5 ms·

In 2012, 59% of British MPs Flunked Probability of Flipping Two Heads in a Row

32 points by Bostonian 5y ago

karmelapple 5y ago
Instead of televised debates with only questions about policy, how about interspersing basic factual questions like this? Maybe even ask them to “show their work,” either aloud or in writing, to demonstrate they know why a particular answer is true? Allow viewers at home to also answer the question. See how the collective audience does against the candidates.
- HWR_14 5y ago
  The NYC mayor's democratic primary race did that. "What is the average price for a new home in Brooklyn". No one was within an order of magnitude, including people who worked in the housing administration a few years ago. Actually, come to think of it, there were similar quizzes in the democratic primary in SF.
  - exegete 5y ago
    A few of the candidates did get the exact answer or were within 10% of it https://www.msn.com/en-us/news/politics/nyc-mayor-candidates-claim-median-cost-of-brooklyn-home-is-below-dollar100k/ar-BB1gCgo6 https://www.msn.com/en-us/news/politics/nyc-mayor-candidates... I think only one was “an order of magnitude” off.
    - reducesuffering 5y ago
      One said 80-90k and another said 100k. Median is 900k, so yes only one was literally an order of magnitude, but these are both absolutely delusional. Where do they find these charlatans? Oh wait… “ Donovan who was the New York Housing and Urban Development secretary from 2009 to 2014, and director of the US Office of Management and Budget from 2014 to 2017.”
      - exegete 5y ago
        Agreed. The ones that were way off should know better. The candidate that said 90k was laughable!
    - HWR_14 5y ago
      Two were an order of magnitude off. You are correct that others were much closer. The winner of the primary only about 40% under - and he was the Brooklyn Borough President.
RcouF1uZ4gsC 5y ago
> Among Conservative members, 47% gave the wrong answer, which is disappointing enough. But of the 44 Labour MPs who took part, 77% answered incorrectly. I did not expect such a large difference between parties. Any guesses why this would be the case?
- JamilD 5y ago
  One potential hypothesis: the Conservative Party in the UK tends to be centered around a particular social and educational class; many front-bench cabinet members in the Cameron government went to the same schools for their entire lives. The traditionally working-class Labour vs aristocratic Conservative dichotomy is breaking now (as it already has in the US), but it was certainly the case in the UK in 2012.
- porjo 5y ago
  The article's author hints at a possible reason: "In the Parliament elected in 2010, 34% of Tory MPs were women vs. 57% of Labour MPs." Not politically correct. Anecdotally at least holds true. My wife, who has had a good education, seems to have a poor grasp of basic maths and science - she's just not interested. For example, the other day she said she didn't know that stars are in the sky during the day! For a stay-at-home mum I guess this doesn't matter but I'd expect more from our elected politicians.
- kbelder 5y ago
  "Conservatives don't understand science; Liberals don't understand math."
  - whatatita 5y ago
    "Conservatives don't understand morality; Liberals don't understand Conservatives." Fixed it for you. /s
ab_testing 5y ago
I think the real surprise is that 41% of them had the correct answer to this question.
dooglius 5y ago
I had a professor in college--teaching a queueing theory class no less--claim it was 1/3 as long as you didn't care about the order, and I interrupted the class for a good amount to explain it was not.
- jobigoud 5y ago
  Are you sure this wasn't a variant of this problem where one of the result is already known? (Hence the "order" bit). There is a famous problem with endless debate about it, it goes like: a family has two children, one is a girl, what is the probability that the other one is a boy? Depending on the exact wording you can get 2/3 or 1/2. In your case say, A: let two coin flips, one is known to be tails, what's the proba of two tails? B: two coin flips, I show you one which is tail, what's the proba of the other also being tail? In the first case we don't care about the order and the answer is 1/3, in the second case we do and the answer is 1/2.
  - jfengel 5y ago
    And that makes me take the study with a grain of salt. Probability problems are prone to different answers based on subtleties of phrasing and assumptions, like the famous Monty Hall problem. This question was, of course, pretty straightforward. But I suspect that with some further questioning, you'd find that they thought they were asking a different question than the one they were actually asked -- in very specific mathematical terms. Not being familiar with the way mathematicians pose questions is not the same as failing to grasp how probability affects your life. People are famously bad at judging risks, which are more important than the abstractions of flipping coins. And also much harder than flipping coins, since they depend so much on your assumptions and on the question you think your answering, as well as the difference between appetite for risk and your actual feelings about getting caught short. All of which is to say... a lot of people read this and said, "Aha, X is bad at math and therefore not to be trusted". Whereas I read those and say, "Aha, you are bad at understanding how questions work and how people think."
  - dooglius 5y ago
    That may have been what he had in mind, but he made no indication as to there being a conditional probability. Furthermore, in the context of where he was going with it, I recall that there wasn't one either so he was getting the wrong answer as a result. He believed the not-looking-at-the-order was the critical thing making it 1/3 rather than 1/4.
mensetmanusman 5y ago
It’s hard for me to understand how others think about the world around them when I read things like this. I use probability intuition all the time in daily work and personal life.
- ohuf 5y ago
  But that's the problem with these students as well: their intuition tells them that when it's warmer the sun has to be nearer. the fact that the amount of sunlight throughout the day (timespan) causes warmer seasons is an indirection in thinking. Of course they should know what causes seasons if they had payed attention in class. I wonder how they reacted if you'd ask them about the hemispherical difference in summer/winter, e.g. how can the southern hemisphere have winter when the whole earth is nearer to the sun...
  - ohuf 5y ago
    apologies: I was watching the YouTube video that's in the bottom of this article, where graduates were asked "what causes summer and winter" that's what my comment above is about!.
- im3w1l 5y ago
  My guess is that they see the world in a black and white where things are either 100% safe or 100% dangerous. Where theories are either 100% proven or 100% disproven.
- mateo411 5y ago
  Most people don't. I think many simple things in probability are surprisingly unintuitive.

