Representation theorems are often taken to provide the foundations for decision theory. First, they are taken to characterize degrees of belief and utilities. Second, they are taken to justify two fundamental rules of rationality: that we should have probabilistic degrees of belief and that we should act as expected utility maximizers. We argue that representation theorems cannot serve either of these foundational purposes, and that recent attempts to defend the foundational importance of representation theorems are unsuccessful. As (...) a result, we should reject these claims, and lay the foundations of decision theory on firmer ground. (shrink)

Economics bases the choice theory on the mental experiment that introduces the choice correspondence, which associates to every set of possible actions the subset of preferred actions. If some conditions are satisfied, then the choice correspondence implies a binary preference ordering on actions and an ordinal utility function. This approach applies both to decisions under certainty and decisions under uncertainty. The preference ordering depends on the consequence of actions. Under certainty, there is only one consequence to every action, while, (...) under uncertainty, many consequences are possible, associated with the states of the world. These consequences are represented by the action itself, the states of the world, and the corresponding outcomes. Current theories consider only outcomes, but some theories include state dependent preference. Preference for the action itself is not considered, but it might be relevant. The rationality of the theory is a different question from the rationality of the decision-maker. Moreover, the rationality of the theory may imply the rationality of a preference ordering, but this does not require the rationality of the decision-maker. It is only assumed that he/she behaves according to the calculation made by the theorist. The rationality of the preference ordering requires the rationality of the preference on outcomes, of the expectations on the events, and of their connection with the preference ordering on actions. The normative relevance of rational preferences is removed by the introduction of many alternative rational theories, which justify contrasting behaviors in identical situations. (shrink)

A review and discussion of C. A. Hooker, J. J. Leach, and E. F. McClennen's edited volumes, Foundations and Applications of Decision Theory. Volume 1: Theoretical Foundations. Volume 2: Epistemic and Social Applications.

This book defends the view that any adequate account of rational decision making must take a decision maker's beliefs about causal relations into account. The early chapters of the book introduce the non-specialist to the rudiments of expected utility theory. The major technical advance offered by the book is a 'representation theorem' that shows that both causal decision theory and its main rival, Richard Jeffrey's logic of decision, are both instances of a more general (...) conditional decision theory. The book solves a long-standing problem for Jeffrey's theory by showing for the first time how to obtain a unique utility and probability representation for preferences and judgements of comparative likelihood. The book also contains a major new discussion of what it means to suppose that some event occurs or that some proposition is true. The most complete and robust defence of causal decision theory available. (shrink)

According to accuracy-first epistemology, accuracy is the fundamental epistemic good. Epistemic norms — Probabilism, Conditionalization, the Principal Principle, etc. — have their binding force in virtue of helping to secure this good. To make this idea precise, accuracy-firsters invoke Epistemic Decision Theory (EpDT) to determine which epistemic policies are the best means toward the end of accuracy. Hilary Greaves and others have recently challenged the tenability of this programme. Their arguments purport to show that EpDT encourages obviously epistemically (...) irrational behavior. We develop firmer conceptual foundations for EpDT. First, we detail a theory of praxic and epistemic good. Then we show that, in light of their very different good-making features, EpDT will evaluate epistemic states and epistemic acts according to different criteria. So, in general, rational preference over states and acts won’t agree. Finally, we argue that based on direction-of-fit considerations, it’s preferences over the former that matter for normative epistemology, and that EpDT, properly spelt out, arrives at the correct verdicts in a range of putative problem cases. (shrink)

This book is a unique introductory overview of decision theory. It is completely non-technical, without a single formula in the book. Written in a crisp and clear style it succinctly covers the full range of philosophical issues of rationality and decision theory, including game theory, social choice theory, prisoner's dilemma and much else. The book aims to expand the scope and enrich the foundations of decision theory. By addressing such issues as (...) ambivalence, inner conflict, and the constraints imposed upon us by our attachments to others, Frederic Schick reveals that our thinking is often more subtle than standard theories of rationality allow. Only a theory that respects that subtlety can illumine what is otherwise puzzling. The book contains many examples drawn from history and literature dealing with subjects such as love, war, friendship, and crime. (shrink)

