Two envelopes problem
and
First of all, thank you both for your interesting arguments. I am following them as much as I can understand the OP started by Michael.
I think the main substance of this dilemma is discerning on if it is "rational" or "not" switching one of the envelopes when you chose one already.
Michael showed to us arguments when switching is rational.
Envelope A contains 10 € and Envelope B contains 20 €. Then, according to that dilemma, I have the chance to switch my first option and get the twice I suppose to get in my choice. So, I agree with Michael that it's always going to be a 1/2 probability.
Yet, this scenario only happens if I am expecting a value. I decide to switch the envelopes because I want to expect to double the amount that supposedly is in the envelope. Again, switching is rational or "worthy" because I am expecting a value.
But... What about the indifference on the amount of each envelope? For example:
Let the amounts in the envelopes be X and 2X. Now by swapping, the player may gain X or lose X. So the potential gain is equal to the potential loss.
I agree in this point. It could exist the scenario where switching or not is meaningless to the participant if the expected value doesn't exists.
I am sorry If I were not clear in my point. What I intend to say is the fact that this paradox and dilemma only works if the participant expects a value or loss, but it could be indifferent whatever the amount and the action of switching is not motivated by an expected value.