The Mathematics of Preference, Choice and Order
The Mathematics of Preference, Choice and Order

Author: Steven Brams

Publisher: Springer Science & Business Media

Published: 2009-02-11

Total Pages: 412

ISBN-13: 3540791280

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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.

The Mathematics of Preference, Choice and Order
The Mathematics of Preference, Choice and Order

Author: Steven Brams

Publisher: Springer

Published: 2009-08-29

Total Pages: 420

ISBN-13: 9783540871910

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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.

Utility Maximization, Choice and Preference
Utility Maximization, Choice and Preference

Author: Fuad Aleskerov

Publisher: Springer Science & Business Media

Published: 2013-04-18

Total Pages: 226

ISBN-13: 3662049929

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The utility maximization paradigm forms the basis of many economic, psychological, cognitive and behavioral models. However, numerous examples have revealed the deficiencies of the concept. This book helps to overcome those deficiencies by taking into account insensitivity of measurement threshold and context of choice. The second edition has been updated to include the most recent developments and a new chapter on classic and new results for infinite sets.

The Theory of Social Choice
The Theory of Social Choice

Author: Peter C. Fishburn

Publisher: Princeton University Press

Published: 2015-03-08

Total Pages: 277

ISBN-13: 1400868335

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One fundamental premise of democratic theory is that social policy, group choice, or collective action should be based on the preferences of the individuals in the society, group, or collective. Using the tools of formal mathematical analysis, Peter C. Fishburn explores and defines the conditions for social choice and methods for synthesizing individuals' preferences. This study is unique in its emphasis on social choice functions, the general position that individual indifference may not be transitive, and the use of certain mathematics such as linear algebra. The text is divided into three main parts: social choice between two alternatives, which examines a variety of majority-like functions; simple majority social choice, which focuses on social choice among many alternatives when two-element feasible subset choices are based on simple majority; and a general study of aspects and types of social choice functions for many alternatives. Originally published in 1973. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Consistency, Choice, and Rationality
Consistency, Choice, and Rationality

Author: Walter Bossert

Publisher: Harvard University Press

Published: 2010-10-29

Total Pages: 231

ISBN-13: 0674059212

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In Consistency, Choice, and Rationality, economic theorists Walter Bossert and Kotaro Suzumura present a thorough mathematical treatment of Suzumura consistency, an alternative to established coherence properties such as transitivity, quasi-transitivity, or acyclicity. Applications in individual and social choice theory, fields important not only to economics but also to philosophy and political science, are discussed. Specifically, the authors explore topics such as rational choice and revealed preference theory, and collective decision making in an atemporal framework as well as in an intergenerational setting.

Notes On The Theory Of Choice
Notes On The Theory Of Choice

Author: David Kreps

Publisher: Routledge

Published: 2018-05-04

Total Pages: 228

ISBN-13: 0429967160

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In this book, Professor Kreps presents a first course on the basic models of choice theory that underlie much of economic theory. This course, taught for several years at the Graduate School of Business, Stanford University, gives the student an introduction to the axiomatic method of economic analysis, without placing too heavy a demand on mathematical sophistication.The course begins with the basics of choice and revealed preference theory and then discusses numerical representations of ordinal preference. Models with uncertainty come next: First is von Neumann?Morgenstern utility, and then choice under uncertainty with subjective uncertainty, using the formulation of Anscombe and Aumann, and then sketching the development of Savage's classic theory. Finally, the course delves into a number of special topics, including de Finetti's theorem, modeling choice on a part of a larger problem, dynamic choice, and the empirical evidence against the classic models.