32 points by Bostonian 5y ago

Instead of televised debates with only questions about policy, how about interspersing basic factual questions like this? Maybe even ask them to “show their work,” either aloud or in writing, to demonstrate they know why a particular answer is true? Allow viewers at home to also answer the question. See how the collective audience does against the candidates.

HWR_14 5y ago
The NYC mayor's democratic primary race did that. "What is the average price for a new home in Brooklyn". No one was within an order of magnitude, including people who worked in the housing administration a few years ago. Actually, come to think of it, there were similar quizzes in the democratic primary in SF.
- exegete 5y ago
  A few of the candidates did get the exact answer or were within 10% of it https://www.msn.com/en-us/news/politics/nyc-mayor-candidates-claim-median-cost-of-brooklyn-home-is-below-dollar100k/ar-BB1gCgo6 https://www.msn.com/en-us/news/politics/nyc-mayor-candidates... I think only one was “an order of magnitude” off.
  - reducesuffering 5y ago
    One said 80-90k and another said 100k. Median is 900k, so yes only one was literally an order of magnitude, but these are both absolutely delusional. Where do they find these charlatans? Oh wait… “ Donovan who was the New York Housing and Urban Development secretary from 2009 to 2014, and director of the US Office of Management and Budget from 2014 to 2017.”
    - exegete 5y ago
      Agreed. The ones that were way off should know better. The candidate that said 90k was laughable!
  - HWR_14 5y ago
    Two were an order of magnitude off. You are correct that others were much closer. The winner of the primary only about 40% under - and he was the Brooklyn Borough President.

RcouF1uZ4gsC 5y ago

> Among Conservative members, 47% gave the wrong answer, which is disappointing enough. But of the 44 Labour MPs who took part, 77% answered incorrectly. I did not expect such a large difference between parties. Any guesses why this would be the case?

