3 ms·

IMO the one urn problem does nothing to get away from this. Recapping the one urn problem: 90 balls in one urn. 30 are red, 60 are black or yellow in unknown p

IMO the one urn problem does nothing to get away from this. Recapping the one urn problem: 90 balls in one urn. 30 are red, 60 are black or yellow in unknown proportion. Users must pick a set of gambles called a scenario, then pick a particular gamble. All balls are equally likely to be pulled. I'll list out the possible probabilities based on possible ground state truth: Scenario 1: Gamble A: Receive $100 if you draw a red ball P(0.33~) Gamble B: Receive $100 if you draw a black ball P(0)-P(0.66~) Scenario 2: Gamble C: Receive $100 if you draw a red or yellow ball P(0.33~)-P(1) Gamble D: Receive $100 if you draw a black or yellow ball P(0.66~) Per my earlier argument, this scenario triggers my "someone is trying to trick and/or scam me" heuristic which creates an expectation that my choice of scenario will be predicted somehow, and that the color distribution will be chosen to maximally disadvantage me. I think most people would feel the same way and so I'd assume that most people would prefer gambles A and D respectively and that's exactly what happens.

dash2 3y ago
Right, but note that you've made two arguments. The first was "you can explain this simply using 'P(red) ≠ 0.5'". The second is "you can explain this using a heuristic". The difference is that the first argument saves standard expected utility theory. The second does not. Someone who has this heuristic is violating expected utility. Maybe you didn't believe EUT to start with. But many people did, and so this paradox still resonates.
- Hermitian909 3y ago
  > but note that you've made two arguments. Apologies if I was not clear, but I only intended to present the "heuristic" argument. > The second does not. Someone who has this heuristic is violating expected utility. Maybe you didn't believe EUT to start with. I did not think this was the case, but I think I disagree with any utilitarianism that did not allow me to weight probabilities via epistemic uncertainty. Another way to frame my argument here that people have a justified belief that the prima facie probabilities for these gambles are misleading in a way that disadvantages them. If you allow this to change the probabilities then EUT would seem to explain the behavior e.g. if I believe Gamble A has P(0.33~) and Gamble B is weighted down to P(0.3) due to epistemic uncertainty the experimental results match up with the math. If we allow the above calculation I think we're still in bounds for EUT.
  - dash2 3y ago
    Sure, but you can't simultaneously hold P(red) = 0.33 and P(red) = 0.3. Yet people asked to make two choices will strictly prefer "red" but also strictly prefer "black or yellow". If red is a better gamble, then red or black must be a better gamble too! It's the same urn. You're right in general that uncertainty aversion has been put forward as an explanation. But to model it, you have to break EUT.

dash2 3y ago

Right, but note that you've made two arguments. The first was "you can explain this simply using 'P(red) ≠ 0.5'". The second is "you can explain this using a heuristic". The difference is that the first argument saves standard expected utility theory. The second does not. Someone who has this heuristic is violating expected utility. Maybe you didn't believe EUT to start with. But many people did, and so this paradox still resonates.

Hermitian909 3y ago
> but note that you've made two arguments. Apologies if I was not clear, but I only intended to present the "heuristic" argument. > The second does not. Someone who has this heuristic is violating expected utility. Maybe you didn't believe EUT to start with. I did not think this was the case, but I think I disagree with any utilitarianism that did not allow me to weight probabilities via epistemic uncertainty. Another way to frame my argument here that people have a justified belief that the prima facie probabilities for these gambles are misleading in a way that disadvantages them. If you allow this to change the probabilities then EUT would seem to explain the behavior e.g. if I believe Gamble A has P(0.33~) and Gamble B is weighted down to P(0.3) due to epistemic uncertainty the experimental results match up with the math. If we allow the above calculation I think we're still in bounds for EUT.
- dash2 3y ago
  Sure, but you can't simultaneously hold P(red) = 0.33 and P(red) = 0.3. Yet people asked to make two choices will strictly prefer "red" but also strictly prefer "black or yellow". If red is a better gamble, then red or black must be a better gamble too! It's the same urn. You're right in general that uncertainty aversion has been put forward as an explanation. But to model it, you have to break EUT.