[AaronBrown]

[ QUOTE ]
I got frustrated with Aaron in this dialogue before. Sure am glad you started it up again. [img]/images/graemlins/smile.gif[/img]

Here's how my dialogue would go when I hear the problem.

Paradoxer: "I put a random amount X in one envelope and 2X in the other."
Me: "Wait, how was X chosen?"
P: "I'm not telling you. Now, you open and find $100. Should you switch?"
M: "Man, I dunno. I can tell you the correct move if you describe the opponent."
P: "I'm not going to tell you. So, what's the best move?!"

It's retarded. Of course you and I can arrive at different answers if we try to fill-in the gaping hole differently. That doesn't show that the problem's clever; all that shows is that the problem has gaping holes.
-Sam

[/ QUOTE ]
I understand your frustration because I refuse to answer the question. I think the problem is people assume there must be a right answer, and then use that to reason, usually to the idea that you shouldn't switch. My objection is that there is only a right answer if you assume a lot of mathematical machinery, perhaps consistent finite prior beliefs or the existence of an expected value.

It's not just theoretical hair-splitting, as the FX example and years in Purgatory example show. You can make reasonable assumptions that make it +EV to switch. The useful thing is to understand why both the switching and indifference arguments have force, and when to follow one versus the other.

I also understand it's frustrating that life forces us to play a game without clearly specified rules or odds. But don't blame me for that one. The point of this example is not to prove it's a clever question, it's to help you think about real decisions in which you don't how amounts were selected for the envelopes.

Don't argue with me, argue with the Clash:

Clash: "Should I stay or should I go? If I go there will be trouble."
SamIam: "Wait, how was the amount of trouble chosen?"
Clash: "If I stay there will be double."
SamIAM: "Man, I dunno. I can tell you the correct move if you describe the opponent."
Clash: "So you gotta let me know. Should I stay or should I go?"

Sorry SamIAM, you have to choose.