This book, first published in 1997, is an introductory overview of decision theory. It is completely non-technical, without a single formula in the book. Written in a crisp and clear style it succinctly covers the full range of philosophical issues of rationality and decision theory, including game theory, social choice theory, prisoner's dilemma and much else. The book aims to expand the scope and enrich the foundations of decision theory. By addressing (...) such issues as ambivalence, inner conflict, and the constraints imposed upon us by our attachments to others, Frederic Schick reveals that our thinking is often more subtle than standard theories of rationality allow. Only a theory that respects that subtlety can illumine what is otherwise puzzling. The book contains many examples drawn from history and literature dealing with subjects such as love, war, friendship, and crime. (shrink)

This book makes a significant contribution to the standard decision theory, that is, the theory of choice built around the principle of maximizing expected utility, both to its causal version and to the more traditional noncausal approach. The author’s success in clarifying the foundations of the standard decision theory in general, and causal decision theory in particular, also makes the book uniquely suitable for a person whose research in philosophy has led her (...) to want to learn about contemporary decision theory. The book presupposes some mathematical sophistication, and it contains more philosophical and mathematical argumentation per page than may be suitable for an undergraduate level course; but it stands out as an ideal textbook for a graduate-level course focused on the foundations of the standard decision theory. (shrink)

These two books jointly constitute volume 13 of the University of Western Ontario Series in the Philosophy of Science and consist of papers resulting from a workshop held at that university in the spring of 1975. Contributors to the first volume include such notables as Richard C. Jeffrey, Isaac Levi, and R. Duncan Luce. As an introduction to the papers, the editors’ preface is a statement of the goals of the original conference distributed to the invited participants. Twelve of the (...) eighteen papers in the first volume, and five out of nine in the second, deal with technical topics in decision theory and thus call for consideration by experts. This is so even though decision theory is broadly conceived by the editors to include the theory of games, of rational acceptance or rational belief, of value dynamics, and of individual decision-making. One of their main aims is "to explore the view that the concept of rationality [derivable from game theory] has both explanatory and normative force, that both dimensions of this concept can be theoretically integrated, that the explanatory force has far-reaching applications in all social scientific disciplines, and that the normative theories must become empirically controlled by the results of the explanatory theory". (shrink)

I apply some of the lessons from quantum theory, in particular from Bell’s theorem, to a debate on the foundations of decision theory and causation. By tracing a formal analogy between the basic assumptions of causal decision theory (CDT)—which was developed partly in response to Newcomb’s problem— and those of a local hidden variable theory in the context of quantum mechanics, I show that an agent who acts according to CDT and gives any (...) nonzero credence to some possible causal interpretations underlying quantum phenomena should bet against quantum mechanics in some feasible game scenarios involving entangled systems, no matter what evidence they acquire. As a consequence, either the most accepted version of decision theory is wrong, or it provides a practical distinction, in terms of the prescribed behaviour of rational agents, between some metaphysical hypotheses regarding the causal structure underlying quantum mechanics. (shrink)

