data point can switch your findings to be opposite, then you just have to admit that you do not have enough data to make determination one way or another. In science it is sometimes ok to exclude an outlier, since it often indicates a measurement error. But in venture capital, you make most of your money off of the Uber-like outliers. So if you are trying to study the data to be the best venture capitalist possible, throwing out outliers is not valid. Also, the initial premise is incorrect too. You cannot measure bias by comparing average results, because the average is not the marginal. Consider PG's footnote: "Although I used female founders as an example because that is a kind of bias people often talk about, the most striking thing was the degree to which First Round undervalue founders who went to elite colleges." Does he honestly believe that First Round is biased against founders from elite colleges? At my last company my sense was that the MIT grads were better than the average programmer. So were we biased against MIT grads? Should we have hired more MIT grads until the average performance of MIT grads overall equaled the average performance of an employee overall? Should we have done more outreach to MIT? Should the industry as a whole hired more MIT grads? If a talent distribution has a bunch of elite, and then a steep drop-off filled with "pretenders", then you can get this type of effect without being biased. When we got an elite MIT grad, we hired them. When we got a "pretender", someone who was trading on the name but did not put in the work, we rejected them. And yes, I personally saw MIT grads that did terrible on simple coding exercises. So even though the average MIT grad we hired was better than the average programmer at our company, there was no way to alter our hiring process to get more MIT grads. If we hired the marginal MIT grad that we rejected, we would have been worse off. Now we could do more outreach to MIT, and we did, but that is a highly competitive process. There were diminishing marginal returns to how much outreach we can do to get more applicants. The statistical illiteracy of PG's post is simply stunning. Imagine a YC company gets a 100% ROI from PPC ads, and a 50% ROI from banner ads. Are they biased against PPC ads? Should they buy more PPC ads? Such an analysis is ridiculous. You look at what you are spending on the marginal PPC ad, and you stop spending when the ROI on the marginal ad is at zero, regardless of what the average is. That one advertising channel has a higher ROI on average does not mean that the company is biased against that channel.
nkurz 11y ago
This approach relies on the unspoken "positivity" assumption that the pool of applicants is large enough that there exist individuals in the biased-against category that were not selected, and moreover that these denied applicants are "exchangeable" with the successful ones. For example, assume that we find that founders who won a MacArthur "genius" grant outperformed the others. Further assume that there are only a limited number of such founders, and that all available were selected. Certainly one wouldn't want to conclude in this case that there is a bias against MacArthur fellows. That seems obvious, but it gets trickier once you have lots of factors involved. What if the group you find to outperform consists of female founders with a PhD, substantial industry experience, and red hair[1]. Can you conclude that the process is biased against females? Males with PhD's? Anyone with red hair? Generally no, unless you are willing to assume that all of your factors are causal. Worse, you can't even assume that it's biased against people with all of the measured factors unless you also assume that all unmeasured factors are randomly distributed. If it turns out that "a positive mental attitude" is an unmeasured but defining characteristic of success, if the interviewers rejected applicants who had less of this but you failed to include this in your category, you would be wrong to conclude that there is an unfair bias. [1] http://www.nature.com/nature/journal/v453/n7194/full/453562a.html http://www.nature.com/nature/journal/v453/n7194/full/453562a...
WildUtah 11y ago
On a simple mathematical basis, this is false. Consider two groups of candidates for a scholarship, A and B. We want to select all candidates that have an 80% or better chance of graduation. Group A comes from a population where the chance of graduation is distributed uniformly from 0% to 100% and group B is from one where the chance is distributed uniformly from 10% to 90%, with the same average but less variation in group B. Now suppose that we select without bias or inaccuracy all the applicants that have an 80% or better chance of graduation. That means we select a subset of A with a range of 80% to 100% and a subset of B with a range from 80% to 90%. The average graduation rate of scholarship winners from group A will be 90% and that from group B will be 85%. But we haven't been biased against A. We've selected according to the exact same perfect evaluation process and criterion from both groups. It was just their prior distribution that was different. The actual applicant groups for jobs or financing in the real world, when they are divided by demographic factors like age, sex, race, and educational level, will almost always manifest different variances in success levels even when the averages are the same. That makes this test useless and mathematically illiterate. And when we use a normal distribution, as we should always expect given the central limit theorem, the mathematical problems get even more intense. This short comment is not up to pg's usual high standards for his essays.
- eoi 11y ago
  The article defines bias as follows: > Want to know if the selection process was biased against some type of applicant? Check whether they outperform the others. This is not just a heuristic for detecting bias. It's what bias means. Under that definition, you have been biased against A. [edit: on reflection I see this as a weakness of his definition. I missed that your selection process does in fact select the best candidates.]
  - bjwbell 11y ago
    Yes, but that's not the common usage of the word. Or how most people understand it. With that usage you could say ivy league schools are NOT biased against Asians since Asian graduates aren't more successful than non-Asian ones, except nobody does.
pbnjay 11y ago
Fittingly, another type of bias observed in the linked report is that against Solo Founders. The report states that solo founders do worse when measured against the same yardstick as multiple founders. Maybe from a VC perspective this is intended (big raise => bigger exit?), but I'd argue that you don't need to raise as much when you have a solo founder because dilution is less of a concern.
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nartz 11y ago
Interesting thoughts. However, this argument is biased because it assumes that the performance of the applicants WHO WERE ACCEPTED is not biased by the selection process itself, and that the performance characteristics of the selected sample are representative of the performance characteristics of the total, which could be a weak assumption. An attempt at translating to mathematics (feel free to correct me!): X = event that person belongs to group x Y = event that person belongs to group y S = event that person is selected W = event that person will perform like a 'winner' for simplicity P(X) + P(Y) = 1 Naturally, 'unbiased' in this case is simply P(S|X) = P(S1), and P(S|Y) = P(S2), i.e. that the selection process is independent of a certain variable X or Y PG says we can measure the the performance of these selected applicant winners for each class, i.e. P(X|S,W). I believe PG assumes that: P(X|W) / P(Y|W) should equal P(X|S,W)/P(Y|S,W). We can see that these are different distributions, since the second is already conditioned on the selection process. Simplified, PG assumes that P(X|S,W) = P(X|W) i.e. that conditioning on the selection process does not bias the winning results. Its left for the reader exercise to determine the 'pathological' cases where this selection variable's distribution makes PG's assumption correct or incorrect. However, this is simply theoretical - the actual distribution may or may not be 'pathological' and the assumptions made by PG could very well be good.
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earljwagner 11y ago
The phenomena of "stereotype threat" complicates this conclusion however: https://en.wikipedia.org/wiki/Stereotype_threat https://en.wikipedia.org/wiki/Stereotype_threat When a member of a group is primed with a stereotype that their group underperforms at a task, they are more likely to underperform. So there could be a selection process biased against a group, and a selected member could be an above-average performer otherwise but, because of work environment, be underperforming. Some universities work to remedy this through support groups or other practices aimed at under-represented minorities, and they appear to help students be more successful academically. On the other hand, there's the Hawthorne effect... https://en.wikipedia.org/wiki/Hawthorne_effect https://en.wikipedia.org/wiki/Hawthorne_effect
- yummyfajitas 11y ago
  This is only a bias if the stereotype effect is stronger on measurements than in real life. If stereotype threat affects test performance and real performance the same way, then it means that the stereotyped group is truly inferior. Do you have evidence that stereotype threat hurts test performance more than real performance? (Of course, in a hypothetical world which only eliminated the stereotype, the group would cease to be inferior. I.e., the inferiority is based on context, and is not intrinsic.)
  - earljwagner 11y ago
    I wouldn't agree with the conclusion of being truly inferior - there could be ongoing issues with the work context. I'll put it another way: Graham says we can look at just the performance by group to detect bias in selection. But there could be bias in selection, and A) different treatment after selection, which would not be revealed through Graham's test. Or could also be bias in selection and B) continuous reminders of stereotypes triggering stereotype threat, and this would also not be revealed. Now you could point to a tech company with few underrepresented minorities, let's say 1%. If there's no overt bias in the work environment then people should succeed and if they don't they're just worse performers. On the other hand, if you're in the 1%, just noticing the underrepresentation among your coworkers might be a constant reminder of stereotypes. I don't claim to have a simple solution for this.
yummyfajitas 11y ago
People, most of whom clearly are not that good at math, are being really harsh on Paul Graham. Graham is mostly right, but slightly incorrect. In particular, suppose group A has the distribution f(x) and B has the distribution g(x). If f(x) and g(x) are shaped significantly differently past the cutoff, then mean(H(x-C)f(x)) and mean(H(x-c)g(x)) might not agree even though there is no bias by construction. (Here H(x) is a step function and C the cutoff). However, there is an easy fix: compute the minima of the support of the distribution rather than mean. min(H(x-C)f(x)) = min(H(x-C)g(x)) = C. In practice, measure the weakest male and weakest female to be accepted in your sample set, or some similar approximation. I'm pretty sure this is a valid frequentist hypothesis test. I've got half a proof worked out on paper already. It depends very weakly (and non-parametrically) on f(x) and g(x), but it works in basically the exact way Graham wants it to. Every counterexample I can think of is really pathological. My next blog post will probably be a proof of this. All this negativity is really an overreaction. I know it's fun to totally debunk someone on details, but these are mostly fixable details.
- MattHeard 11y ago
  Wouldn't the weakest male and weakest female founders be underperforming more due to individual factors than bias? Maybe a mean of the lower quartile would remove some the the noise.
  - yummyfajitas 11y ago
    Suppose the cutoff for men is C but for women is C+K. Then the weakest man can be expected to have quality C+epsilon, while the weakest woman will have quality C+K+epsilon. Here epsilon is how close a typical candidate will be to the cutoff, and is mainly a function of the sample size. I don't know the behavior of epsilon off the top of my head.
    - tprice7 11y ago
      I think MattHeard understood this and his point was that the weakest man will realistically have quality C + epsilon + random, and the weakest woman will have quality C + K + epsilon + random. The random term arises because no evaluation process is going to perfectly tell you how people are going to end up performing. But yeah, this seems fixable also, by averaging some number of the lowest performing members of each group, as MattHeard suggested.
logicallee 11y ago
Could someone who read it more attnetively tell me, by this methodology, -> If in retrospect YC finds any factor that its selected founders who turn into unicorns ($1b, $10b etc) have in common (more than its non-unicorn, also accepted founders) -> Then by this method, could it conclude retroactively that it had been "biased" against that factor? (since it is present more than in its non-unicorns whom it had also admitted; i.e. in other words, those with the factor are more performant than "would be expected" without the bias against it?) Or have I misunderstood?
proveanegative 11y ago
If candidates from group A perform more strongly on average than those from group B there are other possible causes than bias in the selection process itself. For instance, members of group A may only apply at a higher level of self-assessment for how likely they are to succeed than those in group B. The reason for this could be opportunity cost not present for group B, overconfidence or lack of underconference in group B or underconference or lack of overconfidence in group A.
