Overview

"Aggregation of individual opinions into a social decision is a problem widely observed in everyday life. For centuries people tried to invent the ""best"" aggregation rule. In 1951, young American scientist and future Nobel Prize winner Kenneth Arrow formulated the problem in an axiomatic way, in that he specified a set of axioms which every reasonable aggregation rule has to satisfy, and obtained that these axioms are inconsistent. This result, often called Arrow's Paradox or General Impossibility Theorem, had become a cornerstone of social choice theory. The main condition used by Arrow was his famous independence of irrelevant alternatives. This very condition pre-defines the ""local"" treatment of the alternatives (or pairs of alternatives, or sets of alternatives) in aggregation procedures. Remaining within the framework of the axiomatic approach and based on the consideration of local rules, this book investigates three formulations of the aggregation problem according to the form in which the individual opinions about the alternatives are defined, as well as to the form of desired social decision. In other words, the book looks at three aggregation models. What is common between them is that in all models some analogue of the independence of irrelevant alternatives condition is used, which is why these models are called Arrovian aggregation models. The first chapter presents a general description of the problem of axiomatic synthesis of local rules, and introduces problem formulations for various versions of formalization of individual opinions and collective decision. Chapter two formalizes precisely the notion of ""rationality"" of individual opinions and social decision, while chapter three deals with the aggregation model for the case of individual opinions and social decisions formalized as binary relations. Chapter four deals with Functional Aggregation Rules which transform into a social choice function individual opinions defined as choice functions. Chapter five considers another model, Social Choice Correspondences, when the individual opinions are formalized as binary relations, and the collective decision is looked for as a choice function."

Full Product Details

Author:   F. Aleskerov
Publisher:   Springer
Imprint:   Springer
Edition:   1999 ed.
Volume:   39
Dimensions:   Width: 15.50cm , Height: 1.50cm , Length: 23.50cm
Weight:   1.200kg
ISBN:  

9780792384519

ISBN 10:   0792384512
Pages:   244
Publication Date:   31 March 1999
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 Aggregation: A General Description.- 2 Rationality of Individual Opinions and Social Decisions.- 3 Social Decision Functions.- 4 Functional Aggregation Rules.- 5 Social Choice Correspondences.

Reviews

'This monograph is excellent and should belong to every social choice theorist's library. it is also highly recommended to mathematicians working in discrete mathematics since it offers many applications of this mathematical domain.' Mathematical Reviews, 2001c

'This monograph is excellent and should belong to every social choice theorist's library. it is also highly recommended to mathematicians working in discrete mathematics since it offers many applications of this mathematical domain.' Mathematical Reviews, 2001c

This monograph is excellent and should belong to every social choice theorist's library. it is also highly recommended to mathematicians working in discrete mathematics since it offers many applications of this mathematical domain.' Mathematical Reviews, 2001c

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