Mathematics of Social Choice

An accessible exposition of social choices such as selecting a winning competitor, or dividing up resources.

Author: Christoph Borgers

Publisher: SIAM

ISBN: 0898716950

Category: Political Science

Page: 245

View: 797

An accessible exposition of social choices such as selecting a winning competitor, or dividing up resources.

Social Choice and the Mathematics of Manipulation

A mathematical look at why it is impossible to devise a completely unmanipulable voting system, first published in 2005.

Author: Alan D. Taylor

Publisher: Cambridge University Press

ISBN: 9780521008839

Category: Mathematics

Page: 176

View: 737

A mathematical look at why it is impossible to devise a completely unmanipulable voting system, first published in 2005.


Mathematical Methods in Economics and Social Choice

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 ...

Author: Norman Schofield

Publisher: Springer Science & Business Media

ISBN: 3642398189

Category: Business & Economics

Page: 262

View: 833

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.

Application of Fuzzy Logic to Social Choice Theory

Filling this gap, Application of Fuzzy Logic to Social Choice Theory provides a comprehensive study of fuzzy social choice theory.The book explains the concept of a fuzzy max

Author: John N. Mordeson

Publisher: CRC Press

ISBN: 1482250993

Category: Mathematics

Page: 352

View: 703

Fuzzy social choice theory is useful for modeling the uncertainty and imprecision prevalent in social life yet it has been scarcely applied and studied in the social sciences. Filling this gap, Application of Fuzzy Logic to Social Choice Theory provides a comprehensive study of fuzzy social choice theory. The book explains the concept of a fuzzy maximal subset of a set of alternatives, fuzzy choice functions, the factorization of a fuzzy preference relation into the "union" (conorm) of a strict fuzzy relation and an indifference operator, fuzzy non-Arrowian results, fuzzy versions of Arrow’s theorem, and Black’s median voter theorem for fuzzy preferences. It examines how unambiguous and exact choices are generated by fuzzy preferences and whether exact choices induced by fuzzy preferences satisfy certain plausible rationality relations. The authors also extend known Arrowian results involving fuzzy set theory to results involving intuitionistic fuzzy sets as well as the Gibbard–Satterthwaite theorem to the case of fuzzy weak preference relations. The final chapter discusses Georgescu’s degree of similarity of two fuzzy choice functions.

Social Choice and Individual Values

The work culminated in what Arrow called the "General Possibility Theorem," better known thereafter as Arrow's (impossibility) theorem.

Author: Kenneth Joseph Arrow

Publisher: Martino Fine Books

ISBN: 9781614273455

Category: Political Science

Page: 110

View: 317

2012 Reprint of 1951 Edition. Exact facsimile of the original edition, not reproduced with Optical Recognition Software. Kenneth Arrow's monograph "Social Choice and Individual Values" and a theorem within it created modern social choice theory, a rigorous melding of social ethics and voting theory with an economic flavor. The work culminated in what Arrow called the "General Possibility Theorem," better known thereafter as Arrow's (impossibility) theorem. The theorem states that, absent restrictions on either individual preferences or neutrality of the constitution to feasible alternatives, there exists no social choice rule that satisfies a set of plausible requirements. The result generalizes the voting paradox, which shows that majority voting may fail to yield a stable outcome.

Mathematics for Social Scientists

J . T . Richelson , A comparative analysis of social choice functions , Behavioral
Science , 23 ( 1978 ) , 169 - 176 . J . Riordan , An Introduction to Combinatorial
Analysis , Wiley , New York , 1958 . F . S . Roberts , Discrete Mathematical
Models ...

Author: Ki Hang Kim

Publisher:

ISBN:

Category: Mathematics

Page: 277

View: 769



The Mathematics of Voting and Apportionment

In addition, this book will be a suitable read for to any curious mathematician looking for an exposition to these unpublicized mathematical applications. No political science prerequisites are needed.