jblow 11y ago
All other arguments aside ... this idea also fails if the judging party's idea of quality is mostly uncorrelated with actual quality. Which Graham says in other essays is usually the case (it's what you mean when you say it's almost impossible to predict which companies will be successful). Graham says the subjects of bias "have to be better to get selected", but what is really going on is they have to be better according to the metrics of the judge which are essentially arbitrary.
- yummyfajitas 11y ago
  This is false - noise doesn't hurt this test at all. See my comment explaining why: https://news.ycombinator.com/item?id=10483991 https://news.ycombinator.com/item?id=10483991 Bad measurements add noise (and increase the sample size required) but they don't invalidate the bias detection procedure.
- gizmo 11y ago
  This is also in large part why people tend to hire/fund younger versions of themselves. If judgement wasn't arbitrary much more diversity should be expected.
d0m 11y ago
I don't get it :-/ Why is there a bias? Even if the VCs are totally unbiased, why couldn't the startups with women outperformed the others? It could happen for a variety of reasons. Just hypothetically speaking, maybe startups-with-women have different networking connections or insight that male-only-startups don't have?
- Alex3917 11y ago
  > Why is there a bias? Applications by definition are supposed to be biased. If an application weren't biased then it wouldn't be an application, it would just be a lottery. And while that's a system that a lot of charter schools actually use, or a least pretend to, I think it would be a tough sell to convince venture capitalists to allocate their capital this way.
- esfandia 11y ago
  Then, if I understand PG's argument correctly, the VCs should invest in even more startups-with-women, and lower their threshold on investing them, at least until they perform no better than startups-without-women.
  - wycats 11y ago
    Indeed!
- wycats 11y ago
  If that were the case, VCs should accept more companies-with-women, which would change the TOTAL mix of accepted candidates so that the women no longer overperformed. The issue, interestingly, is that there are a lot of women (or biased-against group) between the median performance and 160% performance who are being rejected. In other words, only the best women can get accepted, which means that above-median (but not superstars) are getting rejected, while many more above-median men are getting accepted. This has the ring of truth to me (as pg says, it's the definition of bias).
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TomGullen 11y ago
> A couple months ago, one VC firm (almost certainly unintentionally) published a study showing bias of this type. First Round Capital found that among its portfolio companies, startups with female founders outperformed those without by 63%. Well, they also said in their study: > And we are not claiming that our data is representative of the industry...or even statistically significant. Also, the wording is "startups with a female founder", not exclusively female founders... I think this is a detail that shouldn't be ignored. And, the study doesn't show how many companies out of the 300 had female founders! Maybe it was just 1! They also say "Solo Founders do Much Worse Than Teams", so this is an important detail if there are no solo female teams ever backed in their firm! etc etc, the list goes on. Not exactly strong evidence to support the point PG is making, that bias would be easy to detect. Measuring performance purely in terms of "how much money I make" is one way of doing it, but not the only way. And it wont cover the majority of jobs on the planet (how do you measure performance of someone who stacks shelves in a supermarket?)
MichaelGG 11y ago
I don't understand his point about First Round Capital showing their female founders did better than companies without female founders. What does that show? How do we know that female founders aren't simply better? Or maybe women are scared of applying, so out of women, only the best apply? In that case, the mere idea that there is a bias can cause "pre-selection" bias. I lack the mathematics to prove this, but it seems that on the face of it, pg is simply wrong. Or I'm misreading terribly. Tangentially: Speaking of bias, why doesn't YC publish information on their companies' tech choices? PG racked up a lot of inferred cachet (positive) by stating that use of Lisp gave them a huge advantage. Now that YC has data, they should be able to show how choice of technology correlates to performance.
- esfandia 11y ago
  The argument is that First Round Capital must have implictly made it harder for female founders to get funding, since the ones who do perform better. The rational course of action for First Round Capital would be to lower their threshold on female founders (or, conversely, raise the threshold on male founders) until they perform no better or no worse than male founders.
  - MichaelGG 11y ago
    And that's not proven by the evidence. It might be a good thing to look into, but pg's statement that you don't need more info is wrong.
    - esfandia 11y ago
      Yeah, I was just rephrasing PG's argument for the OP, not saying whether it was right or wrong. I'm not smart enough to know.
- YokoZar 11y ago
  It's certainly possible that the observed bias isn't the fault of First Round Capital's selection process if the applying populations are different -- the "pre-selection" bias you're talking about. If that's the case, First Round Capital could profitably benefit from encouraging more female founders to apply.
wycats 11y ago
The implication of this analysis of http://10years.firstround.com/ http://10years.firstround.com/ is that First Round is biased against founding teams with experience at Amazon, Facebook, Apple, Google, Microsoft or Twitter. Can this be true?
- tedsanders 11y ago
  Yes, it can be true. FirstRound could still positively value that experience, but just not be valuing it enough.
  - wycats 11y ago
    Makes sense. Fascinating.
compbio 11y ago
PG: Assumption: There is no fundamental difference between a female and a male founder for achieving start-up success (average rates and variance/distribution of rates is the same) Observation: VC funded start-ups with female founders are (on average) 60% more successful than start-ups with male founders Hypothesis: VC funding is biased against female founders. The ones that do receive funding are better vetted, less risky, and have higher individual qualities. Experiment: Start funding more female founders. If we then observe: The numbers start to even out, then there is no fundamental difference. VC funding bias may have been the cause of the difference in success rate. If we then observe: The numbers stay the same, then there is a fundamental difference and our assumption is flawed. Rational choice: Start funding more female founders. This either removes a bias (levels the playing field), or increases your profit (funding more potentially successful founders). PG should of course not use an hypothesis to prove an assumption (experiment/probing is needed for verification). But also: The possibility of an uneven distribution should not invalidate such an experiment (or PG's line of reasoning), it will merely bring it to light (the numbers would stay the same, thus we have shown that the difference is fundamental and not caused by a sampling bias).
tracker1 11y ago
I just asume there is bias... I mean the fact is, bias is what youare trying to work in favor of... that bias being factors of success. Chasing your tail against random statistics won't really show much, and a person is more complex that a few statistical groups. As far as investing goes, there's also the product, and how that leader/founder matches to that product category itself. A founder that succeeds in one category won't definitively succeed in another. Many founders fail their first few times, and later succeed. Others fail after some success(es). I think as long as reasonable steps are made to avoid certain obvious bias, the rest is mostly chance.
j2kun 11y ago
There is an emerging subfield of computer science that studies what it means for data (or algorithms, or decision-making rules) to be biased, and how to remove certain forms of bias. See http://fatml.org http://fatml.org
jsprogrammer 11y ago
All selection processes are biased. ■
graycat 11y ago
Okay, PG has an hypothesis test. There's a large literature for that, e.g., E. L. Lehmann, Testing Statistical Hypotheses. E. L. Lehmann, Nonparametrics: Statistical Methods Based on Ranks. Sidney Siegel, Nonparametric Statistics for the Behavioral Sciences. In this case, PG will be more interested in the non-parametric case, i.e., distribution-free where we make no assumptions about probability distributions. We start an hypothesis test with an hypothesis, commonly called the null hypothesis which is an assumption that there is no effect or, in PG's case, no bias. Then with that assumption, we are able to do some probability calculations. Then we look at the real data and calculate the probability of, say, the evidence of bias being as large as we observed. If that probability is small, say, less than 1%, then we reject the null hypothesis, that is, reject the assumption of no bias, and conclude that the null hypothesis is false and that there is bias. The role of the assumption about the sample is so that we know that the problem is bias and not something about the sample. In hypothesis testing, about all that matters are just two numbers -- the probability of Type I error and that of Type II error. We want both probabilities to be as low as possible. Type I Error: We reject the null hypothesis when it is true, e.g., we conclude bias when there is none. Type II Error: We fail to reject (i.e., we accept) the null hypothesis when it is false. When looking for bias, Type I error can be called a false alarm of bias, and Type II error can be called a missed detection of bias. In PGs case, suppose we have 100 startups and five of those have women founders. Suppose for each of the startups we have the data from "their subsequent performance is measured". Our null hypothesis is that the expected performance of the women is the same as that of the men. So, let's find those two averages and take the difference, say, the average of the women less the average of the men. PG says if this difference is positive, then there was bias, but PG has not given us any estimate of the probability of Type I error, that is, of the probability (or rate) of a false alarm. I mean we don't want to get First Round Capital in trouble with Betty Friedan, Gloria Steinem, Marissa Mayer, Sheryl Sandberg, Hillary Clinton, Ivanka Trump, or Lady Gaga unjustly! :-). Let's call this difference our test statistic. So, let's find the probability of a false alarm: So, let's put all 100 measurements in a pot, stir the pot vigorously (we can use a computer for this), pull out five numbers and average, pull out the other 95 numbers and average, take the difference in the two averages, that of the five less that of the 95, and do this, say, 1000 times. Ah, computers are cheap; let's be generous and do this 10,000 times. For a random number, how about starting with a 32 bit integer, with appropriately long precision arithmetic multiply by 5^15, add 1, take modulo 2^47, and scale as we want? So, we get an empirical distribution of these differences, from the five less the 95. Looking at the distribution, we see what the probability is of getting a difference as high or high or higher than our test statistic. If that probability is low, say, 1% or less, then we reject the null hypothesis of no bias and conclude bias with our estimate of probability of Type I error 1% or less. If with the 1% we reject, then it looks like First Round has done a transgression, will get retribution from Betty, et al., and needs to seek redemption and Betty, et al., are happy to have their suspicions confirmed. Else First Round looks like the good guys, are "certified statistically fair to women", may get more deal flow from women, and Betty, et al., can be happy that First Round is so nice! Notice that either way Betty, et al., are "happy". That's called "happy women, happy life"! Or, heads, the women win, tails they lose, and in no event is there a huge crowd of angry women in front of First Round's offices with a bonfire of lingerie screaming "bias"! When we reject the null hypothesis, we want to know that the reason was men versus women and not something else, e.g., a biased sample. So here is where we use our assumption of independence with the same mean. Now we have a handle on Type I error. Here we have done a non-parametric statistical hypothesis test, i.e., have made no assumptions, except the means, about the distributions of the male/female CEO performance measurements. And we can select our desired false alarm rate in advance and get that rate almost exactly. For Type II error, that is more difficult. Bottom line, what we really want is, for whatever rate of false alarms we are willing to tolerate, the lowest rate of missed detections we can get. Can we do that? With enough more data, yup. There is a classic result due to J. Neyman (long at Berkeley) and K. Pearson (early in statistics) that shows how. How? Regard false alarm rate as money and think of investing in SF real estate. We put our money done on the opportunities with highest expected ROI until we have spent all our money. Done. For details, an unusually general proof can follow from the Hahn decomposition from the Radon-Nikodym theorem in measure theory, e.g., Rudin, Real and Complex Analysis. Right, in the discrete case, we have a knapsack problem, known to be in NP-complete. What we have done with our pot stirring