JamilD 5y ago
One potential hypothesis: the Conservative Party in the UK tends to be centered around a particular social and educational class; many front-bench cabinet members in the Cameron government went to the same schools for their entire lives. The traditionally working-class Labour vs aristocratic Conservative dichotomy is breaking now (as it already has in the US), but it was certainly the case in the UK in 2012.
porjo 5y ago
The article's author hints at a possible reason: "In the Parliament elected in 2010, 34% of Tory MPs were women vs. 57% of Labour MPs." Not politically correct. Anecdotally at least holds true. My wife, who has had a good education, seems to have a poor grasp of basic maths and science - she's just not interested. For example, the other day she said she didn't know that stars are in the sky during the day! For a stay-at-home mum I guess this doesn't matter but I'd expect more from our elected politicians.
kbelder 5y ago
"Conservatives don't understand science; Liberals don't understand math."
- whatatita 5y ago
  "Conservatives don't understand morality; Liberals don't understand Conservatives." Fixed it for you. /s

ab_testing 5y ago

I think the real surprise is that 41% of them had the correct answer to this question.

dooglius 5y ago

I had a professor in college--teaching a queueing theory class no less--claim it was 1/3 as long as you didn't care about the order, and I interrupted the class for a good amount to explain it was not.

jobigoud 5y ago
Are you sure this wasn't a variant of this problem where one of the result is already known? (Hence the "order" bit). There is a famous problem with endless debate about it, it goes like: a family has two children, one is a girl, what is the probability that the other one is a boy? Depending on the exact wording you can get 2/3 or 1/2. In your case say, A: let two coin flips, one is known to be tails, what's the proba of two tails? B: two coin flips, I show you one which is tail, what's the proba of the other also being tail? In the first case we don't care about the order and the answer is 1/3, in the second case we do and the answer is 1/2.
- jfengel 5y ago
  And that makes me take the study with a grain of salt. Probability problems are prone to different answers based on subtleties of phrasing and assumptions, like the famous Monty Hall problem. This question was, of course, pretty straightforward. But I suspect that with some further questioning, you'd find that they thought they were asking a different question than the one they were actually asked -- in very specific mathematical terms. Not being familiar with the way mathematicians pose questions is not the same as failing to grasp how probability affects your life. People are famously bad at judging risks, which are more important than the abstractions of flipping coins. And also much harder than flipping coins, since they depend so much on your assumptions and on the question you think your answering, as well as the difference between appetite for risk and your actual feelings about getting caught short. All of which is to say... a lot of people read this and said, "Aha, X is bad at math and therefore not to be trusted". Whereas I read those and say, "Aha, you are bad at understanding how questions work and how people think."
- dooglius 5y ago
  That may have been what he had in mind, but he made no indication as to there being a conditional probability. Furthermore, in the context of where he was going with it, I recall that there wasn't one either so he was getting the wrong answer as a result. He believed the not-looking-at-the-order was the critical thing making it 1/3 rather than 1/4.

mensetmanusman 5y ago

It’s hard for me to understand how others think about the world around them when I read things like this. I use probability intuition all the time in daily work and personal life.

ohuf 5y ago
But that's the problem with these students as well: their intuition tells them that when it's warmer the sun has to be nearer. the fact that the amount of sunlight throughout the day (timespan) causes warmer seasons is an indirection in thinking. Of course they should know what causes seasons if they had payed attention in class. I wonder how they reacted if you'd ask them about the hemispherical difference in summer/winter, e.g. how can the southern hemisphere have winter when the whole earth is nearer to the sun...
- ohuf 5y ago
  apologies: I was watching the YouTube video that's in the bottom of this article, where graduates were asked "what causes summer and winter" that's what my comment above is about!.
im3w1l 5y ago
My guess is that they see the world in a black and white where things are either 100% safe or 100% dangerous. Where theories are either 100% proven or 100% disproven.
mateo411 5y ago
Most people don't. I think many simple things in probability are surprisingly unintuitive.