6 ms·

I think this is less about Bayesian thinking and more about misinterpreting the question, as another poster mentions: https://twitter.com/farrwill/status/175178

• eigenvalue 3y ago
  I'd argue that it's not so much a difference of opinion than it is just a reasoning error given the question as stated. That's sort of the whole point of this post-- this is a case where "doing the math" in the expected way gives the wrong answer, because the state of the system is cast in stone (in terms of the ratio of red/green balls in the urn) when you first start out, so it's all about leveraging the information you get from your first choice. I think this sort of reasoning is actually surprisingly useful and widely applicable in everyday life, like in investing or diagnosing the likely cause of a software bug from incomplete information.
  • danielmarkbruce 3y ago
    It's definitely a poorly worded question. "More likely" is ill-defined. More likely than what? Than the last draw? Than drawing the other color just on this pick?
    • posix86 3y ago
      More likely than the other option, given the information. Getting an accurate grasp on the information is the whole point of the question.
      • danielmarkbruce 3y ago
        Why is that the question? Why not "more likely than the last draw" ?
        • thfuran 3y ago
          How could the next draw be more likely to be red than the draw already known to be red?
          • danielmarkbruce 3y ago
            You are basically asking "how could it possibly be the wrong answer?". Yes, under that definition of "more likely", it cannot be more likely. It can be equally likely or less likely. And then weighted it would be less likely. And that would be the answer. Which is one of the choices.
            • thfuran 3y ago
              No, I'm saying "Your interpretation of the sentence is obviously wrong". With that interpretation, parts of the question are nonsense. The more straightforward interpretation does not have that problem.
              • danielmarkbruce 3y ago
                1 - I said it's poorly worded, I didn't interpret it that way. I could see how people would misinterpret it (as pointed out by the parent comment) and people did misinterpret it that way. Look at the other posts here. If someone posts a question in english and a bunch of english speakers misinterpret the question, it's poorly worded by definition. 2 - Exactly what parts of the question are nonsense under that interpretation?
          • sampo 3y ago
            > How could the next draw be more likely to be red than the draw already known to be red? Under this interpretation, the second ball is more likely to be green.
    • amalcon 3y ago
      Yes, it's a bit of a pet peeve of mine to use the word "more" while leaving vague the point of comparison. Especially in something like a twitter poll -- twitter isn't exactly renowned as a place where people think closely about things before clicking.
    • chrismcb 3y ago
      How is "more likely"I'll defined? They are two options red or green. Are you more likely to draw red or are you more likely to draw green.. how is it poorly worded?
      • danielmarkbruce 3y ago
        Because it could be more likely red than green, or more likely red than it was likely that the first choice was red (which is where some people got confused, they thought the question was asking about the relative chances of red on the first choice v second choice), more likely green than the first one was likely to be green(same basic problem).
      • bo1024 3y ago
        My first interpretation of "more likely" was also "more likely than the previous ball". It makes more sense in the context of the previous sentence. For example: > The first time you shoot a basketball, you will almost certainly miss. The second time, you are more likely to make it. Does the second sentence mean "more likely to make it than to miss"? No.
        • danielmarkbruce 3y ago
          Great example.
    • smohare 3y ago
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  • simiones 3y ago
    You don't need to think in terms of information to get the right answer, you just need to be careful of the setup. You can easily apply frequentist probability reasoning and still get the right answer. You have to start from P(n > 50 | first pull is a red ball), and compute P(second ball red | first ball red) based on that. Basically the mistake is computing the frequency over 100 balls, instead of computing it over the 100 possible values of n multiplied by the 100 balls.
    • eigenvalue 3y ago
      Yes, you make a good point.
• posix86 3y ago
  Why would n be "uniformly randomly chosen" but then suddenly be known? I would mark this mis interpretation simply as wrong if I was a teacher.
  • tqi 3y ago
    That's definitely fair, and I assuming in a classroom setting you'd be very consistent and precise about what that means. But this is a twitter poll, and I doubt people are that consistent. Ultimately I'm just pushing back on the conclusion that this is because "Bayesian thinking is really foreign to people." I think if the question had instead been "would you bet on the urn having started out with more red balls, green balls, or equal number of balls" the distribution would have been very different.
    • travisjungroth 3y ago
      That question is quite a bit of handholding. A closer analogue would be “would you bet the next ball is red / green / they’re equally likely?”. Personally I’d word it as “The next ball is… more likely to be red than green / more likely to be green than red / equally likely to be red or green / I don’t know.”
      • chrismcb 3y ago
        But isn't that exactly how it is worded? Just showing it a bit?
        • travisjungroth 3y ago
          Not quite. People are arguing that “more likely to be red” can be interpreted as “more likely to be red than it was last time”. I guess you could do that with this wording, but that seems like quite a stretch.
  • thornewolf 3y ago
    i personally would throw out the question if i was a teacher. i still feel it's ambiguous
• aaron695 3y ago
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