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Old 06-20-2006, 06:35 PM
NaobisDad NaobisDad is offline
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Join Date: Feb 2004
Posts: 519
Default The envelope problem, and a possible solution

Recently I read a post on the 2 envelopes paradox ( Here).

I will not elaborate on what the problem is, because it is stated and discussed clearly in the provided link and I ask you to please read the OP. I want to discuss a solution put forward by a friend of mine.

A friend of mine argued the following:
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If we were te simulate the envelope problem, it would show that looking at the amount of money in your envelope is not going to affect the EV of always switchin envelopes. Which would be in line with the argument that switching envelopes is neutral EV. He asked me, "if we were to play this game, do you expect that looking at the amount would change anything to you EV?" And I answered: "I do not see how always switching can possibly become anything other than neutral EV, when the only change you make is that you are merely passivily looking at the value now". After which he followed:

Most likely the argument that switching is EV neutral is the correct one. The other argument then cannot be correct, so somewhere in the argument there must be flaw. He argued that the point of determination is key. The amounts in the envelope are determined before the start of the game, not after you learn the value.

If the value of the second envelope was determined after you had learned the value of the first (for example by flipping a coin) then idd switching would be +EV. This is comparable to saying, I give you $100, you can keep it, or I flip a coin; heads you double it, tails you lose half.

However, this is not the case in the envelope problem he said. The values are assigned to the envelopes on beforehand. Even though intuitively it may feel like a switch might double your money or cut it in half after you learn the value; in reality there is only one possible outcome. For example, if you look at the value in envelope 1, and it is $100. Then intuitively it might feel like you have a 50% shot at $50 or $200, but you don't have it. Say the ammount in the second envelope was $50, it would not be possible to get $200 on that trial. The flaw would boil down to using the $100 as new information in determining your EV when it doesn't provide any new information really. So, even though the method of determining your EV is right in argument 1, it is not applicable in that situation.

What I am wondering is, how is this line of reasoning? He is fully convinced that it is the solution to the problem, and a colleague of mine basically suggests the same solution.
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I still am not sure, I'd appreciate some imput.
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