• The Allais paradox assumes that you believe the probabilities you’re given. A supposedly 3334 chance of \$27000 is worth less than a guarantee of \$24000, because that 134 chance might conceal a much larger chance of being conned. If you take the \$24000 offer and don’t receive the money, you can cry foul; if you take the \$27000 offer, and the 134 chance turns out to be implemented with weighted dice, then you can’t prove you were cheated. When choosing between a 33% and 34% chance, that isn’t a factor, because neither choice protects you.

• Least Convenient Possible World: Either you do trust the odds (because it’s, say, a regulated casino game), or the probability you estimate of this being a con works out so that it’s an Allais situation. You can’t avoid it in general!

• This is a misapplication of the Least Convenient Possible World principle. Yes, it is possible to construct an Allais-like problem in the least convenient possible world. However, the evidence that the Allais paradox exists does not come from a world of your choosing, but from the worlds that survey-takers construct in their minds. You can’t say “least convenient possible world!” when data has already been collected from an inconvenient one!

• The researcher could take you to a large state-certified casino (which I think we can trust not to rig their games) and offer you two options: A) pay you \$55 straight up, or B) place both a \$30 bet on red and a \$30 bet on black (this nets you \$60 unless it lands on 0 or 00, so a 1819 chance of \$60)

She could also offer you other combinations of bets that add up to the second pair of Allais gambles.

Do you predict that if an Allais experiment were done in this sort of trustworthy situation, the effect would disappear?

• Do you predict that if an Allais experiment were done in this sort of trustworthy situation, the effect would disappear?

Yes, I do.

• Well, there’s only one thing to be done then. I’ll be waiting at Caesar’s Palace; you bring the experimental funds.

Anyhow, the primary reason I disagree with you is that most people just don’t expected to be cheated outright in psychology experiments; again and again it’s found that the majority of subjects trust the experimenters.

Take for example the study on guilt where the volunteer signed up more often for a painful experiment if he thought he had broken an expensive machine, when in fact it was rigged to appear to break. You’d find different behavior if most of the subjects were suspicious at the outset.

• I don’t have primary literature with me now, so this is from the Wikipedia article

Allais asserted that, presented with the choice between 1A and 1B, most people would choose 1A, and presented with the choice between 2A and 2B, most people would choose 2B. This has been borne out in various studies involving hypothetical and small monetary payoffs, and recently with health outcomes.

You don’t expect to be cheated in a hypothetical. You don’t expect to be cheated by a doctor giving probabilities of different outcomes.

ETA: Here’s an abstract, but the paper itself is gated.

ETA2: Paper!