With this treatise, an insightful exploration of the probabilistic connection between philosophy and the history of science, the famous economist breathed new life into studies of both disciplines. Originally published in 1921, this important mathematical work represented a significant contribution to the theory regarding the logical probability of propositions. Keynes effectively dismantled the classical theory of probability, launching what has since been termed the “logical-relationist” theory. In so doing, he explored the logical relationships between classifying a proposition as “highly probable” (...) and as a “justifiable induction.” Unabridged republication of the classic 1921 edition. (shrink)

An examination of topics involved in statistical reasoning with imprecise probabilities. The book discusses assessment and elicitation, extensions, envelopes and decisions, the importance of imprecision, conditional previsions and coherent statistical models.

"The best book available for non-mathematicians." — Contemporary Psychology. Superb nontechnical introduction to game theory and related disciplines, primarily as applied to the social sciences. Clear, comprehensive coverage of utility theory, 2-person zero-sum games, 2-person non-zero-sum games, n-person games, individual and group decision-making, much more. Appendixes. Bibliography. Graphs and figures.

Role of the entrepreneur in a distinct role of profit.

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

This book presents the definitive exposition of 'prospect theory', a compelling alternative to the classical utility theory of choice. Building on the 1982 volume, Judgement Under Uncertainty, this book brings together seminal papers on prospect theory from economists, decision theorists, and psychologists, including the work of the late Amos Tversky, whose contributions are collected here for the first time. While remaining within a rational choice framework, prospect theory delivers more accurate, empirically verified predictions in key test cases, as well as (...) helping to explain many complex, real-world puzzles. In this volume, it is brought to bear on phenomena as diverse as the principles of legal compensation, the equity premium puzzle in financial markets, and the number of hours that New York cab drivers choose to drive on rainy days. Theoretically elegant and empirically robust, this volume shows how prospect theory has matured into a new science of decision making. (shrink)

This is the classic work upon which modern-day game theory is based. What began as a modest proposal that a mathematician and an economist write a short paper together blossomed, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry (...) it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences. (shrink)

Bas C. van Fraassen presents an original exploration of how we represent the world.

This article described three heuristics that are employed in making judgements under uncertainty: representativeness, which is usually employed when people are asked to judge the probability that an object or event A belongs to class or process B; availability of instances or scenarios, which is often employed when people are asked to assess the frequency of a class or the plausibility of a particular development; and adjustment from an anchor, which is usually employed in numerical prediction when a relevant value (...) is available. These heuristics are highly economical and usually effective, but they lead to systematic and predictable errors. A better understanding of these heuristics and of the biases to which they lead could improve judgements and decisions in situations of uncertainty. (shrink)

It is a familiar argument that advocates accommodating the so-called paradoxes of decision theory by abandoning the “independence” postulate. After all, if we grant that choice reveals preference, the anomalous choice patterns of the Allais and Ellsberg problems violate postulate P2 of Savage's system. The strategy of making room for new preference patterns by relaxing independence is adopted in each of the following works: Samuelson, Kahneman and Tversky's “Prospect Theory”, Allais and Hagen, Fishburn, Chew and MacCrimmon, McClennen, and in closely (...) argued essays by Machina. (shrink)

We discuss several features of coherent choice functions—where the admissible options in a decision problem are exactly those that maximize expected utility for some probability/utility pair in fixed set S of probability/utility pairs. In this paper we consider, primarily, normal form decision problems under uncertainty—where only the probability component of S is indeterminate and utility for two privileged outcomes is determinate. Coherent choice distinguishes between each pair of sets of probabilities regardless the “shape” or “connectedness” of the sets of probabilities. (...) We axiomatize the theory of choice functions and show these axioms are necessary for coherence. The axioms are sufficient for coherence using a set of probability/almost-state-independent utility pairs. We give sufficient conditions when a choice function satisfying our axioms is represented by a set of probability/state-independent utility pairs with a common utility. (shrink)

This paper reorganizes and further develops the theory of partial meet contraction which was introduced in a classic paper by Alchourron, Gardenfors, and Makinson. Our purpose is threefold. First, we put the theory in a broader perspective by decomposing it into two layers which can respectively be treated by the general theory of choice and preference and elementary model theory. Second, we reprove the two main representation theorems of AGM and present two more representation results for the finite case that (...) "lie between" the former, thereby partially answering an open question of AGM. Our method of proof is uniform insofar as it uses only one form of "revealed preference", and it explains where and why the finiteness assumption is needed. Third, as an application, we explore the logic characterizing theory contractions in the finite case which are governed by the structure of simple and prioritized belief bases. (shrink)

This paper presents a formal characterization of a two stage decision rule. This characterization involves three conditions which, together, are satisfied by any choice function that can be represented as a two-tier choice function. And any choice function satisfying these three conditions can be represented as a two-tier choice function. The first condition identifies particular features of two-tier choice functions when they violate Property α. The other two conditions are essentially existence claims, required to ensure that the two tiers of (...) a choice function can be represented as (pseudo-) rationalizable choice functions. My aim is to offer a formal result that provides insight into the nature of two-tier decisions. The more we understand how a particular decision procedure operates, the more we should expect to predict its results accurately, and the more we should be able to understand the circumstances under which its use is (and is not) appropriate. (shrink)

This major work challenges some widely held positions in epistemology - those of Peirce and Popper on the one hand and those of Quine and Kuhn on the other.

