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The Monty Hall Problem

Is this problem still taught in philosophy class? or logic or probability classes or wherever one might want to teach it? Have they (teachers in general) changed the name? Do undergraduate students in philosophy classes learn in this way for the first time in their lives who the heck Monty Hall was? Hmmm. I'm too fascinated by those question to actually discuss the Monty Hall problem today. So that will be all. Class dismissed,

Thoughts About Risk Aversion

Risk aversion is a straightforward name for the psychological fact that humans are often willing to pay a premium for certainly, or at least for limiting the zone of uncertainty. Suppose you, dear reader, appear on a television game show. The master of ceremonies says to you, "I can give you a nice crisp $100 bill right now!" You say, "oh, goodie." "Or!" he continues with a dramatic flourish, "I can flip a coin. If the coin comes up tails, you'll get nothing. If the coin comes up heads, you'll get $200." Let us suppose there is no element of what finance types call "counter-party risk" here. Your counter-party is the emcee. We'll assume he is entirely trustworthy and that there is nothing tricky about the coin flip itself. The expected value of the coin flip, in simple arithmetical terms, is ($200 + 0) ÷ 2 = $100. The value of the payoff if you reject the coin flip is, again, $100. So you should o...

The Monty Hall Paradox

An old paradox, named after a game show host, the emcee of "Let's Make a Deal" continuously from 1963 to 1976, and intermittently as revived thereafter. Monty Hall presented contestants with three curtains, often labeled A,B, and C, and asked them to make a choice. They would get whatever gift was behind the curtain they chose. In the story/paradox, Monty tells you that behind one of the curtains is a magnificent new car, the car of your dreams. Behind the other two curtains, not-so-desirable gifts. You tell him: "I pick A, Monty." Monty: "Not so fast! I will now reveal what is behind curtain C." The curtain opens, and there is some worthless gag gift, say a pile of shaving cream. Monty: "Now, you can stay with your choice of A, or you can switch to B." What should you do? The usual first response, and for many people a very powerful intuitive response, is that it doesn't matter what you do. You now have just two curtai...