is called resampling, and for more such look for B. Efron, long at Yale, and P. Diaconis, once at Harvard, now long at Stanford. Tom, with a reputation as a hacker, likes to work late, say, till 2 AM. So, we look at the intrusion alerts each minute between 2 AM and 3 AM (something like the performance of the women) and compare with those of the other minutes of 24 hours (like the performance of the men) much as above and ask if Tom is trying to hack the servers. Or, we have a server farm and/or a network, and we want to detect problems never seen before, e.g., zero day problems. So, we have no data at all on the problems we are trying to detect because we have never seen any of those before. So, to do a good job, let's pick some system we want to monitor and for that system, get data on, say, each of 10 variables at, say, 20 times a second. Now what? Our work with bias in women venture applications used just one number for our measurement and test statistic. So we were uni-dimensional. Here we have 10 numbers and need to be multi-dimensional. Well, in principle we should be able to do much better (pair of Type I and Type II error rates) with 10 numbers than just one. The usual ways will require us to have, with our null hypothesis, the probability distribution of the 10 numbers, but can only get something like that from smoking funny stuff -- not even big data is that big. So, we want to need no assumptions about distribution, that is, be distribution-free. So, we want some statistical a hypothesis test that is both multi-dimensional and distribution free. Can we do that? Yup. "You mean you can select false alarm rate in advance and get that rate essentially exactly, as in PG's bias example?" Yup. "Could that be used in a real server farm or network to detect zero day problems -- security, performance, hard/software failures, system management errors?" Yup -- just what it was invented for. "Attempted credit card fraud?" Ah, once a guy in an audience thought so! How? Ah, sadly there is no more room in this post! What else might we do with hypothesis tests? Well, look around at, right, big data or just small data. Do we have a case of big data analytics or artificial intelligence (AI)? Ah, I've given a sweetheart outline of statistical hypothesis testing, and now you are suggesting some things really low grade? Where did I go wrong to deserve such an insult?
mrwilliamchang 11y ago
I think I have a simpler counterexample to disprove pg's hypothesis than any other counterexample I've read in the comments. Suppose our goal is to admit the top 5 applicants with the following performances: A - 30,000 A - 10,000 A - 9,000 B - 7,000 B - 5,000 # Cutoff point below this line A - 4 B - 3 B - 2 Even though admitting the top 5 by score is perfectly fair, the applicants from group A perform better.
- Nimitz14 11y ago
  I don't see what you're getting at. Group A is better and there are more of them. What's the problem?
  - mrwilliamchang 11y ago
    pg's argument is that if the average performance of one admitted group is better than the other the admission process has a bias. This example shows that you can have an unbiased process, but the average performance of the groups differs.
    - nkurz 11y ago
      It's likely that the two of you are talking across each other because you read slightly different articles. Paul added an assumption to his article, possibly after William read it, which is intended to rule out his posited distribution: "(c) the groups of applicants you're comparing have roughly equal distribution of ability". This strikes me as a "heroic assumption", but it's true that if you make it most of the flaws in his argument go away. Add in the unspoken assumption that the groups are both are large enough that sampling variation does not matter, and I think he's probably logically correct. On the other hand, once you make these assumptions, the rest of his argument seems unnecessary, since all you need to know is the ratio of males and females funded. If male and female founders are exchangeable, the process is biased if one group is funded more often than they are represented in the applicants. You don't even need to look at outcome, since we've already assumed the founders are of equal ability. I think that Paul is aiming at the case where we don't know the ratio of applicants. I think his argument can be useful in this case, but only if you have already accepted his assumptions.
danieltillett 11y ago
While we can have lots of fun arguments about the mathematics of this approach, the basic problem is the underlying data is too small and poor to draw any valid conclusion from.
dthal 11y ago
In the post, PG states that First Round's study is evidence of gender bias in VC financing. But footnote [2] is important: Uber was excluded as an outlier. Now...excluding Uber is reasonable (it is sort of an outlier), but so is not excluding it (it was a company that First Round invested in). When the conclusion from a data analysis depends on which way you go on something like this - which of two reasonable alternatives you pick - then the results are fragile and they don't really support either conclusion very well.
owens99 11y ago
Many of these comments remind me of one of the most potent biases known to man: confirmation bias. If you are smart and want to believe something, you will surely be able to come up with a mathematical (albeit flawed) way to convince yourself you are right.
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bsder 11y ago
Um, the data set pg cites actually shows this to be fallacious. They excluded Uber from the results. Which, if included, makes the male-run companies look "oversuccessful". What would happen if I excluded the top female-run business, I'd bet that makes the differences between the two groups much smaller. Given both the small sample size as well as the outsized influence of outliers, drawing conclusions from this population group is going to be fraught with issues.
eatkinson 11y ago
This isn't really sound reasoning, for reasons mentioned elsewhere and because of the following. You need to know that the probability of acceptance is conditionally independent of the "type" of the applicant given the success of the applicant. For example, consider the following hypothesis for the First Round data: women are more honest than men. A woman presenting a bad idea to a VC will be rejected whereas a man may be able to weasel his way into getting funding. This will make men have a lower success rate, and correspondingly women will have a higher success rate. However, this isn't really the same thing as having an across-the-board hidden bias against women.
mirimir 11y ago
correlation <> causation
bruu_ 11y ago
What is the significance level? What is the model? This is freshman dorm room level analysis
anecon2 11y ago
For a formalized and empirical version of this argument applied to the entirety of the US economy, check out the following article: The Allocation of Talent and U.S. Economic Growth by Hsieh et al. (http://klenow.com/HHJK.pdf http://klenow.com/HHJK.pdf). It quantifies the gains from the decreases in misallocation of women and african americans as racial discrimination in employment decreased over the past 50 years.
kenko 11y ago
"What it means for a selection process to be biased against applicants of type x is that it's harder for them to make it through. Which means applicants of type x have to be better to get selected than applicants not of type x. [1] Which means applicants of type x who do make it through the selection process will outperform other successful applicants." There are many, many reasons that both sentences beginning "which means" are false that someone who is as smart as we're told Graham is should be able to come up with quite easily. It's astonishing that he made this tripe public. Here's a gimme for each. Say I'm selecting people to receive a prize; there are ten recipients and they're putatively chosen by [whatever]. But I don't like people with green eyes, so green-eyed candidates had better be pretty pleasing to me. But they can please me in any way, not necessarily in ways relevant to the metric for which the prize is awarded—maybe I also like tall people so a really tall green-eyed person averages out in terms of my predilections. They aren't relevantly better. For the second, again, the question is "better" at what? Better at getting whatever is involved in getting selected? That doesn't necessarily correlate with outperforming anyone subsequently, especially if it's a matter of startupland. (Remember that New Yorker profile of Marc Andreessen, where Sam Altman basically admitted that he didn't know what he was doing in terms of selecting what to invest in? The flipside of that is being selected by Altman for an investment.)
jameshart 11y ago
There's a flaw right in the assumptions here: "(c) the groups of applicants you're looking at have roughly equal distribution of ability." Oh. See, the problem is that if an application process is biased, and applicants perceive that bias, then those against whom it is biased will be dissuaded from applying unless they far exceed the required standards. Whereas those towards whom the process is biased will be more likely to apply, even if they are marginally qualified, because they expect to benefit from the bias. So that means that if you do have a biased process, there's a good chance it doesn't meet criterion c - applicants in the different groups between which its bias discriminates are not equal in ability. So your test might verify a lack of bias, when there is in fact bias present. You can't verify a lack of bias just by looking at the outcomes of successful applicants - you need to look at the outcomes for unsuccessful applicants too, to determine whether your applicant pools really do meet criterion c. Or you could look at the outcomes for nonapplicants, but that's clearly a much harder problem.
174676 11y ago
Even assuming equal distribution of ability, there is still the problem of whether you can measure performance without bias.
somberi 11y ago
This how I understand this: Look back at decisions you have made under various lenses and learn about your decisions and what biases they have, so that you can avoid them or amplify them (if positive) in future.
felipeerias 11y ago
In which a crowd of overwhelmingly white male American SW engineers tries to find a mathematical explanation to bias... "For Bourdieu, cultural capital is the status culture of a society's elite insofar as that group has embedded it in social institutions, so that it is widely and stably understood to be prestigious. Schools take it as a sign of native academic ability but do not themselves impart it, performing acts of social alchemy that transform class privilege into individual merit."
fanzhang 11y ago
The test pg suggests was also proposed by the economist Gary Becker [1]. Like many people here noticed, the catch is that the test only works if you compare marginal performance and not average performance. Economists call this the inframarginality problem [2]. There are a number of solutions to this problem to restore pg's result: - As pg himself says, if we assume certain statistical distributions of ability and selection rules, the inframarginality problem goes away. - We'd also solve the inframarginality problem if we can tell roughly who the marginal applicants were. If pg could ask the VC firm, see who almost got rejected, and compare these two groups, he'd be set. pg is well-positioned to test this on the YC dataset. Likewise, he could solve this problem if he can observe another variable that reveals who the marginal applicants likely were (for example, the startups that had the fewest co-investors). - There's also an entire literature out there that tries to solve the problem using other ways. For example if a system follows the "KPT" sufficient conditions then the inframarginality problem also goes away. [1] One prominent approach ... is the “outcome test,” which originated in Gary S. Becker (1957). In the context of motor vehicle searches, the outcome test is based on the following intuitive notion: if troopers are profiling minority motorists due to racial prejudice, they will search minorities even when the returns from searching them, i.e., the probabilities of successful searches against minorities, are smaller than those from searching whites. More precisely, if racial prejudice is the reason for racial profiling, then the success rate against the marginal minority motorist (i.e., the last minority motorist deemed suspicious enough to be searched) will be lower than the success rate against the marginal white motorist. (From [3]) [2] "While this idea has been well understood, it is problematic in empirical applications because researchers will never be able to directly observe search success rates against marginal motorists. This is due to the fact that we cannot identify the marginal motorist, since accomplishing this would require having complete information on all of the variables that troopers use in determining the suspicion level of motorists. Because of this omitted-variables problem, we can observe only the average success rate of searches against white and minority motorists, and not the marginal success rate. Since the equality of marginal search success rates does not imply, and is not implied by, the equality of the average search success rates, we cannot determine the relationship between the marginal search success rates of white and minority motorists by looking at average success rates. In past literature, this has been referred to as the “infra-marginality” problem. (From [3]). [3] Anwar, Shamena, and Hanming Fang, "An Alternative Test of Racial Prejudice in Motor Vehicle Searches: Theory and Evidence." American Economic Review. (2006) http://economics.sas.upenn.edu/~hfang/publication/racial-profiling/aer_final.pdf http://economics.sas.upenn.edu/~hfang/publication/racial-pro...

