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The Mathematics of Preference, Choice and Order
Peter Fishburn has had a splendidly productive career that led to path-breaking c- tributions in a remarkable variety of areas of research. His contributions have been published in a vast literature, ranging through journals of social choice and welfare, decision theory, operations research, economic theory, political science, mathema- cal psychology, and discrete mathematics. This work was done both on an individual basis and with a very long list of coauthors. The contributions that Fishburn made can roughly be divided into three major topical areas, and contributions to each of these areas are identi?ed by sections of this monograph. Section 1 deals with topics that are included in the general areas of utility, preference, individual choice, subjective probability, and measurement t- ory. Section 2 covers social choice theory, voting models, and social welfare. S- tion 3 deals with more purely mathematical topics that are related to combinatorics, graph theory, and ordered sets. The common theme of Fishburn’s contributions to all of these areas is his ability to bring rigorous mathematical analysis to bear on a wide range of dif?cult problems.
Multiple Criteria Decision Analysis: State of the Art Surveys
Multiple Criteria Decision Analysis: State of the Art Surveys provides survey articles and references of the seminal or state-of-the-art research on MCDA. The material covered ranges from the foundations of MCDA, over various MCDA methodologies (outranking methods, multiattribute utility and value theories, non-classical approaches) to multiobjective mathematical programming, MCDA applications, and software. This vast amount of material is organized in 8 parts, with a total of 25 chapters. More than 2000 references are listed.
The Foundations of Expected Utility
This book offers a unified treatment of my research in the foundations of expected utility theory from around 1965 to 1980. While parts are new, the presentation draws heavily on published articles and a few chapters in my 1970 monograph on utility theory. The diverse notations and styles of the sources have of course been reconciled here, and their topics arranged in a logical sequence. The two parts of the book take their respective cues from the von Neumann-Morgenstern axiomatization of preferences between risky options and from Savage's foundational treatment of decision making under uncertainty. Both parts are studies in the axiomatics of preferences for decision situations and in numer...
Multiperson Decision Making Models Using Fuzzy Sets and Possibility Theory
Decision making is certainly a very crucial component of many human activities. It is, therefore, not surprising that models of decisions play a very important role not only in decision theory but also in areas such as operations Research, Management science, social Psychology etc . . The basic model of a decision in classical normative decision theory has very little in common with real decision making: It portrays a decision as a clear-cut act of choice, performed by one individual decision maker and in which states of nature, possible actions, results and preferences are well and crisply defined. The only compo nent in which uncertainty is permitted is the occurence of the different state...
Handbook of Social Choice and Welfare
The Handbook of Social Choice and Welfare presents, in two volumes, essays on past and on-going work in social choice theory and welfare economics. The first volume consists of four parts. In Part 1 (Arrovian Impossibility Theorems), various aspects of Arrovian general impossibility theorems, illustrated by the simple majority cycle first identified by Condorcet, are expounded and evaluated. It also provides a critical survey of the work on different escape routes from impossibility results of this kind. In Part 2 (Voting Schemes and Mechanisms), the operation and performance of voting schemes and cost-sharing mechanisms are examined axiomatically, and some aspects of the modern theory of in...
Handbook of Game Theory with Economic Applications
This is the second of three volumes surveying the state of the art in Game Theory and its applications to many and varied fields, in particular to economics. The chapters in the present volume are contributed by outstanding authorities, and provide comprehensive coverage and precise statements of the main results in each area. The applications include empirical evidence. The following topics are covered: communication and correlated equilibria, coalitional games and coalition structures, utility and subjective probability, common knowledge, bargaining, zero-sum games, differential games, and applications of game theory to signalling, moral hazard, search, evolutionary biology, international relations, voting procedures, social choice, public economics, politics, and cost allocation. This handbook will be of interest to scholars in economics, political science, psychology, mathematics and biology. For more information on the Handbooks in Economics series, please see our home page on http://www.elsevier.nl/locate/hes
Graphs and Order
This volume contains the accounts of the principal survey papers presented at GRAPHS and ORDER, held at Banff, Canada from May 18 to May 31, 1984. This conference was supported by grants from the N.A.T.O. Advanced Study Institute programme, the Natural Sciences and Engineering Research Council of Canada and the University of Calgary. We are grateful for all of this considerable support. Almost fifty years ago the first Symposium on Lattice Theory was held in Charlottesville, U.S.A. On that occasion the principal lectures were delivered by G. Birkhoff, O. Ore and M.H. Stone. In those days the theory of ordered sets was thought to be a vigorous relative of group theory. Some twenty-five years ago the Symposium on Partially Ordered Sets and Lattice Theory was held in Monterey, U.S.A. Among the principal speakers at that meeting were R.P. Dilworth, B. Jonsson, A. Tarski and G. Birkhoff. Lattice theory had turned inward: it was concerned primarily with problems about lattices themselves. As a matter of fact the problems that were then posed have, by now, in many instances, been completely solved.
