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p8 - 16 Chapter 2 Arm As if But I’m not Barbara Well this...

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Unformatted text preview: 16 Chapter 2 Arm: As if? But I’m not. Barbara: Well, this is up to you. But let’s start by agreeing that this is now only a matter of representation. One can say, “Ann is choosing among her alternatives by maximizing a utility function” and one can also say, “Ann is choosing whom to date in a complete and transitive way, or a decisive and faithful way,” and these two statements mean exactly the same thing. It’s a mathematical theorem. Arm: What is? Barbara: That if you have a preference—~61 way to compare pairs of altemativesuthat is complete and transitive, then it can be represented by a utility function, so that between any two alternatives the one with the higher utility is chosen. Arm: Always? Barbara: Well, at least if you have finitely many alternatives. And, pretty as you are, i think that even you don’t have infinitely many suitors. Arm: You’re so clever. Barbara: More than you’d believe. There’s even more: not only can I look at you and say, ”Ann is maximizing a utility function,” without thinking anything bad about you, i can even tell you that finding a utility function and maximizing it is the only method I know that can guarantee that you will indeed be complete and transitive in your preferences. Arm: So you seriously suggest that I assign a number-”call it utility if this makes you happy~—to each guy and choose the one with the high- est number. Barbara: Yes, that is precisely what I suggest. Amt: But I really hate the word utility. It makes me think of gas, elec— tricity, and cable TV, not of love. Barbara: Can we call it payoff? Arm: Payoff is what you get when you gamble on horses. Or when you’re killed by the mafia. Barbara: Call it whatever you like. i thought we agreed not to attach too much importance to names. lust assign numbers to your alternatives. Arm: But i really don’t know how 1 would do that. How do I know if Bob should have a higher number than, say, Jim? Utility Maximization 17 Barbara: Ask yourself, which one do you like better? Arm: But that’s precisely the point; i don’t know which one i like better! [Barbara is silentl Arm: I mean, this is what you were supposed to help me sort out in the first place, weren’t you? Barbara: You know what? l’ll think about it. 2.2 Two Points The example in the previous section illustrates two main points. The first is that terms like utility and maximization should not turn you off. They do not preclude emotional decision making, love and hate, lofty or base motives. To say that someone maximizes a utility function is merely to say that she is coherent in her choices. Mother Teresa could possibly be described as maximizing the number of healthy children in the world. That is, she maximized a certain function. Adolf Hitler tried to maximize the percentage of Aryan people in Germany. He also maximized a function. Thinking of Mother Teresa and Adolf Hitler as utility maximizers only says that each of them pursued a goal in a coherent way. it does not mean that they are equivalent in terms of ethical judgments, character, or anything of the sort. You are likely to admire Mother Teresa for her utility function and to loathe Adolf Hitler for his. The notion of utility maximization leaves room for all these attitudes. The second important point, made at the end of the dialogue, is that it doesn’t always help to want to maximize a utility function. In the ab sence of additional structure in the problem, the mathematical equiva— lence mentioned in the dialogue leaves us no better off than we were when we started. The dialogue refers to a theorem stating that comparison between pairs is complete and transitive if and only if it can be described by maximization of a function (a utility function). Appendix B provides mathematical details and two formal versions of this theorem. 1 now turn to the theorem’s interpretations. 2.3 Interpretations The theorem in appendix 8 has three types of interpretations. One ...
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