Paul Weirich

The expected utility of an option for a decision maker is defined with respect to probability and utility functions that represent the decision maker’s beliefs and desires. Therefore, as the decision maker’s beliefs and desires change, the expected utility of an opinion may change. Some options are such that their realizations change beliefs and desires in ways that change the expected utilities of the options. If a decision is made among options that include one or more of these special options, I call it a decision made in a dynamic setting.The rule to maximize expected utility, MEU, is insufficient for decisions in dynamic settings. It does not say how to take account of information about the way in which the realization of an option would change the expected utility of the option.

Does rational bargaining yield a social contract that is efficient and so inclusive? A core allocation, that is, an allocation that gives each coalition at least as much as it can get on its own, is efficient. However, some coalitional games lack a core allocation, so rationality does not require one in those games. Does rationality therefore permit exclusion from the social contract? I replace realization of a core allocation with another type of equilibrium achievable in every coalitional game. Fully rational agents coordinate the pursuit of incentives so that equilibria of this type are efficient. They adopt a social contract that is efficient and inclusive

An agent often does not have precise probabilities or utilities to guide resolution of a decision problem. I advance a principle of rationality for making decisions in such cases. To begin, I represent the doxastic and conative state of an agent with a set of pairs of a probability assignment and a utility assignment. Then I support a decision principle that allows any act that maximizes expected utility according to some pair of assignments in the set. Assuming that computation of an option's expected utility uses comprehensive possible outcomes that include the option's risk, no consideration supports a stricter requirement.

A philosophical account of risk, such as this book provides, states what risk is, which attitudes to it are rational, and which acts affecting risks are rational. Attention to the nature of risk reveals two types of risk, first, a chance of a bad event, and, second, an act’s risk in the sense of the volatility of its possible outcomes. The distinction is normatively significant because different general principles of rationality govern attitudes to these two types of risk. Rationality strictly regulates attitudes to the chance of a bad event and is more permissive about attitudes to an act’s risk. Principles of rationality governing attitudes to risk also justify evaluating an act according to its expected utility given that the act’s risk, if any, belongs to every possible outcome of the act. For a rational ideal agent, the expected utilities of the acts available in a decision problem explain the agent’s preferences among the acts. Maximizing expected utility is just following preferences among the acts. This view takes an act’s expected utility, not just as a feature of a representation of preferences among acts, but also as a factor in the explanation of preferences among acts. The view extends to evaluations of combination of acts, either simultaneous or in a sequence. It takes account of an agent’s attitudes to an act’s risk without weakening the standard of expected-utility maximization. The book’s theory of risk also grounds a justification of the risk-return evaluation of investments that finance advances, and a generalized version of this type of evaluation that a professional may use to advise clients about risks and that a government regulatory agency may use to make decisions about risks on behalf of the public.

Margaret Gilbert (1990) argues that although the rationality of the agents in a standard coordination problem does not suffice for their coordination, a social convention of coordination, understood as the agents’ joint acceptance of a principle requiring their coordination, does the job. Gilbert’s argument targets agents rational in the game-theoretic sense, which following Sobel (1994: Chap. 14), I call hyperrational agents. I agree that hyperrational agents may fail to coordinate in some cases despite the obvious benefits of coordination. However, I add that fully rational agents, who rationally exercise rationality’s permissions, may coordinate in these cases without jointly accepting a principle of coordination. I make this point using a model that adopts common simplifying assumptions about agents and their coordination problems.

A common type of change in science occurs as theorists generalize a model of a phenomenon by removing some idealizations of the model. This type of change occurs in the decision sciences and also in the normative branch of the decision sciences that treats rational choice. After presenting a general ac-count of model generalization, the paper illustrates generalization of models in normative decision theory. The principal illustration generalizes a standard model of rational choice by removing the idealization that deliberation has no cost.

Expected-utility theory advances representation theorems that do not take the risk an act generates as a consequence of the act. However, a principle of expected-utility maximization that explains the rationality of preferences among acts must, for normative accuracy, take the act’s risk as a consequence of the act if the agent cares about the risk. I defend this conclusion against the charge that taking an act’s consequences to comprehend all the agent cares about trivializes the principle of expected-utility maximization.

