Theory and Decision Library B

Arrovian Aggregation Models

Authors: Aleskerov, Fuad T.

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About this book

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, i.e., 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, etc.) in aggregation procedures.
Remaining within the framework of the axiomatic approach and based on the consideration of local rules, Arrovian Aggregation Models 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, we study 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 we call these models Arrovian aggregation models.
Chapter 1 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 2 formalizes precisely the notion of `rationality' of individual opinions and social decision. Chapter 3 deals with the aggregation model for the case of individual opinions and social decisions formalized as binary relations. Chapter 4 deals with Functional Aggregation Rules which transform into a social choice function individual opinions defined as choice functions. Chapter 5 considers another model &endash; Social Choice Correspondences when the individual opinions are formalized as binary relations, and the collective decision is looked for as a choice function. Several new classes of rules are introduced and analyzed.

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

Table of contents (5 chapters)

  • Aggregation: A General Description

    Aleskerov, Fuad

    Pages 1-16

  • Rationality of Individual Opinions and Social Decisions

    Aleskerov, Fuad

    Pages 17-44

  • Social Decision Functions

    Aleskerov, Fuad

    Pages 45-122

  • Functional Aggregation Rules

    Aleskerov, Fuad

    Pages 123-176

  • Social Choice Correspondences

    Aleskerov, Fuad

    Pages 177-226

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-1-4757-4542-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $199.00
price for USA
  • ISBN 978-0-7923-8451-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $199.00
price for USA
  • ISBN 978-1-4419-5079-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Arrovian Aggregation Models
Authors
Series Title
Theory and Decision Library B
Series Volume
39
Copyright
1999
Publisher
Springer US
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4757-4542-9
DOI
10.1007/978-1-4757-4542-9
Hardcover ISBN
978-0-7923-8451-9
Softcover ISBN
978-1-4419-5079-6
Edition Number
1
Number of Pages
XII, 244
Topics