On the fictitious television game show, Marginal Analysis for Everyone, the host subjects contestants to unusual tests
Question:
“Switching is clearly advantageous,” intones the host persuasively. “Suppose you have amount x in your Envelope A. Then B must contain either x/2 (with probability 0.5) or 2 x (also with probability 0.5). Thus, the expected value of switching is 1.25 x. In fact now that I think about it, I’ll only let you switch if you give me a 10% cut of your winnings. What do you say? You’ll still be ahead. ”
“No deal,” replies the contestant. “But I’ll be happy to switch for free. In fact, I’ll even let you choose which envelope I get. I won’t even charge you anything!”
What is wrong with the host’s analysis?
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Related Book For
Making Hard Decisions with decision tools
ISBN: 978-0538797573
3rd edition
Authors: Robert Clemen, Terence Reilly
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