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Sequential composition of voting rules in multi-issue domains

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  • Lang, Jrme
  • Xia, Lirong

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.

Suggested Citation

  • Lang, Jrme & Xia, Lirong, 2009. "Sequential composition of voting rules in multi-issue domains," Mathematical Social Sciences, Elsevier, vol. 57(3), pages 304-324, May.
    • Handle: RePEc:eee:matsoc:v:57:y:2009:i:3:p:304-324
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    Cited by:

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    3. Joseph, Rémy-Robert, 2010. "Making choices with a binary relation: Relative choice axioms and transitive closures," European Journal of Operational Research, Elsevier, vol. 207(2), pages 865-877, December.

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