282 points by bakztfuture 11y ago

I think the first footnote in this is extremely valid. It all depends on what performance metric the selection process is identifying compared to the performance metric you use to determine success. I would suspect the larger issue is that people are probably much worse at identifying what performance metrics for selection convert to their respective performance for success.

newjersey 11y ago
If students of Asian origin outperform the whole student body, can we conclude admissions folks are biased against students of Asian origin?
- aceperry 11y ago
  That's possible. Without concrete data to give you, there are some suspicions that because of the much better performance of Asian students, they're being limited in the admissions process. Otherwise, Asian students would make up the vast majority of the students admitted. This would crowd out the non-Asian students accepted for admission. In this case, it would be more accurate to say that admissions officers limit the number of Asian students accepted instead of saying admissions folks are biased against Asian students.
  - pbhjpbhj 11y ago
    >admissions officers limit the number of Asian students accepted instead of saying admissions folks are biased against Asian students // The effect is the same isn't it? Less chance for a student with ancestors from a particular geographic locale getting a placement.
    - aceperry 11y ago
      The effect would result in the same situation, but the cause is much different.
- cookiecaper 11y ago
  Alternately, you could conclude that instead of "mediocre" Asians being excluded by bias, Asians have an external advantage that makes them perform better. Maybe it's cultural, since most Asians are taught a very strong work ethic and heavy emphasis is placed on formal schooling, succeeding, and fitting in. Maybe Asians are physically better adapted to that type of work, with brains that retain information more easily or buttocks that don't get sore from sitting in a chair all day. The "high performance means there's a bias" theory only works if you assume that everyone is starting from the same social, cultural, and physical baseline. They aren't. Maybe a better metric would be if there were no mediocre data points among a certain group; that would be more evidence (but still not necessarily good evidence) that you have to exceptional to get attention and overcome the "bias barrier", not simply that most of a certain type of performer does better than a different type.
  - srtjstjsj 11y ago
    Even if Asians perform better for external reasons, the selection process should account for that before the selection is made, and the admitted class should be roughly equal performers, as a group. Unless Asians have a very lumpy shaped performance curve across the group
    - cookiecaper 11y ago
      This presupposes that we should not accept unequal representation among groups. I don't believe that, and I don't think it's an implicit Western value. People should be allowed to flourish according to their natural advantages. The value is to try not to make an early judgment and exclude people based on assumptions about their group's capability, whether that exclusion is based on the group's perceived disadvantage or advantage. The idea is that the individual shouldn't be held accountable for things he had nothing to do with, and shouldn't be assumed to be automatically compliant with stereotypes. I don't see a need to start throttling groups that are doing "too well".
      - srtjstjsj 11y ago
        You misunderstood what I wrote. I didn't claim that a high performing subgroup should be throttled, I claimed that the Asians that pass an unbiased bar would be roughly as successful as the non-Asians that pass the same bar. I

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Phemist 11y ago

Footnote one should be put more generally, biases in the performance metrics (either appearance for women vs ability for men, or how many words of the US national anthem someone knows for US citizens vs rest of the world) will cause this method to fail. Unfortunately, unbiased performance metrics are quite hard on single dimensions, let alone when moving to multi-dimensional metrics

SeriousM 11y ago

Isn't every selection process based on experience, knowledge and/or mood and therefore baised?

newjersey 11y ago
He makes a few assumptions. But he is probably correct within those assumptions. We assume all candidate pools are homogeneous. If all members of a certain subset A of a global population P is simply better at a task than any member of another subset B of the global population, we will see that this holds true for members of our sample as well. Thus, members of A in our sample will consistently outperform members of B in our sample. Does this mean there is a bias against A? Well, yes because if there wasn't then there would be fewer members of B or perhaps no members of B in our sample based on this result alone. However, real life is not one-dimensional. Sometimes we need to consider other factors as well.

gizmo 11y ago

A related observation (which I've been making for a long time) is that the absence of mediocre women in positions of power is strong evidence of bias. Men can succeed when they're mediocre, but women have to be exceptional. Likewise for minorities.

