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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