The envelope paradoxon - think of it as different regimes

[cwes]

Discussion here and here .

I say we may think of being in different regimes. We are either in regime N (having picked the envelope with N in it) or regime 2N. From our point of view being in either of these regimes is equally likely (.5).

Switching envelopes in regime N will gain us N. Switching envelopes in regime 2N will lose us N. As both regimes are equally likely the expected value of switching is .5 N - .5 N = 0. Therefore switching is ev neutral.