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cookiecaper 11y ago
What's "exceptional"? I've known many women in my career and many of them were mediocre. Some were in positions of authority and some weren't. Another commenter lists several "mediocre" women in the corporate and political world (and leaves out some big ones, like Meg Whitman). If you're talking about becoming a CEO, you have to be an "exceptional" man to get there too, in absolute terms. I feel like the root erroneous assumption here is that an equal amount of people of all types are interested in the same things and that the only reason any group becomes more represented than another is that the others are getting alienated or funneled out somewhere along the way. That is a completely incorrect and invalid assumption. The fact that there are a lot more non-English-speakers in janitorial work in the US (when I worked as a janitor, I was 1 of 2 English speakers on the 12-person janitorial staff) doesn't necessarily mean the janitorial manager is biased against English speakers; it means that due to external considerations, like the fact that almost all other jobs require you to speak the native language, non-English-speakers are better suited for janitorial work, and therefore people do the logical thing, apply for work that they can do, and end up comprising a larger section of the application pool. People make decisions based on social, cultural, and physical expectations of them, and there's not anything wrong with that. By and large, women do not have an interest in computer sciencey or entrepreneurial work. It's OK if a woman does, but it's also OK to note that most women don't. There's nothing we need to fix about it. Most women don't want to do it, and there's no reason to force them. Why do you see fewer women becoming CEOs? Because fewer women want that kind of job and fewer women are qualified for that kind of job due to the biological realities of humanity that require women to take time out for pregnancy and child-rearing (sorry denialists, I didn't invent biology and choose that only women could bear and nurse children, so don't take it up with me), and the social and cultural expectations that have formed around these biological realities. In short, the serious applicant pool includes only a very small amount of women, so only a very small number of women obtain that position.

Mz 11y ago

Actual real world example (and application of an antidote) of this basic idea: https://en.wikipedia.org/wiki/Rooney_Rule https://en.wikipedia.org/wiki/Rooney_Rule

in3d 11y ago

Graham's statement about the possible bias of First Round is unfounded. This was not any sort of a real study like Graham thinks and First Round clearly notes that. When the returns are as skewed as they are in venture capital (http://www.sethlevine.com/archives/2014/08/venture-outcomes-are-even-more-skewed-than-you-think.html http://www.sethlevine.com/archives/2014/08/venture-outcomes-...), a small sample size and a simple analysis won't do. First Round even excluded their investment in Uber because it would skew the results too much.

khed 11y ago
Even if it were a statistically appropriate sample size and female founders still out performed male founders it still wouldn't exlcude other likely explanations other than bias. What if the culture in venture capital is more willing to assist and mentor female founders leading to greater success? In academia there is a women are selected over equally qualified men 2:1 for tenure positions now [1]. It is not unreasonable to wonder if a similiar hand up is being given to female founders in terms of training, social network inclusion, and mentorship leading to greater success. Alternatively, there may be a selection process in society that means only the most motivated women become entrepeneurs and so beat the average male entrepeneur. [1]. http://www.pnas.org/content/early/2015/04/08/1418878112.abstract http://www.pnas.org/content/early/2015/04/08/1418878112.abst...
- TomGullen 11y ago
  > female founders still out performed male founders That's not what the study says, it says groups that have at least 1 female founder, not female founders.

eridius 11y ago

There's a few trivial ways to be biased that would not be detected in this way. The first is if you have multiple people accepting applicants and some of them are biased to the point of not accepting applicants of particular types. That means all the applicants that are discriminated against that did make it were simply selected by people who weren't biased, and therefore won't outperform anyone. The second is if the actual selection process is somewhat random instead of being based on pure performance. The ones who make it through that process won't necessarily perform any better, they'll just be luckier. The third is if the application process accepts everyone equally, and then randomly prunes out people according to a bias. This is similar to the second except the acceptance criteria is still performance-based, but because it randomly throws out people (instead of throwing out low-performers), the remaining people are still going to perform the same as those who were not pruned. The first footnote on the page also points out that if the selection criteria are different for the different groups then this process won't work, which seems like a pretty important caveat that I wish was in the article proper. One really common form of bias (especially in tech) is being biased against women, and that's also a situation where it's very common to (unconsciously or otherwise) use appearance in judging female applicants but ignore appearance for male applicants.

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yummyfajitas 11y ago
The second example adds statistical noise, but does not invalidate Graham's procedure. In the absence of noise, the distribution of accepted people will be H(x-C) f(x) for the main group, and H(x-C-K)g(x) for the other group (where H(x) is a step function, f(x) and g(x) are the distributions of quality of the two groups). If noise is present, then you get convolve(H(x-C)f(x), k(x)) instead, where k(x) is the pdf of the noise distribution. You'll need more samples to measure this, but it's completely measurable via Graham's method.
lisper 11y ago
A fourth is to deliberately select low-performing members of the discriminated-against group in order to game Graham's metric and justify the bias.

devalier 11y ago

Fortunately there's a way to measure bias that's much more reliable, when it can be used....A couple months ago, one VC firm (almost certainly unintentionally) published a study showing bias of this type. First Round Capital found that among its portfolio companies, startups with female founders outperformed those without by 63%. Except if you want to use statistics to measure bias, you need a statistically significant sample. And actually, if you are studying complex human affairs, with a hundred different variables, you need more than statistical significance, you need a sensitivity analysis. It is similar to nutrition studies. There are so many variables at play that something can always be found to increase or decrease your risk of cancer by 50%. You really only need to pay attention when statistics show an order-of-magnitude correlation, as with the link between smoking and lung cancer. With the First Round Capital data, they excluded Uber from their calculations, because it would skew everything. If a single data point can switch your findings to be opposite, then you just have to admit that you do not have enough data to make determination one way or another. In science it is sometimes ok to exclude an outlier, since it often indicates a measurement error. But in venture capital, you make most of your money off of the Uber-like outliers. So if you are trying to study the data to be the best venture capitalist possible, throwing out outliers is not valid. Also, the initial premise is incorrect too. You cannot measure bias by comparing average results, because the average is not the marginal. Consider PG's footnote: "Although I used female founders as an example because that is a kind of bias people often talk about, the most striking thing was the degree to which First Round undervalue founders who went to elite colleges." Does he honestly believe that First Round is biased against founders from elite colleges? At my last company my sense was that the MIT grads were better than the average programmer. So were we biased against MIT grads? Should we have hired more MIT grads until the average performance of MIT grads overall equaled the average performance of an employee overall? Should we have done more outreach to MIT? Should the industry as a whole hired more MIT grads? If a talent distribution has a bunch of elite, and then a steep drop-off filled with "pretenders", then you can get this type of effect without being biased. When we got an elite MIT grad, we hired them. When we got a "pretender", someone who was trading on the name but did not put in the work, we rejected them. And yes, I personally saw MIT grads that did terrible on simple coding exercises. So even though the average MIT grad we hired was better than the average programmer at our company, there was no way to alter our hiring process to get more MIT grads. If we hired the marginal MIT grad that we rejected, we would have been worse off. Now we could do more outreach to MIT, and we did, but that is a highly competitive process. There were diminishing marginal returns to how much outreach we can do to get more applicants. The statistical illiteracy of PG's post is simply stunning. Imagine a YC company gets a 100% ROI from PPC ads, and a 50% ROI from banner ads. Are they biased against PPC ads? Should they buy more PPC ads? Such an analysis is ridiculous. You look at what you are spending on the marginal PPC ad, and you stop spending when the ROI on the marginal ad is at zero, regardless of what the average is. That one advertising channel has a higher ROI on average does not mean that the company is biased against that channel.

nkurz 11y ago

This approach relies on the unspoken "positivity" assumption that the pool of applicants is large enough that there exist individuals in the biased-against category that were not selected, and moreover that these denied applicants are "exchangeable" with the successful ones. For example, assume that we find that founders who won a MacArthur "genius" grant outperformed the others. Further assume that there are only a limited number of such founders, and that all available were selected. Certainly one wouldn't want to conclude in this case that there is a bias against MacArthur fellows. That seems obvious, but it gets trickier once you have lots of factors involved. What if the group you find to outperform consists of female founders with a PhD, substantial industry experience, and red hair[1]. Can you conclude that the process is biased against females? Males with PhD's? Anyone with red hair? Generally no, unless you are willing to assume that all of your factors are causal. Worse, you can't even assume that it's biased against people with all of the measured factors unless you also assume that all unmeasured factors are randomly distributed. If it turns out that "a positive mental attitude" is an unmeasured but defining characteristic of success, if the interviewers rejected applicants who had less of this but you failed to include this in your category, you would be wrong to conclude that there is an unfair bias. [1] http://www.nature.com/nature/journal/v453/n7194/full/453562a.html http://www.nature.com/nature/journal/v453/n7194/full/453562a...

WildUtah 11y ago

On a simple mathematical basis, this is false. Consider two groups of candidates for a scholarship, A and B. We want to select all candidates that have an 80% or better chance of graduation. Group A comes from a population where the chance of graduation is distributed uniformly from 0% to 100% and group B is from one where the chance is distributed uniformly from 10% to 90%, with the same average but less variation in group B. Now suppose that we select without bias or inaccuracy all the applicants that have an 80% or better chance of graduation. That means we select a subset of A with a range of 80% to 100% and a subset of B with a range from 80% to 90%. The average graduation rate of scholarship winners from group A will be 90% and that from group B will be 85%. But we haven't been biased against A. We've selected according to the exact same perfect evaluation process and criterion from both groups. It was just their prior distribution that was different. The actual applicant groups for jobs or financing in the real world, when they are divided by demographic factors like age, sex, race, and educational level, will almost always manifest different variances in success levels even when the averages are the same. That makes this test useless and mathematically illiterate. And when we use a normal distribution, as we should always expect given the central limit theorem, the mathematical problems get even more intense. This short comment is not up to pg's usual high standards for his essays.

eoi 11y ago
The article defines bias as follows: > Want to know if the selection process was biased against some type of applicant? Check whether they outperform the others. This is not just a heuristic for detecting bias. It's what bias means. Under that definition, you have been biased against A. [edit: on reflection I see this as a weakness of his definition. I missed that your selection process does in fact select the best candidates.]
- bjwbell 11y ago
  Yes, but that's not the common usage of the word. Or how most people understand it. With that usage you could say ivy league schools are NOT biased against Asians since Asian graduates aren't more successful than non-Asian ones, except nobody does.

pbnjay 11y ago

Fittingly, another type of bias observed in the linked report is that against Solo Founders. The report states that solo founders do worse when measured against the same yardstick as multiple founders. Maybe from a VC perspective this is intended (big raise => bigger exit?), but I'd argue that you don't need to raise as much when you have a solo founder because dilution is less of a concern.