Author: Sherif El-Helaly

Publisher: Springer

ISBN: 3030147681

Category: Mathematics

Page: 264

View: 662

This textbook contains a rigorous exposition of the mathematical foundations of two of the most important topics in politics and economics: voting and apportionment, at the level of upper undergraduate and beginning graduate students. It stands out among comparable books by providing, in one volume, an extensive and mathematically rigorous treatment of these two topics. The text’s three chapters cover social choice, yes-no voting, and apportionment, respectively, and can be covered in any order, allowing teachers ample flexibility. Each chapter begins with an elementary introduction and several examples to motivate the concepts and to gradually lead to more advanced material. Landmark theorems are presented with detailed and streamlined proofs; those requiring more complex proofs, such as Arrow’s theorems on dictatorship, Gibbard’s theorem on oligarchy, and Gärdenfors’ theorem on manipulation, are broken down into propositions and lemmas in order to make them easier to grasp. Simple and intuitive notations are emphasized over non-standard, overly complicated symbols. Additionally, each chapter ends with exercises that vary from computational to “prove or disprove” types. The Mathematics of Voting and Apportionment will be particularly well-suited for a course in the mathematics of voting and apportionment for upper-level undergraduate and beginning graduate students in economics, political science, or philosophy, or for an elective course for math majors. In addition, this book will be a suitable read for to any curious mathematician looking for an exposition to these unpublicized mathematical applications. No political science prerequisites are needed. Mathematical prerequisites (included in the book) are minimal: elementary concepts in combinatorics, graph theory, order relations, and the harmonic and geometric means. What is needed most is the level of maturity that enables the student to think logically, derive results from axioms and hypotheses, and intuitively grasp logical notions such as “contrapositive” and “counterexample.”


Handbook of Social Choice and Welfare

Le Breton , M . , and J . A . Weymark ( 2002b ) , “ Social choice with analytic
preferences ” , Social Choice and Welfare , forthcoming . Leclerc , B . ( 1984 ) , “
Efficient and binary consensus functions on transitive valued relations " ,
Mathematical ...

Author: Kenneth J. Arrow

Publisher: North Holland

ISBN:

Category: Business & Economics

Page: 680

View: 893

One of two volumes, 'The Handbook of Social Choice and Welfare' contains a series of essays that examine past and on-going social choice theory and welfare economics. It provides a means to making collective decisions on such issues.

Conversations on Social Choice and Welfare Theory Vol 1

Starting with a brief history of social choice and welfare theory written by the book editors, it features 15 conversations with four Nobel Laureates and other key scholars in the discipline. The volume is divided into two parts.

Author: Marc Fleurbaey

Publisher: Springer Nature

ISBN: 3030627691

Category: Business & Economics

Page: 334

View: 953

This volume presents interviews that have been conducted from the 1980s to the present with important scholars of social choice and welfare theory. Starting with a brief history of social choice and welfare theory written by the book editors, it features 15 conversations with four Nobel Laureates and other key scholars in the discipline. The volume is divided into two parts. The first part presents four conversations with the founding fathers of modern social choice and welfare theory: Kenneth Arrow, John Harsanyi, Paul Samuelson, and Amartya Sen. The second part includes conversations with scholars who made important contributions to the discipline from the early 1970s onwards. This book will appeal to anyone interested in the history of economics, and the history of social choice and welfare theory in particular.

Social Choice Theory

There is such a subject as moral philosophy for much the same reason that there
is such a subject as the philosophy of mathematics . In moral judgements , as in
mathematical ones , we have a set of putatively objective beliefs in which we are
 ...

Author: Charles K. Rowley

Publisher: Edward Elgar Pub

ISBN:

Category: Social Science

Page: 1716

View: 414

This major reference collection presents in three volumes the key articles and papers on social choice theory.

Social Choice and Resource Allocation

This is the area of continuous or topological approaches to the study of social
choice , and the analysis of what have come to be known as " Chichilnisky rules "
. Initiated by Chichilnisky in a paper in Advances in Mathematics in 1980 ( 14 ) ,
the ...

Author: G. M. Heal

Publisher:

ISBN:

Category: Social choice

Page: 12

View: 630


Mathematics and Politics

The first partofthe text is made up of a single chapter devoted to each topic. The second part of the text revisits each topic, again with a single chapter devoted to each.

Author: Alan D. Taylor

Publisher: Springer Science & Business Media

ISBN: 1461225124

Category: Mathematics

Page: 284

View: 786

interest in a particular application, however, often depends on his or hergeneralinterestintheareainwhichtheapplicationistakingplace. My experience at Union College has been that there is a real advan tage in having students enter the course knowing thatvirtually all the applications will focus on a single discipline-in this case, political science. The level ofpresentation assumes no college-level mathematicalor social science prerequisites. The philosophy underlying the approach we have taken in this book is based on the sense that we (mathemati cians)havetendedtomaketwoerrorsinteachingnonsciencestudents: wehaveoverestimatedtheircomfortwithcomputationalmaterial,and we have underestimated their ability to handle conceptual material. Thus, while there is very little algebra (and certainly no calculus) in our presentation, we have included numerous logical arguments that students in the humanitiesand the socialscienceswill find accessible, but not trivial. The book contains five main topics: a m.odel of escalation, game theoretic models of international conflict, yes-no voting systems, political power, and social choice. The first partofthe text is made up of a single chapter devoted to each topic. The second part of the text revisits each topic, again with a single chapter devoted to each. The organizationofthe bookisbasedonpedagogicalconsiderations, with the material becoming somewhat more sophisticated as one moves through the ten chapters. On the other hand, within any given chap terthere is little reliance on material from earlierchapters, except for those devoted to the same topic.

