6 ms·

A pet issue I have that is in line with the “illusions” in the article is what I might call the “bound by statistics” fallacy. The shape of it is that there is

A pet issue I have that is in line with the “illusions” in the article is what I might call the “bound by statistics” fallacy. The shape of it is that there is a statistic about population and then that statistic is used to describe a member of that population. For example, a news story that starts with “70% of restaurants fail in their first year, so it’s surprising that new restaurant Pete’s Pizza is opening their third location!” But it’s only surprising if you know absolutely nothing about Pete and his business. Pete’s a smart guy. He’s running without debt and has community and government ties. His aunt ran a pizza business and gave him her recipes. In a Bayesian way of thinking, the newscasters statement only makes sense if the only prior they have is the average success rate of restaurants. But that is an admittance that they know nothing about the actual specifics of the current situation, or the person they are talking about. Additionally there is zero causal relationship between group statistics and individual outcomes, the causal relationship goes the other way. Pete’s success will slightly change that 70% metric, but the 70% metric never bound Pete to be “likely to fail”. Other places I see the “bound by statistics” problem is in healthcare, criminal proceedings, racist rhetoric, and identity politics.

zmgsabst 1y ago
It’s not even surprising without knowing about Pete: the newspaper isn’t going to publish the many that failed, so their own selection bias is the dominant effect. Even if we take the probability of the group to be the probability of individuals, eg, rolling dice (“1 in 6 people rolls a 4!”). Lots of them opened, of them 70% failed, and one who didn’t happened to be named Pete. No more interesting than “Pete rolled a 4!” even though 83% of people don’t.
- skybrian 1y ago
  If a newspaper only publishes surprising results, but it’s unsurprising when they appear in the newspaper, then you’ve set up a paradox: a set that only contains nonmembers. I don’t think it’s valid to define “surprising” in such a self-referential way. When something unusual appears in the news, that doesn’t make it common. The probabilities are different before and after applying a filter.
  - nemomarx 1y ago
    It doesn't make it a common outcome overall, but it makes it a common outcome for it to appear in the newspaper, right? It's just different meanings of "common".
    - skybrian 1y ago
      Yes, that's what I meant.
  - zmgsabst 1y ago
    I didn’t say that, nor use any self-reference. > When something unusual appears in the news, that doesn’t make it common. This in particular isn’t even close to what I said, which was: rare events can be unsurprising in large datasets — as is the case with both dice rolls and restaurants succeeding.
    - skybrian 1y ago
      If rare events are unsurprising then I think you've defined surprising events out of existence? I mean, sure, someone will win the lottery, but it would very surprising if it happened to you. I guess this is just point of view. "Someone won the lottery" and "I won the lottery" describe the same event from very different perspectives.
      - deleted 1y ago
        [deleted]
  - yusina 1y ago
    If 99.9% fail and you see one that didn't, then would it be surprising that it didn't? No! It's not 100%, so there must be some example. For that one it's not surprising. More precisely, it's not surprising that one exists. It may be surprising that this particular one survived, just as it wouldbe surprising that it's my neighbor who wins the lottery next week. But it's likely that somebody will, so if somebody has won, it won't be a surprise that somebody did.
- steveBK123 1y ago
  People are also very even worse with conditional probabilities
skybrian 1y ago
People sometimes talk about this as “taking the outside view” or “reference class forecasting.” [1] It doesn’t work when there are important differences between the case being considered and other members of the reference class. Nationwide statistics are especially zoomed-out and there are going to be a lot of people in the same country who are quite different from you. Worldwide statistics are even worse. It doesn’t mean the statistics are wrong, though. If there is a 70% chance of failure, there’s also a 30% chance of success. But it’s subjective: use a different reference class and you’ll get a different number. The opposite problem is also common: assuming that “this time it’s different” without considering the reasons why others have failed. The general issue is overconfidence and failure to consider alternative scenarios. The future isn’t known to us and it’s easy to fool yourself into thinking it is known. [1] https://en.m.wikipedia.org/wiki/Reference_class_forecasting https://en.m.wikipedia.org/wiki/Reference_class_forecasting
yusina 1y ago
I agree with your description, but the pizza place case is even simpler: Statistics don't guarantee future single sample properties. 70% fail in the first year. So, 30% don't. Why would it be surprising to see one that didn't? It would be surprising to see none that didn't fail. So, it's expected to see lots that don't fail, Pete's being one of them.

zmgsabst 1y ago

It’s not even surprising without knowing about Pete: the newspaper isn’t going to publish the many that failed, so their own selection bias is the dominant effect. Even if we take the probability of the group to be the probability of individuals, eg, rolling dice (“1 in 6 people rolls a 4!”). Lots of them opened, of them 70% failed, and one who didn’t happened to be named Pete. No more interesting than “Pete rolled a 4!” even though 83% of people don’t.

skybrian 1y ago
If a newspaper only publishes surprising results, but it’s unsurprising when they appear in the newspaper, then you’ve set up a paradox: a set that only contains nonmembers. I don’t think it’s valid to define “surprising” in such a self-referential way. When something unusual appears in the news, that doesn’t make it common. The probabilities are different before and after applying a filter.
- nemomarx 1y ago
  It doesn't make it a common outcome overall, but it makes it a common outcome for it to appear in the newspaper, right? It's just different meanings of "common".
  - skybrian 1y ago
    Yes, that's what I meant.
- zmgsabst 1y ago
  I didn’t say that, nor use any self-reference. > When something unusual appears in the news, that doesn’t make it common. This in particular isn’t even close to what I said, which was: rare events can be unsurprising in large datasets — as is the case with both dice rolls and restaurants succeeding.
  - skybrian 1y ago
    If rare events are unsurprising then I think you've defined surprising events out of existence? I mean, sure, someone will win the lottery, but it would very surprising if it happened to you. I guess this is just point of view. "Someone won the lottery" and "I won the lottery" describe the same event from very different perspectives.
    - deleted 1y ago
      [deleted]
- yusina 1y ago
  If 99.9% fail and you see one that didn't, then would it be surprising that it didn't? No! It's not 100%, so there must be some example. For that one it's not surprising. More precisely, it's not surprising that one exists. It may be surprising that this particular one survived, just as it wouldbe surprising that it's my neighbor who wins the lottery next week. But it's likely that somebody will, so if somebody has won, it won't be a surprise that somebody did.
steveBK123 1y ago
People are also very even worse with conditional probabilities

skybrian 1y ago

People sometimes talk about this as “taking the outside view” or “reference class forecasting.” [1] It doesn’t work when there are important differences between the case being considered and other members of the reference class. Nationwide statistics are especially zoomed-out and there are going to be a lot of people in the same country who are quite different from you. Worldwide statistics are even worse. It doesn’t mean the statistics are wrong, though. If there is a 70% chance of failure, there’s also a 30% chance of success. But it’s subjective: use a different reference class and you’ll get a different number. The opposite problem is also common: assuming that “this time it’s different” without considering the reasons why others have failed. The general issue is overconfidence and failure to consider alternative scenarios. The future isn’t known to us and it’s easy to fool yourself into thinking it is known. [1] https://en.m.wikipedia.org/wiki/Reference_class_forecasting https://en.m.wikipedia.org/wiki/Reference_class_forecasting

yusina 1y ago

I agree with your description, but the pizza place case is even simpler: Statistics don't guarantee future single sample properties. 70% fail in the first year. So, 30% don't. Why would it be surprising to see one that didn't? It would be surprising to see none that didn't fail. So, it's expected to see lots that don't fail, Pete's being one of them.