Mathematics of Social Choice
Mathematics of Social Choice

Author: Christoph Borgers

Publisher: SIAM

Published: 2010-01-01

Total Pages: 233

ISBN-13: 0898717620

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Mathematics of Social Choice is a fun and accessible book that looks at the choices made by groups of people with different preferences, needs, and interests. Divided into three parts, the text first examines voting methods for selecting or ranking candidates. A brief second part addresses compensation problems wherein an indivisible item must be assigned to one of several people who are equally entitled to ownership of the item, with monetary compensation paid to the others. The third part discusses the problem of sharing a divisible resource among several people. Mathematics of Social Choice can be used by undergraduates studying mathematics and students whose only mathematical background is elementary algebra. More advanced material can be skipped without any loss of continuity. The book can also serve as an easy introduction to topics such as the Gibbard-Satterthwaite theorem, Arrow's theorem, and fair division for readers with more mathematical background.

Representations of Preferences Orderings
Representations of Preferences Orderings

Author: Douglas S. Bridges

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 171

ISBN-13: 3642514952

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This monograph is devoted to a rigorous presentation of results about the representation of preference orderings by real-valued order isomorphisms ("utility functions"). The authors have gathered together, from sources scattered throughout a wide range of the literature of mathematics and economics, the most significant theorems and methods in their field. The book will be a valuable resource for theoretical economists, mathematicians, and all interested in partial orders and their representation. It could also be used as the text for an advanced graduate course in mathematical economics.

Mathematical Methods in Economics and Social Choice
Mathematical Methods in Economics and Social Choice

Author: Norman Schofield

Publisher: Springer Science & Business Media

Published: 2013-10-11

Total Pages: 269

ISBN-13: 3642398189

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In recent years, the usual optimization techniques, which have proved so useful in microeconomic theory, have been extended to incorporate more powerful topological and differential methods, and these methods have led to new results on the qualitative behavior of general economic and political systems. These developments have necessarily resulted in an increase in the degree of formalism in the publications in the academic journals. This formalism can often deter graduate students. The progression of ideas presented in this book will familiarize the student with the geometric concepts underlying these topological methods, and, as a result, make mathematical economics, general equilibrium theory, and social choice theory more accessible.

Preference Economics
Preference Economics

Author: Fouad Sabry

Publisher: One Billion Knowledgeable

Published: 2024-01-07

Total Pages: 245

ISBN-13:

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What is Preference Economics In economics and other social sciences, the term "preference" refers to the order in which an agent ranks options based on their relative usefulness, often with the goal of finding the "optimal choice." Generally speaking, preferences are assessments that are concerned with considerations of value and are often related to practical reasoning. A person's preferences are not influenced by factors like as the costs of the commodities, their availability, or their own personal income; rather, they are decided solely by the individual's tastes, requirements, and other factors. Classical economics, on the other hand, relies on the assumption that individuals behave in their own best (rational) interest. Taking this scenario into consideration, logic would require that when an individual is presented with a choice, they will choose the alternative that optimizes their own self-interest. Preferences, on the other hand, are not necessarily transferable. This is due to the fact that actual people are not always rational, and also because preferences might form cycles under some circumstances, in which case there is no clearly defined best decision. The Efron dice are a good illustration of this. How you will benefit (I) Insights, and validations about the following topics: Chapter 1: Preference (economics) Chapter 2: Utility Chapter 3: Indifference curve Chapter 4: Arrow's impossibility theorem Chapter 5: Social welfare function Chapter 6: Consumer choice Chapter 7: Budget constraint Chapter 8: Marginal rate of substitution Chapter 9: Loss function Chapter 10: Expected utility hypothesis Chapter 11: Utility maximization problem Chapter 12: Ordinal utility Chapter 13: Cardinal utility Chapter 14: Revealed preference Chapter 15: Sonnenschein-Mantel-Debreu theorem Chapter 16: Quasilinear utility Chapter 17: Utility-possibility frontier Chapter 18: Von Neumann-Morgenstern utility theorem Chapter 19: Preference Chapter 20: Debreu's representation theorems Chapter 21: Overtaking criterion (II) Answering the public top questions about preference economics. (III) Real world examples for the usage of preference economics in many fields. Who this book is for Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of preference economics.