Ellsberg (The Quarterly Journal of Economics 75, 643–669 (1961); Risk, Ambiguity and Decision, Garland Publishing (2001)) argued that uncertainty is not reducible to risk. At the center of Ellsberg’s argument lies a thought experiment that has come to be known as the three-color example. It has been observed that a significant number of sophisticated decision makers violate the requirements of subjective expected utility theory when they are confronted with Ellsberg’s three-color example. More generally, such decision makers are in conflict with (...) either the ordering assumption or the independence assumption of subjective expected utility theory. While a clear majority of the theoretical responses to these violations have advocated maintaining ordering while relaxing independence, a persistent minority has advocated abandoning the ordering assumption. The purpose of this paper is to consider a similar dilemma that exists within the context of multiattribute models, where it arises by considering indeterminacy in the weighting of attributes rather than indeterminacy in the determination of probabilities as in Ellsberg’s example. (shrink)

Ellsberg elaborates on "Risk, Ambiguity, and the Savage Axioms" and mounts a powerful challenge to the dominant theory of rational decision in this book.

Ellsberg elaborates on "Risk, Ambiguity, and the Savage Axioms" and mounts a powerful challenge to the dominant theory of rational decision in this book.

This important collection of essays is a synthesis of foundational studies in Bayesian decision theory and statistics. An overarching topic of the collection is understanding how the norms for Bayesian decision making should apply in settings with more than one rational decision maker and then tracing out some of the consequences of this turn for Bayesian statistics. There are four principal themes to the collection: cooperative, non-sequential decisions; the representation and measurement of 'partially ordered' preferences; non-cooperative, sequential decisions; and pooling (...) rules and Bayesian dynamics for sets of probabilities. The volume will be particularly valuable to philosophers concerned with decision theory, probability, and statistics, statisticians, mathematicians, and economists. (shrink)

An early, very preliminary edition of this book was circulated in 1962 under the title Set-theoretical Structures in Science. There are many reasons for maintaining that such structures play a role in the philosophy of science. Perhaps the best is that they provide the right setting for investigating problems of representation and invariance in any systematic part of science, past or present. Examples are easy to cite. Sophisticated analysis of the nature of representation in perception is to be found already (...) in Plato and Aristotle. One of the great intellectual triumphs of the nineteenth century was the mechanical explanation of such familiar concepts as temperature and pressure by their representation in terms of the motion of particles. A more disturbing change of viewpoint was the realization at the beginning of the twentieth century that the separate invariant properties of space and time must be replaced by the space-time invariants of Einstein's special relativity. Another example, the focus of the longest chapter in this book, is controversy extending over several centuries on the proper representation of probability. The six major positions on this question are critically examined. Topics covered in other chapters include an unusually detailed treatment of theoretical and experimental work on visual space, the two senses of invariance represented by weak and strong reversibility of causal processes, and the representation of hidden variables in quantum mechanics. The final chapter concentrates on different kinds of representations of language, concluding with some empirical results on brain-wave representations of words and sentences. (shrink)

This book presents Ariel Rubinstein's lecture notes for the first part of his well-known graduate course in microeconomics.

Ellsberg elaborates on "Risk, Ambiguity, and the Savage Axioms" and mounts a powerful challenge to the dominant theory of rational decision in this book.

Classic analysis of the subject and the development of personal probability; one of the greatest controversies in modern statistcal thought.

It is a commonplace that in making decisions agents often have to juggle competing values, and that no choice will maximise satisfaction of them all. However, the prevailing account of these cases assumes that there is always a single ranking of the agent's values, and therefore no unresolvable conflict between them. Isaac Levi denies this assumption, arguing that agents often must choose without having balanced their different values and that to be rational, an act does not have to be optimal, (...) only what Levi terms 'admissible'. This book explores the consequences of denying the assumption and develops a general approach to decision-making under unresolved conflict. Professor Levi discusses conflicts of value in several domains - those arising in moral dilemmas, the drawing of scientific inferences, decisions taken under uncertainty, and in social choice. In each of these he adapts his theoretical framework, showing how conflict may often be reduced though not always altogether eliminated. (shrink)

The thirty-five chapters in this book describe various judgmental heuristics and the biases they produce, not only in laboratory experiments but in important...

The following values have no corresponding Zotero field: PB - JSTOR.

We contrast three decision rules that extend Expected Utility to contexts where a convex set of probabilities is used to depict uncertainty: Γ-Maximin, Maximality, and E-admissibility. The rules extend Expected Utility theory as they require that an option is inadmissible if there is another that carries greater expected utility for each probability in a (closed) convex set. If the convex set is a singleton, then each rule agrees with maximizing expected utility. We show that, even when the option set is (...) convex, this pairwise comparison between acts may fail to identify those acts which are Bayes for some probability in a convex set that is not closed. This limitation affects two of the decision rules but not E-admissibility, which is not a pairwise decision rule. E-admissibility can be used to distinguish between two convex sets of probabilities that intersect all the same supporting hyperplanes. (shrink)