Several philosophers have proposed Knowledge-Based Decision Theories (KDTs)—theories that require agents to maximize expected utility as yielded by utility and probability functions that depend on the agent’s knowledge. Proponents of KDTs argue that such theories are motivated by Knowledge-Reasons norms that require agents to act only on reasons that they know. However, no formal derivation of KDTs from Knowledge-Reasons norms has been suggested, and it is not clear how such norms justify the particular ways in which KDTs relate knowledge (...) and rational action. In this paper, I suggest a new axiomatic method for justifying KDTs and providing them with stronger normative foundations. I argue that such theories may be derived from constraints on the relation between knowledge and preference, and that these constraints may be evaluated relative to intuitions regarding practical reasoning. To demonstrate this, I offer a representation theorem for a KDT proposed by Hawthorne and Stanley (2008) and briefly evaluate it through its underlying axioms. -/- In section 1, I present knowledge-based decision theories generally and the versions of such theories suggested in the literature. In section 2, I argue that KDTs and theories of practical reasoning conjoined with Knowledge-Reasons norms generate constraints on the same relation—the relation between knowledge and preference. In section 3, I present a formal framework in which constraints on this relation may be expressed and from which KDTs may be derived. In section 4, I present a representation theorem for a specific KDT. In section 5, I briefly evaluate the axioms of the theory, and in section 6, I conclude. (shrink)

Decision-theoretic planning is normally based on the assumption that plans can be compared by comparing their expected-values, and the objective is to find an optimal plan. This is typically defended by reference to classical decision theory. However, classical decision theory is actually incompatible with this “simple plan-based decision theory”. A defense of plan-based decision theory must begin by showing that classical decision theory is incorrect insofar as the two theories (...) conflict, so this paper begins by raising objections to classical decision theory. First, there is a discussion of the considerations arising out of the Newcomb problem that have given rise to causal decision theory. Next, counterexamples are constructed for classical decision theory turning on the fact that an agent may be unable to perform an action, and may even be unable to try to perform an action. A proposal is made for how to repair classical decision theory in light of these counterexamples. But then turning to the concept of an “alternative” that is presupposed by classical decision theory, it is argued that actions must often be chosen in groups rather than individually, i.e., the objects of rational choice are plans. It is argued that optimality cannot be defined for plans, and even if it could be, it would not be reasonable to require rational agents to find optimal plans. So simple plan-based decision theory must also be rejected. An alternative called “locally global planning” is proposed as a replacement for both classical decision theory and simple plan-based decision theory. (shrink)

You are given a choice between two envelopes. You are told, reliably, that each envelope has some money in it—some whole number of dollars, say—and that one envelope contains twice as much money as the other. You don’t know which has the higher amount and which has the lower. You choose one, but are given the opportunity to switch to the other. Here is an argument that it is rationally preferable to switch: Let x be the quantity of money in (...) your chosen envelope. Then the quantity in the other is either 1/2x or 2x, and these possibilities are equally likely. So the expected utility of switching is 1/2(1/2x) + 1/2(2x) = 1.25x, whereas that for sticking is only x. So it is rationally preferable to switch. There is clearly something wrong with this argument. For one thing, it is obvious that neither choice is rationally preferable to the other: it’s a tossup. For another, if you switched on the basis of this reasoning, then the same argument could immediately be given for switching back; and so on, indefinitely. For another, there is a parallel argument for the rational preferability of sticking, in terms of the quantity y in the other envelope. But the problem is to provide an adequate account of how the argument goes wrong. This is the two envelope paradox. In an earlier paper Horgan 2000) I offered a diagnosis of the paradox. I argued that the flaw in the argument is considerably more subtle and interesting than is usually believed, and that an adequate diagnosis reveals important morals about both probability and the foundations of decision theory. One moral is that there is a kind of expected utility, not previously noticed as far as I know, that I call nonstandard expected utility. I proposed a general normative principle governing the proper application of nonstandard expected utility in rational decisionmaking. But this principle is inadequate in several respects, some of which I acknowledged in note added in press and some of which I have meanwhile discovered.. (shrink)

This volume is a collects papers originally presented at the 7th Conference on Logic and the Foundations of Game and Decision Theory (LOFT), held at the University of Liverpool in July 2006. LOFT is a key venue for presenting research at the intersection of logic, economics, and computer science, and this collection gives a lively and wide-ranging view of an exciting and rapidly growing area.