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nartz 11y ago

Interesting thoughts. However, this argument is biased because it assumes that the performance of the applicants WHO WERE ACCEPTED is not biased by the selection process itself, and that the performance characteristics of the selected sample are representative of the performance characteristics of the total, which could be a weak assumption. An attempt at translating to mathematics (feel free to correct me!): X = event that person belongs to group x Y = event that person belongs to group y S = event that person is selected W = event that person will perform like a 'winner' for simplicity P(X) + P(Y) = 1 Naturally, 'unbiased' in this case is simply P(S|X) = P(S1), and P(S|Y) = P(S2), i.e. that the selection process is independent of a certain variable X or Y PG says we can measure the the performance of these selected applicant winners for each class, i.e. P(X|S,W). I believe PG assumes that: P(X|W) / P(Y|W) should equal P(X|S,W)/P(Y|S,W). We can see that these are different distributions, since the second is already conditioned on the selection process. Simplified, PG assumes that P(X|S,W) = P(X|W) i.e. that conditioning on the selection process does not bias the winning results. Its left for the reader exercise to determine the 'pathological' cases where this selection variable's distribution makes PG's assumption correct or incorrect. However, this is simply theoretical - the actual distribution may or may not be 'pathological' and the assumptions made by PG could very well be good.

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earljwagner 11y ago

The phenomena of "stereotype threat" complicates this conclusion however: https://en.wikipedia.org/wiki/Stereotype_threat https://en.wikipedia.org/wiki/Stereotype_threat When a member of a group is primed with a stereotype that their group underperforms at a task, they are more likely to underperform. So there could be a selection process biased against a group, and a selected member could be an above-average performer otherwise but, because of work environment, be underperforming. Some universities work to remedy this through support groups or other practices aimed at under-represented minorities, and they appear to help students be more successful academically. On the other hand, there's the Hawthorne effect... https://en.wikipedia.org/wiki/Hawthorne_effect https://en.wikipedia.org/wiki/Hawthorne_effect

yummyfajitas 11y ago
This is only a bias if the stereotype effect is stronger on measurements than in real life. If stereotype threat affects test performance and real performance the same way, then it means that the stereotyped group is truly inferior. Do you have evidence that stereotype threat hurts test performance more than real performance? (Of course, in a hypothetical world which only eliminated the stereotype, the group would cease to be inferior. I.e., the inferiority is based on context, and is not intrinsic.)
- earljwagner 11y ago
  I wouldn't agree with the conclusion of being truly inferior - there could be ongoing issues with the work context. I'll put it another way: Graham says we can look at just the performance by group to detect bias in selection. But there could be bias in selection, and A) different treatment after selection, which would not be revealed through Graham's test. Or could also be bias in selection and B) continuous reminders of stereotypes triggering stereotype threat, and this would also not be revealed. Now you could point to a tech company with few underrepresented minorities, let's say 1%. If there's no overt bias in the work environment then people should succeed and if they don't they're just worse performers. On the other hand, if you're in the 1%, just noticing the underrepresentation among your coworkers might be a constant reminder of stereotypes. I don't claim to have a simple solution for this.

yummyfajitas 11y ago

People, most of whom clearly are not that good at math, are being really harsh on Paul Graham. Graham is mostly right, but slightly incorrect. In particular, suppose group A has the distribution f(x) and B has the distribution g(x). If f(x) and g(x) are shaped significantly differently past the cutoff, then mean(H(x-C)f(x)) and mean(H(x-c)g(x)) might not agree even though there is no bias by construction. (Here H(x) is a step function and C the cutoff). However, there is an easy fix: compute the minima of the support of the distribution rather than mean. min(H(x-C)f(x)) = min(H(x-C)g(x)) = C. In practice, measure the weakest male and weakest female to be accepted in your sample set, or some similar approximation. I'm pretty sure this is a valid frequentist hypothesis test. I've got half a proof worked out on paper already. It depends very weakly (and non-parametrically) on f(x) and g(x), but it works in basically the exact way Graham wants it to. Every counterexample I can think of is really pathological. My next blog post will probably be a proof of this. All this negativity is really an overreaction. I know it's fun to totally debunk someone on details, but these are mostly fixable details.

MattHeard 11y ago
Wouldn't the weakest male and weakest female founders be underperforming more due to individual factors than bias? Maybe a mean of the lower quartile would remove some the the noise.
- yummyfajitas 11y ago
  Suppose the cutoff for men is C but for women is C+K. Then the weakest man can be expected to have quality C+epsilon, while the weakest woman will have quality C+K+epsilon. Here epsilon is how close a typical candidate will be to the cutoff, and is mainly a function of the sample size. I don't know the behavior of epsilon off the top of my head.
  - tprice7 11y ago
    I think MattHeard understood this and his point was that the weakest man will realistically have quality C + epsilon + random, and the weakest woman will have quality C + K + epsilon + random. The random term arises because no evaluation process is going to perfectly tell you how people are going to end up performing. But yeah, this seems fixable also, by averaging some number of the lowest performing members of each group, as MattHeard suggested.

logicallee 11y ago

Could someone who read it more attnetively tell me, by this methodology, -> If in retrospect YC finds any factor that its selected founders who turn into unicorns ($1b, $10b etc) have in common (more than its non-unicorn, also accepted founders) -> Then by this method, could it conclude retroactively that it had been "biased" against that factor? (since it is present more than in its non-unicorns whom it had also admitted; i.e. in other words, those with the factor are more performant than "would be expected" without the bias against it?) Or have I misunderstood?

proveanegative 11y ago

If candidates from group A perform more strongly on average than those from group B there are other possible causes than bias in the selection process itself. For instance, members of group A may only apply at a higher level of self-assessment for how likely they are to succeed than those in group B. The reason for this could be opportunity cost not present for group B, overconfidence or lack of underconference in group B or underconference or lack of overconfidence in group A.

jblow 11y ago

All other arguments aside ... this idea also fails if the judging party's idea of quality is mostly uncorrelated with actual quality. Which Graham says in other essays is usually the case (it's what you mean when you say it's almost impossible to predict which companies will be successful). Graham says the subjects of bias "have to be better to get selected", but what is really going on is they have to be better according to the metrics of the judge which are essentially arbitrary.

yummyfajitas 11y ago
This is false - noise doesn't hurt this test at all. See my comment explaining why: https://news.ycombinator.com/item?id=10483991 https://news.ycombinator.com/item?id=10483991 Bad measurements add noise (and increase the sample size required) but they don't invalidate the bias detection procedure.
gizmo 11y ago
This is also in large part why people tend to hire/fund younger versions of themselves. If judgement wasn't arbitrary much more diversity should be expected.

d0m 11y ago

I don't get it :-/ Why is there a bias? Even if the VCs are totally unbiased, why couldn't the startups with women outperformed the others? It could happen for a variety of reasons. Just hypothetically speaking, maybe startups-with-women have different networking connections or insight that male-only-startups don't have?

Alex3917 11y ago
> Why is there a bias? Applications by definition are supposed to be biased. If an application weren't biased then it wouldn't be an application, it would just be a lottery. And while that's a system that a lot of charter schools actually use, or a least pretend to, I think it would be a tough sell to convince venture capitalists to allocate their capital this way.
esfandia 11y ago
Then, if I understand PG's argument correctly, the VCs should invest in even more startups-with-women, and lower their threshold on investing them, at least until they perform no better than startups-without-women.
- wycats 11y ago
  Indeed!
wycats 11y ago
If that were the case, VCs should accept more companies-with-women, which would change the TOTAL mix of accepted candidates so that the women no longer overperformed. The issue, interestingly, is that there are a lot of women (or biased-against group) between the median performance and 160% performance who are being rejected. In other words, only the best women can get accepted, which means that above-median (but not superstars) are getting rejected, while many more above-median men are getting accepted. This has the ring of truth to me (as pg says, it's the definition of bias).

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TomGullen 11y ago

> A couple months ago, one VC firm (almost certainly unintentionally) published a study showing bias of this type. First Round Capital found that among its portfolio companies, startups with female founders outperformed those without by 63%. Well, they also said in their study: > And we are not claiming that our data is representative of the industry...or even statistically significant. Also, the wording is "startups with a female founder", not exclusively female founders... I think this is a detail that shouldn't be ignored. And, the study doesn't show how many companies out of the 300 had female founders! Maybe it was just 1! They also say "Solo Founders do Much Worse Than Teams", so this is an important detail if there are no solo female teams ever backed in their firm! etc etc, the list goes on. Not exactly strong evidence to support the point PG is making, that bias would be easy to detect. Measuring performance purely in terms of "how much money I make" is one way of doing it, but not the only way. And it wont cover the majority of jobs on the planet (how do you measure performance of someone who stacks shelves in a supermarket?)

