[PairTheBoard]

I'll have to give some thought to what you're saying about the psychology. Since the math is well understood it seems to me that the psychology is the most interesting thing left to consider. It would be interesting to look at how our 2+2 treatment of this problem has evolved through the many threads on it over the years.

Something that bothers me. You said,

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jason1990 -
It should not seem unreal that seeing A causes some sort of change. It definitely changes the experiment. At the very least, it removes the symmetry from the experiment, as I mentioned in my previous post. You may not know how this change affects the probability of having the smaller envelope, but that does not mean you can assume that it does not change it at all.

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and

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jason1990 -
In general, you may not know how to deal with it [the information]. You may not know how it affects the probability of having the smaller envelope. But that does not imply that the information is independent of having the smaller envelope. To assume so is to apply a variation of the indifference principle.


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Which I of course agree with. But in my scenario:

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PairTheBoard -
However, here's the sense in which I think my statement has validity. Suppose many different people are offered such envelopes. Each of them wagers $100 that they have the smaller envelope. Each of them ignores the amount they see in their envelope and continues their $100 bet. At 2-1 odds they will on average make money on their $100 bets. But they will not on average make money from the Envelope Switch. This I think is at the heart of the psychological conundrum.


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Suppose there are two such groups. The First deals with the information by ignoring it (applying the indifference principle?). The Second deals with the information by saying upon opening the envelope that the amount changes the experiment but they don't know how so they call off the $100 wager. The First Group on average makes money while the Second doesn't.

PairTheBoard