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Conditions for Social Preference Transitivity When Cycle Involved and A $\hat{O}\mbox{-}\hat{I}$ Framework

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  • Fujun Hou

Abstract

We present some conditions for social preference transitivity under the majority rule when the individual preferences include cycles. First, our concern is with the restriction on the preference orderings of individuals except those (called cycle members) whose preferences constitute the cycles, but the considered transitivity is, of course, of the society as a whole. In our discussion, the individual preferences are assumed concerned and the cycle members' preferences are assumed as strict orderings. Particularly, for an alternative triple when one cycle is involved and the society is sufficient large (at least 5 individuals in the society), we present a sufficient condition for social transitivity; when two antagonistic cycles are involved and the society has at least 9 individuals, necessary and sufficient conditions are presented which are merely restricted on the preferences of those individuals except the cycle members. Based on the work due to Slutsky (1977) and Gaertner \& Heinecke (1978), we then outline a conceptual $\hat{O}\mbox{-}\hat{I}$ framework of social transitivity in an axiomatic manner. Connections between some already identified conditions and the $\hat{O}\mbox{-}\hat{I}$ framework is examined.

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  • Fujun Hou, 2022. "Conditions for Social Preference Transitivity When Cycle Involved and A $\hat{O}\mbox{-}\hat{I}$ Framework," Papers 2205.08223, arXiv.org, revised May 2022.
  • Handle: RePEc:arx:papers:2205.08223
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    1. Steven Slutsky, 1977. "A Characterization of Societies with Consistent Majority Decision," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(2), pages 211-225.
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    3. John Duggan, 2016. "Preference exclusions for social rationality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 93-118, January.
    4. Inada, Ken-Ichi, 1969. "The Simple Majority Decision Rule," Econometrica, Econometric Society, vol. 37(3), pages 490-506, July.
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    6. Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, vol. 58(4), pages 328-328.
    7. Saposnik, Rubin, 1975. "On transitivity of the social preference relation under simple majority rule," Journal of Economic Theory, Elsevier, vol. 10(1), pages 1-7, February.
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