Suppose the amount in the envelope you choose is $100. If your amount is the smaller one, the other one has $200. If your amount is the larger one, the other one has $50. So the expectation supporting the switching argument is computed over two different scenarios, where the amounts in the envelopes are {50, 100} and {100, 200} respectively.
This calculation seems to violate a hidden logical constraint: the set of amounts in the two envelopes must be the same no matter what conditional branches we consider for the expectation.
Another related issue - if you switch, the argument for switching back assumes the amount in your original envelope is 4x what you originally said it was.
Suppose the amount in the envelope you choose is $100. If your amount is the smaller one, the other one has $200. If your amount is the larger one, the other one has $50. So the expectation supporting the switching argument is computed over two different scenarios, where the amounts in the envelopes are {50, 100} and {100, 200} respectively.
This calculation seems to violate a hidden logical constraint: the set of amounts in the two envelopes must be the same no matter what conditional branches we consider for the expectation.
Another related issue - if you switch, the argument for switching back assumes the amount in your original envelope is 4x what you originally said it was.