Efficient thinking is the foundation of efficient operation. The correct definition of concepts, especially the basic ones for a given field, in order to reach the truth, is a condition for the development of science and its social utility. The Petrażycki’s research methodology of law is a thoroughly modern method, as it enables effective examination of the accuracy of contemporary legal theories created after Petrażycki’s input. A model contemporary theory susceptible to an examination through the research methodology of law (...) by Petrażycki is the normative theory of legal rules and non-legal standards by Dworkin. For this purpose some falsifications will be subject, i.e. selected ad hoc among many others, two important theories of normative law theory Dworkin. The first one is the thesis classifying legal norms into two groups of norms, namely legal rules and non-legal standards. The second one is a thesis about the existence of who are capable of discovering and issuing lawful and, at the same time, fair court decisions, which are also the only ones for resolving particular court disputes. Unfortunately, owing to the seemingly cognitive research methodology of Petrażycki, both Dworkin’s deformed division of legal norms as well as Dworkin’s Hercules judges - cannot stand the test of authenticity. Due to the Petrażycki’s methodology, the legal-normative theory of Dworkin does not lose an innovative outlook on the existence of social norms, which are being discovered by judges in the jurisprudence, indifferently to the doubts over their proper classification. Moreover, Dworkin’s theory is placed between naive theories, regardless of whether they are considered realistically naive theories or nihilistically naive theories A few random reflections on the well-known work of Dworkin with the help of Petrażycki’s methodology serve to provide a new perspective on the contemporary legal normativity. (shrink)

The primary aim of this paper is the presentation of a foundation for causal decision theory. This is worth doing because causal decision theory (CDT) is philosophically the most adequate rational decision theory now available. I will not defend that claim here by elaborate comparison of the theory with all its competitors, but by providing the foundation. This puts the theory on an equal footing with competitors for which foundations have already (...) been given. It turns out that it will also produce a reply to the most serious objections made so far against CDT and against the particular version of CDT I will defend. (shrink)

Naive versions of decision theory take probabilities and utilities as primitive and use expected value to give norms on rational decision. However, standard decision theory takes rational preference as primitive and uses it to construct probability and utility. This paper shows how to justify a version of the naive theory, by taking dominance as the most basic normatively required preference relation, and then extending it by various conditions under which agents should be indifferent between (...) acts. The resulting theory can make all the decisions of classical expected utility theory, plus more in cases where expected utilities are infinite or undefined. Although the theory requires similarly strong assumptions to classical expected utility theory, versions of the theory can be developed with slightly weaker assumptions, without having to prove a new representation theorem for the weaker theory. This alternate foundation is particularly useful if probability is prior to preference, as suggested by the recent program to base probabilism on accuracy and alethic considerations rather than pragmatic ones. (shrink)

Many criticisms have been made of optimization theory (Laville, 1999a). These objections may be explained by the fact that human rationality is bounded – that decisions are constrained by cognitive limitations (Simon, 1982). In the present paper, I will show that if rationality is bounded, then we must study the processes of decision. My thesis is that cognitive limitations lead to procedural rationality. Although this assertion has already been sustained implicitly by Simon (1959) and explicitly by Mongin (1986), (...) it has not been argued in sufficient depth. (shrink)

An introduction to the special issue on epistemic logic and the foundations of game theory edited by Michael Bacharach and Philippe Mongin. Contributors are Michael Bacharach, Robert Stalnaker, Salvatore Modica and Aldo Rustichini, Luc Lismont and Philippe Mongin, and Hyun-Song Shin and Timothy Williamson.

