Arrovian aggregation models / Fuad Aleskerov.

Format:

Book

Author/Creator:

Aleskerov, F. T. (Faud Tagi ogly)

Contributor:

Anne and Joseph Trachtman Memorial Book Fund.

Series:

Theory and decision library. Mathematical and statistical methods ; Series B, v. 39.

Theory and decision library. Series B, Mathematical and statistical methods ; v. 39

Language:

English

Subjects (All):

Economics, Mathematical.

Econometric models.

Decision making.

Social choice.

Arrow, Kenneth J. (Kenneth Joseph), 1921-2017.

Arrow, Kenneth J.

Physical Description:

x, 242 pages : illustrations ; 25 cm.

Place of Publication:

Boston : Kluwer Academic, [1999]

Summary:

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.

Contents:

1 Aggregation: A General Description 1

1.2 Analysis of examples 2

1.3 Arrow's General Impossibility Theorem 3

1.4 Individual opinion: a formalization 8

1.5 Aggregation: the synthesis problem 11

2 Rationality of Individual Opinions and Social Decisions 17

2.2 Binary relations 17

2.3 Criterial model of choice 22

2.4 Expansion-Contraction Axioms 26

2.5 Relations between the classes of choice functions 35

3 Social Decision Functions 45

3.2 Strong locality 46

3.3 Normative conditions 49

3.4 Rules from Central Class 53

3.5 Rationality constraints 56

3.6 Comparing classes in [Lambda][superscript C] 62

3.7 Arrow's General Impossibility Theorem 65

3.8 Rationality constraints: further results 67

3.9 Aggregation of equivalences 72

3.10 Non-monotonic strongly local SDFs 74

3.11 Locality 78

3.12 Normative conditions 80

3.13 Rules from Central Class 85

3.14 Rationality constraints 97

3.15 Comparing classes in [Lambda][superscript C] 110

4 Functional Aggregation Rules 123

4.2 Locality 124

4.3 Normative conditions 127

4.4 Rules from Central Class 133

4.5 Rationality constraints: non-emptiness 136

4.6 Rationality constraints: domains H, C, and O 142

4.7 Comparing classes in [Lambda][superscript C] 150

4.8 Rules from Basic Class 152

4.9 Non-monotonic rules 158

4.10 Non-monotonic rules: dual domains 165

5 Social Choice Correspondences 177

5.2 Locality 177

5.3 Normative conditions 183

5.4 Boolean representation of Social Choice Correspondences 190

5.5 Rules from Central Class, I 192

5.6 Rules from Central Class, II 200

5.7 Rules from Symmetrically Central Class 204

5.8 Rationality constraints: single-valuedness 212

5.9 Coalitional q-federation rules under rationality constraints 216

5.10 Rationality constraints: domains H, C, O 219

5.11 Comparing classes in [Lambda][superscript C] 222.

Notes:

Includes bibliographical references (pages [227]-237) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Anne and Joseph Trachtman Memorial Book Fund.

ISBN:

0792384512

OCLC:

40668120