MichaelGG 11y ago

I don't understand his point about First Round Capital showing their female founders did better than companies without female founders. What does that show? How do we know that female founders aren't simply better? Or maybe women are scared of applying, so out of women, only the best apply? In that case, the mere idea that there is a bias can cause "pre-selection" bias. I lack the mathematics to prove this, but it seems that on the face of it, pg is simply wrong. Or I'm misreading terribly. Tangentially: Speaking of bias, why doesn't YC publish information on their companies' tech choices? PG racked up a lot of inferred cachet (positive) by stating that use of Lisp gave them a huge advantage. Now that YC has data, they should be able to show how choice of technology correlates to performance.

esfandia 11y ago
The argument is that First Round Capital must have implictly made it harder for female founders to get funding, since the ones who do perform better. The rational course of action for First Round Capital would be to lower their threshold on female founders (or, conversely, raise the threshold on male founders) until they perform no better or no worse than male founders.
- MichaelGG 11y ago
  And that's not proven by the evidence. It might be a good thing to look into, but pg's statement that you don't need more info is wrong.
  - esfandia 11y ago
    Yeah, I was just rephrasing PG's argument for the OP, not saying whether it was right or wrong. I'm not smart enough to know.
YokoZar 11y ago
It's certainly possible that the observed bias isn't the fault of First Round Capital's selection process if the applying populations are different -- the "pre-selection" bias you're talking about. If that's the case, First Round Capital could profitably benefit from encouraging more female founders to apply.

wycats 11y ago

The implication of this analysis of http://10years.firstround.com/ http://10years.firstround.com/ is that First Round is biased against founding teams with experience at Amazon, Facebook, Apple, Google, Microsoft or Twitter. Can this be true?

tedsanders 11y ago
Yes, it can be true. FirstRound could still positively value that experience, but just not be valuing it enough.
- wycats 11y ago
  Makes sense. Fascinating.

compbio 11y ago

PG: Assumption: There is no fundamental difference between a female and a male founder for achieving start-up success (average rates and variance/distribution of rates is the same) Observation: VC funded start-ups with female founders are (on average) 60% more successful than start-ups with male founders Hypothesis: VC funding is biased against female founders. The ones that do receive funding are better vetted, less risky, and have higher individual qualities. Experiment: Start funding more female founders. If we then observe: The numbers start to even out, then there is no fundamental difference. VC funding bias may have been the cause of the difference in success rate. If we then observe: The numbers stay the same, then there is a fundamental difference and our assumption is flawed. Rational choice: Start funding more female founders. This either removes a bias (levels the playing field), or increases your profit (funding more potentially successful founders). PG should of course not use an hypothesis to prove an assumption (experiment/probing is needed for verification). But also: The possibility of an uneven distribution should not invalidate such an experiment (or PG's line of reasoning), it will merely bring it to light (the numbers would stay the same, thus we have shown that the difference is fundamental and not caused by a sampling bias).

tracker1 11y ago

I just asume there is bias... I mean the fact is, bias is what youare trying to work in favor of... that bias being factors of success. Chasing your tail against random statistics won't really show much, and a person is more complex that a few statistical groups. As far as investing goes, there's also the product, and how that leader/founder matches to that product category itself. A founder that succeeds in one category won't definitively succeed in another. Many founders fail their first few times, and later succeed. Others fail after some success(es). I think as long as reasonable steps are made to avoid certain obvious bias, the rest is mostly chance.

j2kun 11y ago

There is an emerging subfield of computer science that studies what it means for data (or algorithms, or decision-making rules) to be biased, and how to remove certain forms of bias. See http://fatml.org http://fatml.org

jsprogrammer 11y ago

All selection processes are biased. ■

graycat 11y ago

Okay, PG has an hypothesis test. There's a large literature for that, e.g., E. L. Lehmann, Testing Statistical Hypotheses. E. L. Lehmann, Nonparametrics: Statistical Methods Based on Ranks. Sidney Siegel, Nonparametric Statistics for the Behavioral Sciences. In this case, PG will be more interested in the non-parametric case, i.e., distribution-free where we make no assumptions about probability distributions. We start an hypothesis test with an hypothesis, commonly called the null hypothesis which is an assumption that there is no effect or, in PG's case, no bias. Then with that assumption, we are able to do some probability calculations. Then we look at the real data and calculate the probability of, say, the evidence of bias being as large as we observed. If that probability is small, say, less than 1%, then we reject the null hypothesis, that is, reject the assumption of no bias, and conclude that the null hypothesis is false and that there is bias. The role of the assumption about the sample is so that we know that the problem is bias and not something about the sample. In hypothesis testing, about all that matters are just two numbers -- the probability of Type I error and that of Type II error. We want both probabilities to be as low as possible. Type I Error: We reject the null hypothesis when it is true, e.g., we conclude bias when there is none. Type II Error: We fail to reject (i.e., we accept) the null hypothesis when it is false. When looking for bias, Type I error can be called a false alarm of bias, and Type II error can be called a missed detection of bias. In PGs case, suppose we have 100 startups and five of those have women founders. Suppose for each of the startups we have the data from "their subsequent performance is measured". Our null hypothesis is that the expected performance of the women is the same as that of the men. So, let's find those two averages and take the difference, say, the average of the women less the average of the men. PG says if this difference is positive, then there was bias, but PG has not given us any estimate of the probability of Type I error, that is, of the probability (or rate) of a false alarm. I mean we don't want to get First Round Capital in trouble with Betty Friedan, Gloria Steinem, Marissa Mayer, Sheryl Sandberg, Hillary Clinton, Ivanka Trump, or Lady Gaga unjustly! :-). Let's call this difference our test statistic. So, let's find the probability of a false alarm: So, let's put all 100 measurements in a pot, stir the pot vigorously (we can use a computer for this), pull out five numbers and average, pull out the other 95 numbers and average, take the difference in the two averages, that of the five less that of the 95, and do this, say, 1000 times. Ah, computers are cheap; let's be generous and do this 10,000 times. For a random number, how about starting with a 32 bit integer, with appropriately long precision arithmetic multiply by 5^15, add 1, take modulo 2^47, and scale as we want? So, we get an empirical distribution of these differences, from the five less the 95. Looking at the distribution, we see what the probability is of getting a difference as high or high or higher than our test statistic. If that probability is low, say, 1% or less, then we reject the null hypothesis of no bias and conclude bias with our estimate of probability of Type I error 1% or less. If with the 1% we reject, then it looks like First Round has done a transgression, will get retribution from Betty, et al., and needs to seek redemption and Betty, et al., are happy to have their suspicions confirmed. Else First Round looks like the good guys, are "certified statistically fair to women", may get more deal flow from women, and Betty, et al., can be happy that First Round is so nice! Notice that either way Betty, et al., are "happy". That's called "happy women, happy life"! Or, heads, the women win, tails they lose, and in no event is there a huge crowd of angry women in front of First Round's offices with a bonfire of lingerie screaming "bias"! When we reject the null hypothesis, we want to know that the reason was men versus women and not something else, e.g., a biased sample. So here is where we use our assumption of independence with the same mean. Now we have a handle on Type I error. Here we have done a non-parametric statistical hypothesis test, i.e., have made no assumptions, except the means, about the distributions of the male/female CEO performance measurements. And we can select our desired false alarm rate in advance and get that rate almost exactly. For Type II error, that is more difficult. Bottom line, what we really want is, for whatever rate of false alarms we are willing to tolerate, the lowest rate of missed detections we can get. Can we do that? With enough more data, yup. There is a classic result due to J. Neyman (long at Berkeley) and K. Pearson (early in statistics) that shows how. How? Regard false alarm rate as money and think of investing in SF real estate. We put our money done on the opportunities with highest expected ROI until we have spent all our money. Done. For details, an unusually general proof can follow from the Hahn decomposition from the Radon-Nikodym theorem in measure theory, e.g., Rudin, Real and Complex Analysis. Right, in the discrete case, we have a knapsack problem, known to be in NP-complete. What we have done with our pot stirring is called resampling, and for more such look for B. Efron, long at Yale, and P. Diaconis, once at Harvard, now long at Stanford. Tom, with a reputation as a hacker, likes to work late, say, till 2 AM. So, we look at the intrusion alerts each minute between 2 AM and 3 AM (something like the performance of the women) and compare with those of the other minutes of 24 hours (like the performance of the men) much as above and ask if Tom is trying to hack the servers. Or, we have a server farm and/or a network, and we want to detect problems never seen before, e.g., zero day problems. So, we have no data at all on the problems we are trying to detect because we have never seen any of those before. So, to do a good job, let's pick some system we want to monitor and for that system, get data on, say, each of 10 variables at, say, 20 times a second. Now what? Our work with bias in women venture applications used just one number for our measurement and test statistic. So we were uni-dimensional. Here we have 10 numbers and need to be multi-dimensional. Well, in principle we should be able to do much better (pair of Type I and Type II error rates) with 10 numbers than just one. The usual ways will require us to have, with our null hypothesis, the probability distribution of the 10 numbers, but can only get something like that from smoking funny stuff -- not even big data is that big. So, we want to need no assumptions about distribution, that is, be distribution-free. So, we want some statistical a hypothesis test that is both multi-dimensional and distribution free. Can we do that? Yup. "You mean you can select false alarm rate in advance and get that rate essentially exactly, as in PG's bias example?" Yup. "Could that be used in a real server farm or network to detect zero day problems -- security, performance, hard/software failures, system management errors?" Yup -- just what it was invented for. "Attempted credit card fraud?" Ah, once a guy in an audience thought so! How? Ah, sadly there is no more room in this post! What else might we do with hypothesis tests? Well, look around at, right, big data or just small data. Do we have a case of big data analytics or artificial intelligence (AI)? Ah, I've given a sweetheart outline of statistical hypothesis testing, and now you are suggesting some things really low grade? Where did I go wrong to deserve such an insult?

mrwilliamchang 11y ago

I think I have a simpler counterexample to disprove pg's hypothesis than any other counterexample I've read in the comments. Suppose our goal is to admit the top 5 applicants with the following performances: A - 30,000 A - 10,000 A - 9,000 B - 7,000 B - 5,000 # Cutoff point below this line A - 4 B - 3 B - 2 Even though admitting the top 5 by score is perfectly fair, the applicants from group A perform better.

