The envelope problem, and a possible solution

[AaronBrown]

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I am stubbornly sticking to my prior my belief about you, Aaron, which is that you are an educated and intelligent man who can communicate effectively via the written word. That's why I've got to believe that there is some gross misunderstanding going on here.

In both the Paradox and in PTB's Prop Bets, the only techniques we need to use in order to arrive at the "sensible" conclusions are the techniques of elementary probability, such as assumptions [1]-[4] of my previous post. These are consistent, they are certainly not ad hoc, and they are extremely helpful in a wide array of realistic problems. Are you denying this? What am I missing here?

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Thank you for your kind words, although you could have left out "stubbornly." At least you didn't say "against all rational evidence."

I think you keep repeating one side of the paradox, and wondering why I can't see something so simple. I do see it. But there's the other side as well, the one that says the probability that you have the smaller amount is 50% so the expected value of switching is positive. You can't refute a paradox by strengthening one side, that just makes the paradox more puzzling. You have to show why one side is wrong.

I maintain the ways people deny the force of the always switch argument result in restrictions that are commonly ignored, and if not ignored would make statisticians useless.