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Reformulating the Value Restriction and the Not-Strict Value Restriction in Terms of Possibility Preference Map

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  • Fujun Hou

Abstract

In social choice theory, Sen's value restriction and Pattanaik's not-strict value restriction are both attractive conditions for testing social preference transitivity and/or non-empty social choice set existence. This article introduces a novel mathematical representation tool, called possibility preference map (PPM), for weak orderings, and then reformulates the value restriction and the not-strict value restriction in terms of PPM. The reformulations all appear elegant since they take the form of minmax.

Suggested Citation

  • Fujun Hou, 2022. "Reformulating the Value Restriction and the Not-Strict Value Restriction in Terms of Possibility Preference Map," Papers 2205.07400, arXiv.org.
    • Handle: RePEc:arx:papers:2205.07400
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Inada, Ken-Ichi, 1969. "The Simple Majority Decision Rule," Econometrica, Econometric Society, vol. 37(3), pages 490-506, July.
    4. Duncan Black, 1976. "Partial justification of the Borda count," Public Choice, Springer, vol. 28(1), pages 1-15, December.
    5. Sen, Amartya & Pattanaik, Prasanta K., 1969. "Necessary and sufficient conditions for rational choice under majority decision," Journal of Economic Theory, Elsevier, vol. 1(2), pages 178-202, August.
    6. Hou, Fujun & Triantaphyllou, Evangelos, 2019. "An iterative approach for achieving consensus when ranking a finite set of alternatives by a group of experts," European Journal of Operational Research, Elsevier, vol. 275(2), pages 570-579.
    7. Pattanaik, Prasanta K, 1970. "Sufficient Conditions for the Existence of a Choice Set Under Majority Voting," Econometrica, Econometric Society, vol. 38(1), pages 165-170, January.
    8. 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.
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    Cited by:

    1. Fujun Hou, 2022. "Conditions for none to be whipped by `Rank and Yank' under the majority rule," Papers 2208.05093, arXiv.org.

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