4 ms·

Monty Hall is really a trick question (you need to know Monty knows the answer and is using that info to know if he should open the door) and the intuitive answ

Monty Hall is really a trick question (you need to know Monty knows the answer and is using that info to know if he should open the door) and the intuitive answer to Two Envelopes is correct. To be honest, I'd expect most people's intuition of this type of thing would be correct. Like, if I'm looking for a needle in a haystack and find one, and the haystack has other needles in it, and the victim of the needle can't pick the needle out in a lineup, and the needle doesn't match the description of the needle that poked the victim... I think most people would say this isn't the needle the victim was poked with. It's difficult to imagine a pre-historic human surviving without understanding this. I think what probably happens is the jury just sees themselves are rubber stamps for the police. They just want to get out of jury duty with a thank you for doing the right thing and putting the baddy behind bars. The facts of the case are half-relevant at best.

adhesive_wombat 4y ago
> I think most people would say this isn't the needle the victim was poked with. Well, yes, except that the haystack is actually a needlestack (everyone has DNA) and a needle identification expert told you the chance that this is the wrong needle is 200 million to one against, that rather changes the logic. It's suddenly not simple any more and if you want to make sense of the probabilities here, you need to be systematic[1], or just admit that this is about gut feeling and not a logical process. Instincts good enough to statistically avoid enough saber-toothed tigers to survive better on average than the others might not map onto million-to-one-scale odds, which is, partly, why lotteries can make money. There's also not enough information given (at least via this telling of it) to even establish what the 200 million figure's priors are. Does it assume an independent distribution of genetic markers? Does the defendent have a large family that might raise the chances of someone in the population being a match? Are matches disproportionately located in the same area, etc? > Monty Hall is really a trick question (you need to know Monty knows the answer and is using that info to know if he should open the door) That's literally the kind of "gotcha" motivational prior that you really do have to take account of when looking at probabilities in a criminal context though. [1] and I certainly do not claim to be able to accurately construct a systematic probability model because it was proven over and over to me in statistics classes that I can't be trusted to get it right.
- tinalumfoil 4y ago
  > the haystack is actually a needlestack (everyone has DNA) But not everyone has matching DNA. Matching DNA makes you a needle. > a needle identification expert told you the chance that this is the wrong needle is 200 million to one against This statistic is incorrect, and if the jurors are paying attention you'll be able to tell them why. If it's possible for multiple people in the world to have matching DNA, say 3, and you have matching DNA the chance at this point is 1 in 3, no? Whatever that statistic represents isn't relevant. If the trial was a gameshow and a false conviction cost the jurors $100 (and a false acquittal something commensurate given the standards of proof -- maybe $10 for 90% burden of proof) each I guarantee you the jurors would acquit.
- throwaway198888 4y ago
  Another good question is why the defendent was picked as a suspect by the police.

adhesive_wombat 4y ago

> I think most people would say this isn't the needle the victim was poked with. Well, yes, except that the haystack is actually a needlestack (everyone has DNA) and a needle identification expert told you the chance that this is the wrong needle is 200 million to one against, that rather changes the logic. It's suddenly not simple any more and if you want to make sense of the probabilities here, you need to be systematic[1], or just admit that this is about gut feeling and not a logical process. Instincts good enough to statistically avoid enough saber-toothed tigers to survive better on average than the others might not map onto million-to-one-scale odds, which is, partly, why lotteries can make money. There's also not enough information given (at least via this telling of it) to even establish what the 200 million figure's priors are. Does it assume an independent distribution of genetic markers? Does the defendent have a large family that might raise the chances of someone in the population being a match? Are matches disproportionately located in the same area, etc? > Monty Hall is really a trick question (you need to know Monty knows the answer and is using that info to know if he should open the door) That's literally the kind of "gotcha" motivational prior that you really do have to take account of when looking at probabilities in a criminal context though. [1] and I certainly do not claim to be able to accurately construct a systematic probability model because it was proven over and over to me in statistics classes that I can't be trusted to get it right.

tinalumfoil 4y ago
> the haystack is actually a needlestack (everyone has DNA) But not everyone has matching DNA. Matching DNA makes you a needle. > a needle identification expert told you the chance that this is the wrong needle is 200 million to one against This statistic is incorrect, and if the jurors are paying attention you'll be able to tell them why. If it's possible for multiple people in the world to have matching DNA, say 3, and you have matching DNA the chance at this point is 1 in 3, no? Whatever that statistic represents isn't relevant. If the trial was a gameshow and a false conviction cost the jurors $100 (and a false acquittal something commensurate given the standards of proof -- maybe $10 for 90% burden of proof) each I guarantee you the jurors would acquit.
throwaway198888 4y ago
Another good question is why the defendent was picked as a suspect by the police.