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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 *

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

Satish K. Jain

Oxford University Press

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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