The essays in this volume, first published in 1986, examine the philosophical foundations of social choice theory. This field, a modern and sophisticated outgrowth of welfare economics, is best known for a series of impossibility theorems, of which the first and most crucial was proved by Kenneth Arrow in 1950. That has often been taken to show the impossibility of democracy as a procedure for making collective decisions. However, this interpretation is challenged by several of the contributors here. (...) Other central issues discussed in the volume include the possibility of making interpersonal comparisons of utility, the question of whether all preferences are equally to be valued, and the normative individualism underlying the theoretical tradition. Criticisms of social choice theory are advanced and suggestions for alternative approaches are developed. (shrink)

The essays in this volume, first published in 1986, examine the philosophical foundations of social choice theory. This field, a modern and sophisticated outgrowth of welfare economics, is best known for a series of impossibility theorems, of which the first and most crucial was proved by Kenneth Arrow in 1950. That has often been taken to show the impossibility of democracy as a procedure for making collective decisions. However, this interpretation is challenged by several of the contributors here. (...) Other central issues discussed in the volume include the possibility of making interpersonal comparisons of utility, the question of whether all preferences are equally to be valued, and the normative individualism underlying the theoretical tradition. Criticisms of social choice theory are advanced and suggestions for alternative approaches are developed. (shrink)

This up-to-date introduction to decision theory offers comprehensive and accessible discussions of decision-making under ignorance and risk, the foundations of utility theory, the debate over subjective and objective probability, Bayesianism, causal decision theory, game theory, and social choice theory. No mathematical skills are assumed, and all concepts and results are explained in non-technical and intuitive as well as more formal ways. There are over 100 exercises with solutions, and a glossary of (...) key terms and concepts. An emphasis on foundational aspects of normative decision theory (rather than descriptive decision theory) makes the book particularly useful for philosophy students, but it will appeal to readers in a range of disciplines including economics, psychology, political science and computer science. • Has over 100 end of chapter review questions and exercises with solutions • Includes a chapter on how to draw a decision matrix • Explains the link between individual decision making, game theory and social choice theory Contents Preface; 1. Introduction; 2. The decision matrix; 3. Decisions under ignorance; 4. Decisions under risk; 5. Utility; 6. The mathematics of probability; 7. The philosophy of probability; 8. Why should we accept the preference axioms; 9. Causal vs. evidential decision theory; 10. Bayesian vs. non-Bayesian decision theory; 11. Game theory I: basic concepts and zero sum games; 12. Game theory II: nonzero sum and co-operative games; 13. Social choice theory; 14. Overview of descriptive decision theory; Appendix A. Glossary; Appendix B. Proof of the von Neumann-Morgenstern theorem; Further reading; Index. (shrink)

In ”Decision Theory and Epistemology,” Mark Kaplan finds it characteristic of orthodox Bayesians to hold that for each person and each hypothesis she comprehends, there is a precise degree of confidence that person has in the truth of that proposition, and no person can be counted as rational unless the degree of confidence assignment she thus harbors satisfies the axioms of the probability calculus. Kaplan's purpose is twofold. First, he aims to show that, as powerful as many criticisms (...) are against orthodox Bayesianism, there is a credible kind of Bayesianism. Without appeal to idealization or false precision, it offers a substantive account of how the probability calculus constrains the opinions of actual persons and of how this account impinges on traditional epistemological concerns. Second, he aims to show how this Bayesianism finds a foundation in considerations concerning rational preference. (shrink)

This book details the underlining philosophical approaches to ethical theories and how these can be used to structure an approach to day-to-day ethical issues, and thereby resolve them. It provides an understanding of the ethical theories which underpin decisions in health care by first laying the foundation with a philosophical framework and then going on to develop this into an examination of contemporary health care dilemmas and professional issues. Not available in the U.S.

Recent work has formally linked the traditional axiomatisation of incomplete preferences à la Anscombe-Aumann with the theory of desirability developed in the context of imprecise probability, by showing in particular that they are the very same theory. The equivalence has been established under the constraint that the set of possible prizes is finite. In this paper, we relax such a constraint, thus de facto creating one of the most general theories of rationality and decision making available today. (...) We provide the theory with a sound interpretation and with basic notions, and results, for the separation of beliefs and values, and for the case of complete preferences. Moreover, we discuss the role of conglomerability for the presented theory, arguing that it should be a rationality requirement under very broad conditions. (shrink)

Evidential Decision Theory is a radical theory of rational decision-making. It recommends that instead of thinking about what your decisions *cause*, you should think about what they *reveal*. This Element explains in simple terms why thinking in this way makes a big difference, and argues that doing so makes for *better* decisions. An appendix gives an intuitive explanation of the measure-theoretic foundations of Evidential Decision Theory.

