The Method of Majority Decision and Rationality Conditions*
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.
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