Special majority rules necessary and sufficient condition for quasi-transitivity with quasi-transitive individual preferences

✍ Scribed by S. K. Jain

• Publisher: Springer
• Year: 1986
• Tongue: English
• Weight: 375 KB
• Volume: 3
• Category: Article
• ISSN: 0176-1714
• DOI: 10.1007/bf00435660

✦ Synopsis

A condition on preferences called strict Latin Square partial agreement is introduced and is shown to be necessary and sufficient for quasitransitivity of the social weak preference relation generated by any special majority rule, under the assumption that individual preferences themselves are quasi-transitive.

An important problem in the context of social decision rules which in some situations fail to yield rational (transitive, quasi-transitive or acyclic) social weak preference relations is that of characterizing configurations of individual weak preference relations which always give rise to rational social weak preference relations. For several classes of social decision rules such characterizations have been obtained. Under the assumption that individual weak preference relations are transitive, necessary and sufficient conditions have been obtained for quasitransitivity and transitivity under the simple majority rule by Inada [3] and Sen and Pattanaik [7], for transitivity under the simple nonminority rule by Fine [1 ], for quasi-transitivity and transitivity under the special majority rules by Jain [5] and for quasi-transitivity and transitivity under the nonminority rules by Jain [6]. For the case when individual weak preference relations are quasi-transitive, Inada [4] and Fishburn [2] have obtained necessary and sufficient conditions for quasitransitivity under the simple majority rule. They have shown that the satisfaction of dichotomous preferences or antagonistic preferences or generalized limited agreement or generalized value-restriction over every triple of alternatives is necessary as well as sufficient for quasi-transitivity under the simple majority rule.

In this paper we consider the class of special majority rules. The term 'special' here is used to signify the fact that the majority required is greater than the simple majority. The simple majority rule declares an alternative x to be better than another alternative y if and only if the number of individuals who prefer x to y is greater than half of the total of those who prefer x to y and those who prefer y to x. Analogously we can define, corresponding to any fractionp lying strictly between ½ and 1, a special majority rule (p-majority rule) by requiring that an alternative x be