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Collective Choice Rules on Convex Restricted Domains

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  • Storcken, Ton

    (METEOR)

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    Abstract

    We study sets of preferences that are convex with respect to the betweeness relation induced by the Kemeny distance for preferences. It appears that these sets consist of all preferences containing a certain partial ordering and the other way around all preferences containing a given partial ordering form a convex set. Next we consider restricted domains where each agent has a convex set of preferences. Necessary and sufficient conditions are formulated under which a restricted domain admits unanimous, strategy-proof and non-dictatorial choice rules. Loosely speaking it boils down to admitting monotone and non-image-dictatorial decision rules on two alternatives where the other alternatives are completely disregarded.

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    Bibliographic Info

    Paper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 003.

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    Date of creation: 2008
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    Handle: RePEc:dgr:umamet:2008003

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    Web page: http://www.maastrichtuniversity.nl/web/UMPublications.htm

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    Keywords: mathematical economics;

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    1. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    2. Kalai, Ehud & Ritz, Zvi, 1980. "Characterization of the private alternatives domains admitting arrow social welfare functions," Journal of Economic Theory, Elsevier, vol. 22(1), pages 23-36, February.
    3. 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.
    4. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    5. Ehud Kalai & Eitan Muller, 1977. "Characterization of Domains Admitting Nondictatorial Social Welfare Functions and Nonmanipulable Voting Procedures," Discussion Papers 234, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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    Cited by:
    1. Can, Burak & Storcken, Ton, 2013. "Update monotone preference rules," Mathematical Social Sciences, Elsevier, vol. 65(2), pages 136-149.

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