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Arguments for a Better World: Essays in Honor of Amartya SenVolume I: Ethics, Welfare, and Measurement$
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Kaushik Basu and Ravi Kanbur

Print publication date: 2008

Print ISBN-13: 9780199239115

Published to Oxford Scholarship Online: May 2009

DOI: 10.1093/acprof:oso/9780199239115.001.0001

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The Method of Majority Decision and Rationality Conditions *

The Method of Majority Decision and Rationality Conditions *

Chapter:
(p.167) Chapter 10 The Method of Majority Decision and Rationality Conditions*
Source:
Arguments for a Better World: Essays in Honor of Amartya Sen
Author(s):

Satish K. Jain

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199239115.003.0011

This chapter extends the earlier work on domain conditions for social rationality under the method of majority decision (MMD) by deriving Inada-type necessary and sufficient conditions for transitivity and quasi-transitivity for cases which were not covered by the earlier results. It presents a unified approach to the problem of obtaining domain conditions by formulating all conditions in terms of Latin Squares. Also, each characterization is obtained in terms of a single condition. These two together result in considerable simplification of proofs. The chapter also provides new proofs for the earlier results. Regarding acyclicity, it is shown that for any non-trivial set of binary relations containing intransitive binary relations, no condition defined only over triples can be an Inada-type necessary and sufficient condition for acyclicity under the MMD.

Keywords:   restricted domain, majority decision, transitivity, quasi-transitivity, acyclicity, extremal restriction, Latin square partial agreeme

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