A computer simulation runs a model generating a phenomenon under investigation. For the simulation to be explanatory, the model has to be explanatory. The model must be isomorphic to the natural system that realizes the phenomenon. This paper elaborates the method of assessing a simulation's explanatory power. Then it illustrates the method by applying it to two simulations in game theory. The first is Brian Skyrms's (1990) simulation of interactive deliberations. It is intended to explain the emergence of a Nash equilibrium in a noncooperative game. The second is Skyrms's (2004) simulation of the evolution of cooperation. It is intended to explain cooperation in assurance games. The final section suggests ways of enhancing the explanatory power of these simulations.

Standard principles of rational decision assume that an option's utility is both comprehensive and accessible. These features constrain interpretations of an option's utility. This essay presents a way of understanding utility and laws of utility. It explains the relation between an option's utility and its outcome's utility and argues that an option's utility is relative to a specification of the option. Utility's relativity explains how a decision problem's framing affects an option's utility and its rationality even for an agent who is cognitively perfect and lacks only empirical information. The essay rewrites standard laws of utility to accommodate relativization to propositions' specifications. The new laws are generalizations of the standard laws and yield them as special cases.

Groups of people perform acts. For example, a committee passes a resolution, a team wins a game, and an orchestra performs a symphony. These collective acts may be evaluated for rationality. Take a committee’s passing a resolution. This act may be evaluated not only for fairness but also for rationality. Did it take account of all available information? Is the resolution consistent with the committee’s past resolutions? Standards of collective rationality apply to collective acts, that is, acts that groups of people perform. What makes a collective act evaluable for rationality? What methods of evaluation apply to collective acts? This paper addresses these two questions. Collective rationality is rationality’s extension from individuals to groups. The paper’s first few sections review key points about rationality. They identify the features of an individual’s act that make it evaluable for rationality and distinguish rationality’s methods of evaluating acts directly and indirectly controlled. This preliminary work yields general principles of rationality for all agents, both individuals and groups. Applying the general principles to groups answers the paper’s two main questions about collective rationality.

To handle epistemic and pragmatic risks, Gärdenfors and Sahlin (1982, 1988) design a decision procedure for cases in which probabilities are indeterminate. Their procedure steps outside the traditional expected utility framework. Must it do this? Can the traditional framework handle risk? This paper argues that it can. The key is a comprehensive interpretation of an option's possible outcomes. Taking possible outcomes more broadly than Gärdenfors and Sahlin do, expected utility can give risk its due. In particular, Good's (1952) decision procedure adequately handles indeterminate probabilities and the risks they generate.

Decision theory aims at a general account of rationality covering humans but to begin makes idealizations about decision problems and agents' resources and circumstances. It treats inerrant agents with unlimited cognitive power facing tractable decision problems. This book systematically rolls back idealizations and without loss of precision treats errant agents with limited cognitive abilities facing decision problems without a stable top option. It recommends choices that maximize utility using quantizations of beliefs and desires in cases where probabilities and utilities are indeterminate and using higher-order utility analysis in cases of limited access to probabilities and utilities. For agents burdened with mistakes, it advocates reasonable attempts to correct unacceptable mistakes before deciding. In decision problems without a stable top option, a topic of game theory, it proposes maximizing self-conditional utility among self-supporting options. In games of strategy, the new principles lead to solutions that are Pareto optimal among equilibria composed of jointly self-supporting strategies. Offering an account of bounded rationality, the bookmakes large strides toward realism in decision theory.

In a decision problem with a dynamic setting there is at least one option whose realization would change the expected utilities of options by changing the probability or utility function with respect to which the expected utilities of options are computed. A familiar example is Newcomb's problem. William Harper proposes a generalization of causal decision theory intended to cover all decision problems with dynamic settings, not just Newcomb's problem. His generalization uses Richard Jeffrey's ideas on ratifiability, and material from game theory on mixed strategies. Harper's proposal has two drawbacks, however. One concerns the mechanism for choosing among ratifiable options. The other concerns the proposal's reliance upon mixed strategies. Here I make another proposal that eliminates these two drawbacks.