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Social scientists are continually confronted with the problem of formulating models which describe how individuals make choices among alternative courses of action with uncertain consequences. Economists have developed a class of models which seem to deal particularly well with problems of this type. These models employ the ``expected utility theorem'' of von Neumann and Morgenstern and, for reasons brought out in the paper, are generally qualitative in nature. Since the approach to modeling human behavior adopted by non-economists is generally very different from that of economists, in this paper we present a rather detailed example of the role of the expected utility theorem in qualitative model building. Specifically, we model an arsonist's decision as to the amount of time to allocate to arson and related activities and examine the responsiveness of this time allocation to changes in various policy parameters. Both the activity modeled and the method of presentation are intended to provide an introduction to the scope and power of the expected utility theorem in modeling situations of ``choice under uncertainty.''