Resumen: En el presente artículo se realiza una comparación crítica de dos enfoques sobre los fundamentos de la teoría microeconómica del comportamiento del consumidor, a saber: el enfoque utilitarista y el de la preferencia revelada. Se lleva a cabo un análisis de la preferencia revelada en el contexto de la introducción de restricciones a la función de elección en la teoría de la decisión. Se evalúan sus ventajas y limitaciones en contraste con el problema de la utilidad propio del punto (...) de vista subjetivista de la teoría utilitarista. Y se confronta la capacidad explicativa de los distintos modelos de agencia racional sobre las bases de las curvas de demanda. Asimismo, se desarrolla una crítica formal al método de la preferencia revelada en entornos estratégicos de decisión.: This article makes a critical comparison of two approaches to the foundations of the microeconomic theory of consumer behavior, namely: the utilitarian approach and that of the revealed preference theory. An analysis of revealed preference is carried out in the context of introducing restrictions to the choice function in decision theory. Its advantages and limitations are evaluated in contrast to the utility problem proper to the subjectivist point of view of utilitarian theory. And the explanatory capacity of the different models of rational agency is confronted on the bases of the demand curves. Furthermore, a formal critique of the revealed preference method is developed in strategic decision-making environments. (shrink)

We’re often unsure what morality requires, but we need to act anyway. There is a growing philosophical literature on how to navigate moral uncertainty. But much of it asks how to rationally pursue the goal of acting morally, using decision-theoretic models to address that question. I argue that using these popular approaches leaves some central and pressing questions about moral uncertainty unaddressed. To help us make sense of experiences of moral uncertainty, we should shift away from focusing on what (...) it’s rational to do when facing moral uncertainty, and instead look directly at what it’s moral to do about moral uncertainty—for example, how risk averse we morally ought to be, or which personal sacrifices we’re morally obligated to make in order to reduce our risk of moral wrongdoing. And orthodox, expectation-maximizing, decision-theoretic models aren’t well-suited to this task—in part because they presuppose the answers to some important moral questions. For example, if approaching moral uncertainty in a moral way requires us to “maximize expected moral rightness,” that’s, itself, a contentious claim about the demands of morality—one that requires significant moral argument, and that I ultimately suggest is mistaken. Of course, it’s possible to opt, instead, for a variety of alternative decision-theoretic models. But, in order to choose between proposed decision-theoretic models, and select one that is well-suited to handling these cases, we first would need to settle more foundational, moral questions—about, for example, what we should be willing to give up in order to reduce the risk that we’re acting wrongly. Decision theory may be able to formalize the conclusions of these deliberations, but it is not a substitute for them, and it won’t be able to settle the right answers in advance. For now, when we discuss moral uncertainty, we need to wade directly into moral debate, without the aid of decision theory’s formalism. (shrink)

As stochastic independence is essential to the mathematical development of probability theory, it seems that any foundational work on probability should be able to account for this property. Bayesian decision theory appears to be wanting in this respect. Savage’s postulates on preferences under uncertainty entail a subjective expected utility representation, and this asserts only the existence and uniqueness of a subjective probability measure, regardless of its properties. What is missing is a preference condition corresponding to stochastic independence. (...) To fill this significant gap, the article axiomatizes Bayesian decision theory afresh and proves several representation theorems in this novel framework. (shrink)

