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Sequential composition of voting rules in multi-issue domains

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  • Lang, Jrme
  • Xia, Lirong
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    Abstract

    In many real-world group decision making problems, the set of alternatives is a Cartesian product of finite value domains for each of a given set of variables (or issues). Dealing with such domains leads to the following well-known dilemma: either ask the voters to vote separately on each issue, which may lead to the so-called multiple election paradoxes as soon as voters' preferences are not separable; or allow voters to express their full preferences on the set of all combinations of values, which is practically impossible as soon as the number of issues and/or the size of the domains are more than a few units. We try to reconciliate both views and find a middle way, by relaxing the extremely demanding separability restriction into this much more reasonable one: there exists a linear order on the set of issues such that for each voter, every issue is preferentially independent of given . This leads us to define a family of sequential voting rules, defined as the sequential composition of local voting rules. These rules relate to the setting of conditional preference networks (CP-nets) recently developed in the Artificial Intelligence literature. Lastly, we study in detail how these sequential rules inherit, or do not inherit, the properties of their local components.

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    Bibliographic Info

    Article provided by Elsevier in its journal Mathematical Social Sciences.

    Volume (Year): 57 (2009)
    Issue (Month): 3 (May)
    Pages: 304-324

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    Handle: RePEc:eee:matsoc:v:57:y:2009:i:3:p:304-324

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    Web page: http://www.elsevier.com/locate/inca/505565

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    Keywords: Voting Multiple elections Preferential independence CP-networks;

    References

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    1. Plott, Charles R & Levine, Michael E, 1978. "A Model of Agenda Influence on Committee Decisions," American Economic Review, American Economic Association, vol. 68(1), pages 146-60, March.
    2. İpek Özkal-Sanver & M. Sanver, 2006. "Ensuring Pareto Optimality by Referendum Voting," Social Choice and Welfare, Springer, vol. 27(1), pages 211-219, August.
    3. Michel Le Breton & Arunava Sen, 1999. "Separable Preferences, Strategyproofness, and Decomposability," Econometrica, Econometric Society, vol. 67(3), pages 605-628, May.
    4. Bradley, W. James & Hodge, Jonathan K. & Kilgour, D. Marc, 2005. "Separable discrete preferences," Mathematical Social Sciences, Elsevier, vol. 49(3), pages 335-353, May.
    5. Steven J. Brams & William S. Zwicker & D. Marc Kilgour, 1998. "The paradox of multiple elections," Social Choice and Welfare, Springer, vol. 15(2), pages 211-236.
    6. Hodge, Jonathan K. & TerHaar, Micah, 2008. "Classifying interdependence in multidimensional binary preferences," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 190-204, March.
    7. Gilbert Laffond & Jean Lainé & Jean-François Laslier, 1996. "Composition-consistent tournament solutions and social choice functions," Social Choice and Welfare, Springer, vol. 13(1), pages 75-93, January.
    8. Marco Scarsini, 1998. "A strong paradox of multiple elections," Social Choice and Welfare, Springer, vol. 15(2), pages 237-238.
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