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p7 - .11 Roiifif’icl A Barbara Would you like to be able...

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Unformatted text preview: .11 Roiifif’icl A Barbara: Would you like to be able to choose between any two? Ami: Yes, of course, that’s what l’m trying to do. Barbara: We. call this completeness. It means that you can always make a choice. that your preferences are complete. Ami: And if I find two of them just as good? Barbara: Ties are allowed. You can say that you are indifferent be— tween the two; each is as good as the other. Then you may choose the first that comes to mind, but you won’t need to change your choice later on. By the way, it’s good for your guys, too. Ami: Huh? Barbara: Otherwise you’d drive them nuts. You’d say yes and no, first you and then him, and then maybe. Do you know, for instance, that Franz. Kafka was twice engaged to marry the same woman, and he canceled the marriage both times? Ami: Really? Barbara: Yes, it didn’t really make her happy. Ann: Why did he do that? Barbara: Well, he was just incapable of making a decision. The point is there’s nothing very romantic about this. Arm: Okay, I get it. Barbara: Good. Now: would your like your choices between pairs to be transitive? Arm: What’s that? Barbara: Transitive. This means that if you think that a is at least as good as b, and b is at least as good as c, you also think that a is at least as good as 6. Arm: i guess so. Barbara: Sure, you want to make such decisions! Arm: Here we go again. Big wise sister telling Ann what she wants. Barbara: No, no, no, not because I’m your big sister, and not because l’m wise, though both are true. [Arm rolls her eyes.) Barbara: You want to be transitive because otherwise you’ll be dating c and leaving him for b, then dating b and leaving him for a, and then you’ll send a away and go back to C, and so on, until they’re all fed up Utility £Y1t‘2Aliii!AflbiUii .13! with you. if you are not transitive, you will be cruel to all the guys involved, and if they have any backbone, you’ll be cruel to yourself, too. drill: Oh, i thought that being faithful to one means being cruel to all the others. Barbara: Did l ever say that? Aim: Da Ponte did, giving this line to Don Giovanni. Barbara: Oh. good. i was afraid I might have been too honest. Arm: Very funny. Barbara: But you get the point—4f you want to be neither as indeci— sive as Kafka nor as fickle as Don Giovanni, you have to be complete and transitive. Arm: Okay, suppose I am. What wouldn’t one do for one’s sister! Barbara: The point is that if you. are complete and transitive in your preferences, then it is as if you are maximizing a utility function. Arm {suspiciously}: Function? This is something with a derivative, isn’t it? Barbara [smiling]: It might have a derivative in calculus. But all I mean is a rule, a way to assign numbers to alternatives. Ami: What’s a way? What is not a way? Barbara: lust think of a table. where in one column you have the name of the alternative, and in another, the numerical value you attach to it. Arm: If you mean a table. why do you call it a function? Sometimes l feel you really don’t want me to understand what you’re saying. Barbara: I’m sorry. Don’t give me this look, i really mean it. The rea— son it’s called a function is that sometimes it will not be given by a table but by a formula. You know, like writing 2x instead of listing the value for each and every value of x Arm: Okay. But I can think of a function as a table? Barbara: Yes, you can think of it as a table of values that is sometimes more succinctly described, by a formula. Arm: Great. But what did you want a function for? Barbara: You’re so argumentative. I nearly forgot why i mentioned a function in the first place. But i think it’s coming back to me. l said that if your preferences are complete and transitive, then I can think of you as if you were maximizing a utility function. ...
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