The reasoning is flawed for the scenario: 'What if you open envelope A?'
Per Marianne
"It tells you that on average (if you repeated the same wager many times with the same amount $x$ in envelope $A$), you’d do better by switching."
If you open envelope A no new relevant information is gained (assuming no practical limitations of likely $ ranges). Suppose person Y opens A and person Z opens B. Would they not conclude using Marianne's logic that each is better off switching? There is no advantage to switching regardless of the amount revealed in the envelope (again assuming normal $ range estimates arising from practical considerations are excluded).
True, if you had a chance at a 50/50 wager of either losing 0.5x or winning 1.0x, then it would be to your benefit to take the wager. But in the example you open envelope A, you still don't know if the fair value of the game. The fair value of the game is 1.5x (where x is the smaller amount). After opening you don't know if you have the smaller or larger amount by definition. Choosing to play the game you in essence wager 0.5x against the 1.5x fair value. Half the time you lose and are left with 1x, half the time you win and have 2x. Switching after opening is no different.
The reasoning is flawed for the scenario: 'What if you open envelope A?'
Per Marianne
"It tells you that on average (if you repeated the same wager many times with the same amount $x$ in envelope $A$), you’d do better by switching."
If you open envelope A no new relevant information is gained (assuming no practical limitations of likely $ ranges). Suppose person Y opens A and person Z opens B. Would they not conclude using Marianne's logic that each is better off switching? There is no advantage to switching regardless of the amount revealed in the envelope (again assuming normal $ range estimates arising from practical considerations are excluded).
True, if you had a chance at a 50/50 wager of either losing 0.5x or winning 1.0x, then it would be to your benefit to take the wager. But in the example you open envelope A, you still don't know if the fair value of the game. The fair value of the game is 1.5x (where x is the smaller amount). After opening you don't know if you have the smaller or larger amount by definition. Choosing to play the game you in essence wager 0.5x against the 1.5x fair value. Half the time you lose and are left with 1x, half the time you win and have 2x. Switching after opening is no different.