Paul Weirich

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.

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.

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.