Thursday, September 29, 2011

Game Theory: Part III: Utility Functions

Now, a short digression (and a comic). How do you compare incomparables? If a life is measured against profits, which is valued higher?


The following material is flagged Green Level. It is intended to reflect material that the author believes to be a matter of consensus among experts in the field. This belief may be incorrect, however; and as the author is not an expert and does not have an expert fact-checking the article, errors may creep in.
 First, the comic.

Now, on to the digression. Suppose I offer you a choice between an apple and an orange.  (Yes, it's hardly a life compared to a work of art, but let's start small). We will say, for the purposes of this post, that you pick the apple.
According to game theory, this means that the apple has a higher utility value than the orange.
And there I go again, using terms. All people are assumed to have a utility function, which is a numerical measure of how much they like a given outcome. Utility functions, though, only work if certain conditions are met:
1) The function must be transitive. If an apple is better than an orange, and a pear is better than an apple, then a pear is better than an orange.
2) The function must be blind to gambling. An apple must be exactly as good as a one in two chance of two apples (assuming that two apples is exactly twice as good as one apple). In other words, the utility of a chance at an object is equal to that chance times the utility of the object.

So then, according to the economist, the utility of the Mona Lisa is equal to 872 times the utility of a human life. If he were faced with a choice between saving the Mona Lisa or saving 872 humans, both outcomes would be equal and he would likely flip a coin to decide.
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