Equity Efficiency and Social Choice

( 1991d ) , ' Public Goods and Arrovian Social Choice ' , Social Choice and
Welfare , forthcoming . ( 1992 ) , ' Quasitransitive Intergenerational Choice for
Economic Environments ' , Journal of Mathematical Economics , forthcoming .
and ...

Author: Donald Edward Campbell

Publisher: Oxford University Press

ISBN:

Category: Social choice.

Page: 188

View: 295

This book presents Professor Campbell's recent work on social choice in economic environments. It addresses the standard social choice questions in the framework of welfare economics; with emphasis on the allocation of public and private goods. But it goes beyond the standard issues to prove fundamental theorems on efficiency and equity in public policy analysis. Arrow's impossibility theorem discloses some elementary conditions under which the Pareto criterion implies that the social welfare function is insensitive to the preferences of all but a single individual. It is proved here that any degree of sensitivity to individual preferences implies that the social welfare function is independent of the preferences of all but one person even if efficiency is not required in any degree. In this and other ways, the absence of meaningful efficiency-equity trade-offs is demonstrated. The framework is a conventional allocation space with standard economic restrictions on the nature of individual preferences. Classical impossibility theorems, including Arrow's are proved en route to the main results. The book will be of interest to academic economists, especially those working in social choice theory and economic theory.

Landmark Papers in General Equilibrium Theory Social Choice and Welfare

ON SOME SYSTEMS OF EQUATIONS OF MATHEMATICAL ECONOMICS BY
ABRAHAM WALD MATHEMATICAL economics has made much progress in
recent times owing to the efforts of the many adherents of this new method . The
areas ...

Author: Kenneth Joseph Arrow

Publisher: Edward Elgar Pub

ISBN:

Category: Political Science

Page: 705

View: 889

A collection of 36 previously published papers focusing on the mathematical modeling of a number of problems in economic theory, one of the most important being the relative possibilities of modeling whether social choices can be determined in a world of infinite economic choice or whether choice leads to impossibilities of resolving social preference. The papers, for the most part, take the work of Kenneth J. Arrow and Gerard Debreu as a starting point and were published between 1934 and 1989. Annotation copyrighted by Book News, Inc., Portland, OR

Collective Decision Making

This book discusses collective decision making from the perspective of social choice and game theory. The chapters are written by well-known scholars in the field.

Author: Adrian Van Deemen

Publisher: Springer Science & Business Media

ISBN: 9783642028656

Category: Business & Economics

Page: 266

View: 390

Harrie de Swart is a Dutch logician and mathematician with a great and open int- est in applications of logic. After being confronted with Arrow’s Theorem, Harrie became very interested in social choice theory. In 1986 he took the initiative to start up a group of Dutch scientists for the study of social choice theory. This initiative grew out to a research group and a series of colloquia, which were held approximately every month at the University of Tilburg in The Netherlands. The organization of the colloquia was in the hands of Harrie and under his guidance they became more and more internationally known. Many international scholars liked visiting the social choice colloquia in Tilburg and enjoyed giving one or more presentations about their work. They liked Harrie’s kindness and hospitality, and the openness of the group for anything and everything in the eld of social choice. The Social Choice Theory Group started up by Harrie consisted, and still c- sists, of scholars from several disciplines; mostly economics, mathematics, and (mathematical) psychology. It was set up for the study of and discussion about anything that had to do with social choice theory including, and not in the least, the supervision of PhD students in the theory. Members of the group were, among o- ers, Thom Bezembinder (psychologist), Hans Peters (mathematician), Pieter Ruys (economist), Stef Tijs (mathematician and game theorist) and, of course, Harrie de Swart (logician and mathematician).

The Theory of Social Choice

These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions.

Author: Peter C. Fishburn

Publisher: Princeton University Press

ISBN: 1400868335

Category: Social Science

Page: 278

View: 486

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.

Game Theory and Mathematical Economics

Then we formulate and discuss the following results : ( a ) strongly monotonic
social choice functions are dictatorial , and ( b ) a simple game has a strongly
monotonic representation if and only if all its cores are non - empty . We conclude
with ...

Author: Otto Moeschlin

Publisher: North Holland

ISBN:

Category: Economics, Mathematical

Page: 463

View: 455