A study of physicians and medical students was conducted to determine the various philosophical positions they hold with respect to ethical decision-making in medicine and their epistemological presuppositions in relationship to the subjective-objective controversy in value theory. The study revealed that most physicians and medical students tend to be objectivists in value theory, i.e., believe that value judgements are knowledge claims capable of being true or false and are expressions of moral requirements and normative imperatives emanating from (...) an external value structure or moral order in the world, but that most physicians and medical students are inconsistent in the philosophical foundations of their medical ethical decision-making, i.e., in decision-making regarding values they tend to hold beliefs which are incompatible with other beliefs they hold about values. The study also revealed that most physicians and medical students think more emphasis should be placed upon medical ethics in medical education. (shrink)

A study of nurses and nursing students was conducted to determine the various philosophical positions they hold with respect to ethical decision-making in nursing and their relationship to the subjective-objective controversy in value theory. The study revealed that most nurses and nursing students tend to be subjectivists in value theory, i.e., believe that value judgments are purely personal, private expressions of one's own opinion or inner-feelings and not believe that value judgments are knowledge claims capable of being (...) true or false and therefore not expressions of moral requirements and normative imperatives emanating from an external value structure or moral order in the world. In addition, the study revealed that most nurses and nursing students are inconsistent in the philosophical foundations of their ethical decision-making, i.e., in decision-making regarding values they tend to hold beliefs which are incompatible with other beliefs they hold about values. (shrink)

A study of clinical medical ethicists was conducted to determine the various philosophical positions they hold with respect to ethical decision making in medicine and their various positions' relationship to the subjective-objective controversy in value theory. The study consisted of analyzing and interpreting data gathered from questionnaires from 52 clinical medical ethicists at 28 major health care centers in the United States. The study revealed that most clinical medical ethicists tend to be objectivists in value theory, i.e., (...) believe that value judgments are knowledge claims capable of being true or false and therefore expressions of moral requirements and normative imperatives emanating from an external value structure or moral order in the world. In addition, the study revealed that most clinical medical ethicists are consistent in the philosophical foundations of their ethical decision making, i.e., in decision making regarding values they tend not to hold beliefs which are incompatible with other beliefs they hold about values. (shrink)

This paper provides new foundations for Bayesian Decision Theory based on a representation theorem for preferences defined on a set of prospects containing both factual and conditional possibilities. This use of a rich set of prospects not only provides a framework within which the main theoretical claims of Savage, Ramsey, Jeffrey and others can be stated and compared, but also allows for the postulation of an extended Bayesian model of rational belief and desire from which they can (...) be derived as special cases. The main theorem of the paper establishes the existence of a such a Bayesian representation of preferences over conditional prospects, i.e. the existence of a pair of real-valued functions respectively measuring the agent’s degrees of belief and desire and which satisfy the postulated rationality conditions on partial belief and desire. The representation of partial belief is shown to be unique and that of partial desire, unique up to a linear transformation. (shrink)

“Since today is Saturday, the grocery store is open today and will be closed tomorrow; so let’s go today”. That is an example of everyday practical reasoning—reasoning directly with the propositions that one believes but may not be fully certain of. Everyday practical reasoning is one of our most familiar kinds of decisions but, unfortunately, some foundational questions about it are largely ignored in the standard decision theory: (Q1) What are the decision rules in everyday practical reasoning (...) that connect qualitative belief and desire to preference over acts? (Q2) What sort of logic should govern qualitative beliefs in everyday practical reasoning, and to what extent is that logic necessary for the purposes of qualitative decisions? (Q3) What kinds of qualitative decisions are always representable as results of everyday practical reasoning? (Q4) Under what circumstances do the results of everyday practical reasoning agree with the Bayesian ideal of expected utility maximization? This paper proposes a rigorous decision theory for answering all of those questions, which is developed in parallel to Savage’s (1954) foundation of expected utility maximization. In light of a new representation result, everyday practical reasoning provides a sound and complete method for a very wide class of qualitative decisions; and, to that end, qualitative beliefs must be allowed to be closed under classical logic plus a well-known nonmonotonic logic—the so-called system ℙ. (shrink)