Nimitz14 11y ago
I don't see what you're getting at. Group A is better and there are more of them. What's the problem?
- mrwilliamchang 11y ago
  pg's argument is that if the average performance of one admitted group is better than the other the admission process has a bias. This example shows that you can have an unbiased process, but the average performance of the groups differs.
  - nkurz 11y ago
    It's likely that the two of you are talking across each other because you read slightly different articles. Paul added an assumption to his article, possibly after William read it, which is intended to rule out his posited distribution: "(c) the groups of applicants you're comparing have roughly equal distribution of ability". This strikes me as a "heroic assumption", but it's true that if you make it most of the flaws in his argument go away. Add in the unspoken assumption that the groups are both are large enough that sampling variation does not matter, and I think he's probably logically correct. On the other hand, once you make these assumptions, the rest of his argument seems unnecessary, since all you need to know is the ratio of males and females funded. If male and female founders are exchangeable, the process is biased if one group is funded more often than they are represented in the applicants. You don't even need to look at outcome, since we've already assumed the founders are of equal ability. I think that Paul is aiming at the case where we don't know the ratio of applicants. I think his argument can be useful in this case, but only if you have already accepted his assumptions.

danieltillett 11y ago

While we can have lots of fun arguments about the mathematics of this approach, the basic problem is the underlying data is too small and poor to draw any valid conclusion from.

dthal 11y ago

In the post, PG states that First Round's study is evidence of gender bias in VC financing. But footnote [2] is important: Uber was excluded as an outlier. Now...excluding Uber is reasonable (it is sort of an outlier), but so is not excluding it (it was a company that First Round invested in). When the conclusion from a data analysis depends on which way you go on something like this - which of two reasonable alternatives you pick - then the results are fragile and they don't really support either conclusion very well.

owens99 11y ago

Many of these comments remind me of one of the most potent biases known to man: confirmation bias. If you are smart and want to believe something, you will surely be able to come up with a mathematical (albeit flawed) way to convince yourself you are right.

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bsder 11y ago

Um, the data set pg cites actually shows this to be fallacious. They excluded Uber from the results. Which, if included, makes the male-run companies look "oversuccessful". What would happen if I excluded the top female-run business, I'd bet that makes the differences between the two groups much smaller. Given both the small sample size as well as the outsized influence of outliers, drawing conclusions from this population group is going to be fraught with issues.

eatkinson 11y ago

This isn't really sound reasoning, for reasons mentioned elsewhere and because of the following. You need to know that the probability of acceptance is conditionally independent of the "type" of the applicant given the success of the applicant. For example, consider the following hypothesis for the First Round data: women are more honest than men. A woman presenting a bad idea to a VC will be rejected whereas a man may be able to weasel his way into getting funding. This will make men have a lower success rate, and correspondingly women will have a higher success rate. However, this isn't really the same thing as having an across-the-board hidden bias against women.

mirimir 11y ago

correlation <> causation

bruu_ 11y ago

What is the significance level? What is the model? This is freshman dorm room level analysis

anecon2 11y ago

For a formalized and empirical version of this argument applied to the entirety of the US economy, check out the following article: The Allocation of Talent and U.S. Economic Growth by Hsieh et al. (http://klenow.com/HHJK.pdf http://klenow.com/HHJK.pdf). It quantifies the gains from the decreases in misallocation of women and african americans as racial discrimination in employment decreased over the past 50 years.

kenko 11y ago

"What it means for a selection process to be biased against applicants of type x is that it's harder for them to make it through. Which means applicants of type x have to be better to get selected than applicants not of type x. [1] Which means applicants of type x who do make it through the selection process will outperform other successful applicants." There are many, many reasons that both sentences beginning "which means" are false that someone who is as smart as we're told Graham is should be able to come up with quite easily. It's astonishing that he made this tripe public. Here's a gimme for each. Say I'm selecting people to receive a prize; there are ten recipients and they're putatively chosen by [whatever]. But I don't like people with green eyes, so green-eyed candidates had better be pretty pleasing to me. But they can please me in any way, not necessarily in ways relevant to the metric for which the prize is awarded—maybe I also like tall people so a really tall green-eyed person averages out in terms of my predilections. They aren't relevantly better. For the second, again, the question is "better" at what? Better at getting whatever is involved in getting selected? That doesn't necessarily correlate with outperforming anyone subsequently, especially if it's a matter of startupland. (Remember that New Yorker profile of Marc Andreessen, where Sam Altman basically admitted that he didn't know what he was doing in terms of selecting what to invest in? The flipside of that is being selected by Altman for an investment.)

jameshart 11y ago

There's a flaw right in the assumptions here: "(c) the groups of applicants you're looking at have roughly equal distribution of ability." Oh. See, the problem is that if an application process is biased, and applicants perceive that bias, then those against whom it is biased will be dissuaded from applying unless they far exceed the required standards. Whereas those towards whom the process is biased will be more likely to apply, even if they are marginally qualified, because they expect to benefit from the bias. So that means that if you do have a biased process, there's a good chance it doesn't meet criterion c - applicants in the different groups between which its bias discriminates are not equal in ability. So your test might verify a lack of bias, when there is in fact bias present. You can't verify a lack of bias just by looking at the outcomes of successful applicants - you need to look at the outcomes for unsuccessful applicants too, to determine whether your applicant pools really do meet criterion c. Or you could look at the outcomes for nonapplicants, but that's clearly a much harder problem.

174676 11y ago

Even assuming equal distribution of ability, there is still the problem of whether you can measure performance without bias.

somberi 11y ago

This how I understand this: Look back at decisions you have made under various lenses and learn about your decisions and what biases they have, so that you can avoid them or amplify them (if positive) in future.

felipeerias 11y ago

In which a crowd of overwhelmingly white male American SW engineers tries to find a mathematical explanation to bias... "For Bourdieu, cultural capital is the status culture of a society's elite insofar as that group has embedded it in social institutions, so that it is widely and stably understood to be prestigious. Schools take it as a sign of native academic ability but do not themselves impart it, performing acts of social alchemy that transform class privilege into individual merit."

fanzhang 11y ago

The test pg suggests was also proposed by the economist Gary Becker [1]. Like many people here noticed, the catch is that the test only works if you compare marginal performance and not average performance. Economists call this the inframarginality problem [2]. There are a number of solutions to this problem to restore pg's result: - As pg himself says, if we assume certain statistical distributions of ability and selection rules, the inframarginality problem goes away. - We'd also solve the inframarginality problem if we can tell roughly who the marginal applicants were. If pg could ask the VC firm, see who almost got rejected, and compare these two groups, he'd be set. pg is well-positioned to test this on the YC dataset. Likewise, he could solve this problem if he can observe another variable that reveals who the marginal applicants likely were (for example, the startups that had the fewest co-investors). - There's also an entire literature out there that tries to solve the problem using other ways. For example if a system follows the "KPT" sufficient conditions then the inframarginality problem also goes away. [1] One prominent approach ... is the “outcome test,” which originated in Gary S. Becker (1957). In the context of motor vehicle searches, the outcome test is based on the following intuitive notion: if troopers are profiling minority motorists due to racial prejudice, they will search minorities even when the returns from searching them, i.e., the probabilities of successful searches against minorities, are smaller than those from searching whites. More precisely, if racial prejudice is the reason for racial profiling, then the success rate against the marginal minority motorist (i.e., the last minority motorist deemed suspicious enough to be searched) will be lower than the success rate against the marginal white motorist. (From [3]) [2] "While this idea has been well understood, it is problematic in empirical applications because researchers will never be able to directly observe search success rates against marginal motorists. This is due to the fact that we cannot identify the marginal motorist, since accomplishing this would require having complete information on all of the variables that troopers use in determining the suspicion level of motorists. Because of this omitted-variables problem, we can observe only the average success rate of searches against white and minority motorists, and not the marginal success rate. Since the equality of marginal search success rates does not imply, and is not implied by, the equality of the average search success rates, we cannot determine the relationship between the marginal search success rates of white and minority motorists by looking at average success rates. In past literature, this has been referred to as the “infra-marginality” problem. (From [3]). [3] Anwar, Shamena, and Hanming Fang, "An Alternative Test of Racial Prejudice in Motor Vehicle Searches: Theory and Evidence." American Economic Review. (2006) http://economics.sas.upenn.edu/~hfang/publication/racial-profiling/aer_final.pdf http://economics.sas.upenn.edu/~hfang/publication/racial-pro...