Paul Weirich

The rule to maximize expected utility is intended for decisions where options involve risk. In those decisions the decision maker's attitude toward risk is important, and the rule ought to take it into account. Allais's and Ellsberg's paradoxes, however, suggest that the rule ignores attitudes toward risk. This suggestion is supported by recent psychological studies of decisions. These studies present a great variety of cases where apparently rational people violate the rule because of aversion or attraction to risk. Here I attempt to resolve the issue concerning expected utility and risk. I distinguish two versions of the rule to maximize expected utility. One adopts a broad interpretation of the consequences of an option and has great intuitive appeal. The other adopts a narrow interpretation of the consequences of an option and seems to have certain technical and practical advantages. I contend that the version of the rule that interprets consequences narrowly does indeed neglect attitudes toward risk. That version of the rule excludes the risk involved in an option from the consequences of the option and, contrary to what is usually claimed, cannot make up for this exclusion through adjustments in probability and utility assignments. I construct a new, general argument that establishes this in a rigorous way. On the other hand, I contend that the version of the rule that interprets consequences broadly takes account of attitudes toward risk by counting the risk involved in an option among the consequences of the option. I rebut some objections to this version of the rules, in particular, the objection that the rule lacks practical interest. Drawing upon the literature on 'mean-risk' decision rules, I show that this version of the rule can be used to solve some realistic decision problems.

Groups of people perform acts that are subject to standards of rationality. A committee may sensibly award fellowships, or may irrationally award them in violation of its own policies. A theory of collective rationality defines collective acts that are evaluable for rationality and formulates principles for their evaluation. This book argues that a group's act is evaluable for rationality if it is the products of acts its members fully control. It also argues that such an act is collectively rational if the acts of the group's members are rational. Efficiency is a goal of collective rationality, but not a requirement, except in cases where conditions are ideal for joint action and agents have rationally prepared for joint action.The people engaged in a game of strategy form a group, and the combination of their acts yields a collective act. If their collective act is rational, it constitutes a solution to their game. A theory of collective rationality yields principles concerning solutions to games. One principle requires that a solution constitute an equilibrium among the incentives of the agents in the game. In a cooperative game some agents are coalitions of individuals, and it may be impossible for all agents to pursue all incentives. Because rationality is attainable, the appropriate equilibrium standard for cooperative games requires that agents pursue only incentives that provide sufficient reasons to act. The book's theory of collective rationality supports an attainable equilibrium-standard for solutions to cooperative games and shows that its realization follows from individuals' rational acts.By extending the theory of rationality to groups, this book reveals the characteristics that make an act evaluable for rationality and the way rationality's evaluation of an act responds to the type of control its agent exercises over the act. The book's theory of collective rationality contributes to philosophical projects such as contractarian ethics and to practical projects such as the design of social institutions.

Agents face serious obstacles to making optimal decisions. For instance, their cognitive limits stand in the way. John Pollock’s book, Thinking about Acting , suggests many ways of revising decision principles to accommodate human limits and to direct limited, artificial agents. The book’s main proposal is to replace optimization, or expected-utility maximization, with locally global planning. This essay describes optimization and locally global planning, and then argues that optimization among salient options has the virtues of locally global planning without certain drawbacks. Although it does not endorse locally global planning, it recommends that decision theory incorporate some of the book’s ideas about settling for improvements when optimization among all options is unrealistic.

When new technologies create risks, government agencies use regulations to control the risks. This paper advances a method of evaluating a democracy’s regulation of risks. It assumes that a regulatory agency should act as the public would act in ideal conditions for negotiation if the public were rational and informed. The method relies on decision theory and game theory to ascertain whether a regulation has the public’s informed support. The Occupational Safety and Health Administration’s regulation of exposure to carcinogens in the workplace illustrates the account of regulation. The illustration draws attention to a distinction between physical and information-sensitive risks. Regulations guided by the physical sciences alone may overlook the value of reducing information-sensitive risks. These risks exist objectively, and rational people generally have an aversion to them. An information-sensitive risk and an aversion to it may persist after acquisition of all available relevant information. Democratic regulation justifiably aims to reduce such risks.

When a trustee makes a decision for a client, a standard objective is to decide as the client would if he had the trustee's information. How can this objective be attained when, given the trustee's information, there is still uncertainty about the consequences of alternative courses of action? A promising approach is to apply the rule to maximize expected utility using the client's utilities for consequences and the trustee's probabilities for states. But taking utilities and probabilities from different sources causes a problem that has to be resolved. Briefly, the problem is that the client's utilities for consequences involve assessments of risks that are uninformed because he does not have informed probabilities. And the resolution of the problem is to reconstruct his utilities for consequences using a component due to risk that the trustee supplies for the client, and a component due to other consequences that the client supplies for himself.

This book represents a major contribution to game theory. It offers this conception of equilibrium in games: strategic equilibrium. This conception arises from a study of expected utility decision principles, which must be revised to take account of the evidence a choice provides concerning its outcome. The argument for these principles distinguishes reasons for action from incentives, and draws on contemporary analyses of counterfactual conditionals. The book also includes a procedure for identifying strategic equilibria in ideal normal-form games. In synthesizing decision theory and game theory in a powerful way this book will be of particular interest to all philosophers concerned with decision theory and game theory as well as economists and other social scientists.

Causal decision theory produces decision instability in cases such as Death in Damascus where a decision itself provides evidence concerning the utility of options. Several authors have proposed ways of handling this instability. William Harper (1985 and 1986) advances one of the most elegant proposals. He recommends maximizing causal expected utility among the options that are causally ratifiable. Unfortunately, Harper's proposal imposes certain restrictions; for instance, the restriction that mixed strategies are freely available. To obtain a completely general method of handling decision instability, I step outside the confines of pure causal decision theory. I introduce a new kind of backtracking expected utility and propose maximizing it among the options that are causally ratifiable. In other words, I propose a hierarchical maximization of (1) conditional causal expected utility and (2) the new backtracking expected utility. I support this proposal with some intuitive considerations concerning the distinction between optimality and conditional optimality. And I prove that the proposal yields a solution in every finite decision problem

I will characterize the utilitarian and maximin rules of social choice game-theoretically. That is, I will introduce games whose solutions are the utilitarian and maximin distributions respectively. Then I will compare the rules by exploring similarities and differences between these games. This method of comparison has been carried out by others. But I characterize the two rules using games that involve bargaining within power structures. This new characterization better highlights the ethical differences between the rules.

This book represents a major contribution to game theory. It offers this conception of equilibrium in games: strategic equilibrium. This conception arises from a study of expected utility decision principles, which must be revised to take account of the evidence a choice provides concerning its outcome. The argument for these principles distinguishes reasons for action from incentives, and draws on contemporary analyses of counterfactual conditionals. The book also includes a procedure for identifying strategic equilibria in ideal normal-form games. In synthesizing decision theory and game theory in a powerful way this book will be of particular interest to all philosophers concerned with decision theory and game theory as well as economists and other social scientists.

Abner Shimony argues that degrees of belief satisfy the axioms of probability because their epistemic goal is to match estimates of objective probabilities. Because the estimates obey the axioms of probability, degrees of belief must also obey them to reach their epistemic goal. This calibration argument meets some objections, but with a few revisions it can surmount those objections. It offers a good alternative to the Dutch book argument for compliance with the probability axioms. The defense of Shimony's calibration argument examines rational pursuit of an epistemic goal, introduces strength of evidence and its measurement, and distinguishes epistemic goals and functions.