Risk and rationality

Decision theory is a theory of rationality. It is supposed to formally represent the preferences of all rational decision makers. And yet, there are some preferences that violate standard decision theory that seem intuitively appealing: on the face of it, counterexamples to the claim that standard decision theory (expected utility theory) can represent all rational agents. An important group of these preferences stem from how ordinary decision makers take risk into account. This dissertation has three main goals. First, it aims to vindicate these preferences - to show that they are not, as the standard theory supposes, irrational. Second, it aims to show that expected utility theory does not have the resources to account for these preferences, because expected utility theory rests on a mistake about what it means to be risk averse (or to be risk seeking), a mistake that conflates two criteria by which decision makers evaluate gambles. Finally, it proposes a positive theory of rationality that is a generalization of expected utility theory. This positive theory allows for a broader range of attitudes towards risk; it better captures what it means to be risk averse; and it has both philosophical and mathematical foundations.;The dissertation begins by explaining my positive proposal and contrasting it with expected utility theory. I then consider and reject three arguments in favor of expected utility theory. I first consider the argument that expected utility theory follows from axioms that would be irrational to violate; while considering this argument, I clarify the notion of rationality that decision theorists take themselves to be analyzing. Second, I consider the argument that decision makers who violate the theory are subject to sure loss at the hands of clever bookies; and third, I consider the argument that decision makers who violate the theory do worse over the long run or in the aggregate. In the next section of the dissertation, I consider a strategy that allows expected utility theory to assimilate seeming counterexamples by re-describing the outcomes in decision problems that people face, but show that this strategy does not work against counterexamples involving risk attitudes. Finally, I show that my theory has a representation theorem: in other words, if a decision maker satisfies certain axioms, then from her preferences we can extract a function that represents her degrees of belief, a function that represents her desires, and a function that represents her attitude towards risk.;While standard decision theory is broadly correct, it rules out certain preferences - preferences that stem from decision makers' attitudes towards risk - that turn out to be rationally permissible. Building on the basic framework of this theory and generalizing the theory allows us to accommodate these preferences and to better capture the way in which decision makers take risk into account, yielding a superior analysis of rationality.;Keywords: decision theory, rationality, risk aversion, expected utility, non-expected utility, Humeanism, sure-thing principle, Dutch books, representation theorem, individuation, global properties, preference, folk psychology.