on the strategic aspects of how to achieve what you want, without worrying about the complications involved in defining what you want.

However, there remained an important aspect of utility that von Neumann and Morgenstern had to address. Was it even possible, in the first place, to define utility in a numerical way, to make it susceptible to a mathematical theory? (Bernoulli had proposed a way to calculate utility, but he had not tried to prove that the concept could be a basis for making rational choices in a consistent way.) Money (which obviously is numerical) could really be a good stand-in for the more complex concept of utility only if utility can really be represented by a numerical concept. And so they had to show that it was possible to define utility in a mathematically rigorous way. That meant identifying axioms from which the notion of utility could be deduced and measured quantitatively.

As it turned out, utility could be quantified in a way not unlike the approach physicists used to construct a scientifically rigorous definition of temperature. After all, primitive notions of utility and temperature are similar. Utility, or preference, can be thought of as just a rank ordering. If you prefer A to B, and B to C, you surely prefer A to C. But it is not so obvious that you can ascribe a number to how much you prefer A to B, or B to C. It was once much the same with heat—you could say that something felt warmer or cooler than something else, but not necessarily how much, certainly not in a precise way—before the development of the theory of heat. But nowadays the absolute temperature scale, based on the laws of thermodynamics, gives temperature an exact quantitative meaning. And von Neumann and Morgenstern showed how you could similarly convert rank orderings into numerically precise measures of utility.

You can get the essence of the method from playing a modified version of Let’s Make a Deal. (For the youngsters among you, that was a famous TV game show, in which host Monty Hall offered contestants a chance to trade their prizes for possibly more valuable prizes, at the risk of getting a clunker.) Suppose Monty offers you three choices: a BMW convertible, a top-of-the-line big-



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