[ExI] Two Envelope Paradox
avantguardian2020 at yahoo.com
Sun Jul 27 15:50:57 UTC 2014
So without further ado: Imagine that Ed McMahon, or somebody suitably cheesy, allows you to choose between two sealed envelopes with money in them. Furthermore he informs that one of the envelopes contains double the money of the other.
So you choose one but before you can open it you are asked if you would like to switch your envelope for the other. So you do the expected value calculations on keeping or switching envelopes-
Your envelope contains x dollars. The expected value of the *other* envelope is (1/2)*2x + (1/2)*(x/2) = 1.25x therefore the *other* envelope has a higher expected value than the one you hold, so you should switch.
But wait a minute. If you switch envelopes, you could do the calculation again and realize the the expected value of the original envelope is one and a quarter of the one you now hold. You could use this reasoning any number of times to switch envelopes. You would be trading envelopes with Ed McMahon indefinitely, the other envelope always being more valuable than the one you hold.
Thereby the paradox.
So to help you make up your mind, Ed McMahon allows you to open the envelope you now hold. You open it up, and it contains $20. Then Ed Mahaon gives you one last chance to switch envelopes, should you?
I think I have cracked this paradox, but I am curious what others have to say before I reveal my reasoning. Especially the decision theorists on the list.
"We speak for Earth. Our obligation to survive is owed not just to ourselves but also to that Cosmos, ancient and vast, from which we spring." - Carl Sagan
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