Re: The envelope problem, and a possible solution
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The EV of the envelope is not relevant. What matters is the conditional EV of switching, which is always well-defined and finite.
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Let's say I pull the envelope, and find that it contains 8 trillion dollars. Now, there is only about 1 trillion dollars in currency in circulation, so there's a problem. If the EV goes to infinity, then, for any scarce resource, there is a non-zero probability that the envelope contains more of the resource than exists, ergo, if the amount in the envelope is close to that (or larger) it makes hardly any sense to switch envelopes.
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It "makes sense" to switch if the conditional probability, p, that the other envelope is larger, satisfies p>1/3. The value p is always a well-defined number between 0 and 1.
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Actually, that's incorrect. It makes sense to switch if the average expected value (EV) of the other envelope is larger than the value of the held envelope.
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