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The Allais Paradox

I wanted to point out that this flaw is not a foolish flaw. That's how we create plans, we project and create expectations, and the anticipated feeling of loss is frustrating to plan for. In a theoretical example you might make a bad decision, but isn't it also that this flaw causes you to make good decisions in actual real-world situations? Since they don't tend to occur in such theoretical forms where you have all the required information available and which lack context.

If you'd actually encounter this problem in a real-world situation, you might end up making a bad decision because of handling it with a too theoretical approach - what if I told you get to play both games and actually get to choose between both, when you come to visit me? But you didn't have money to pay for the ticket to fly over? What if you took a loan? And without the certainty of A1 you might end up in a bad situation where you'll lack the means to pay back your loan - in other words a decision making agent with this flaw handles the situation well. But of course you can take all that into account. And as it's a problem dealing with rationality, I think it's pretty important to note these things.

Anyway I agree with you, Vaniver =)

The Allais Paradox

If you'd ask any person capable of doing the math whether they would want to play 1A or 1B a thousand times you'd probably get a different answer, but not an answer that's more correct.

Also the utility value of money is not directly relative to the amount of money. Imagine that you would need a 1000$ dollars of money to save your dying relative with certainty by paying for his/her treatment. Good enough for explaining 1A > 1B, but doesn't resolve the contradiction with 2B > 2A.

But even a more revealing edit is based exactly onto the certainty. If you would be presented with these two questions, in such a fashion that you would get the money and get to know the result in 1 month after being presented with it. By selecting 1A you would have 0% chance that the plans you make would fail, and with 1B you would have a 1/34 chance that they would fail. Meanwhile regardless of whether you select 2A or 2B you will have to face uncertainty. So you would be frustrated while trying to make plans that are conditionally dependent with you getting the money.

As these conditions are not present in the presentation it's possible to rule these kind of instinctive judgments as flawed, but as it turns out, they're not foolish, on a general level. You could even make a claim that it's costly to perform the calculation that tells you whether the assurance is worth it - but of course instead of saying that you should just figure out how much value this assurance has in each given situation.