Strongly decomposable voting rules on multiattribute domains

  • Authors:

  • Lirong Xia;Jérôme Lang;Mingsheng Ying

  • Affiliations:

  • State Key Laboratory of Intelligent Technology and Systems, Department of Computer Science and Technology, Tsinghua University, Beijing, China;IRIT, Université Paul Sabatier, Toulouse Cedex, France;State Key Laboratory of Intelligent Technology and Systems, Department of Computer Science and Technology, Tsinghua University, Beijing, China

  • Venue:
  • AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
  • Year:
  • 2007

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Abstract

Sequential composition of voting rules, by making use of structural properties of the voters' preferences, provide computationally economical ways for making a common decision over a Cartesian product of finite local domains. A sequential composition is usually defined on a set of legal profiles following a fixed order. In this paper, we generalize this by order-independent sequential composition and strong decomposability, which are independent of the chosen order. We study to which extent some usual properties of voting rules transfer from the local rules to their order-independent sequential composition. Then, to capture the idea that a voting rule is neutral or decomposable on a slightly smaller domain, we define nearly neutral, nearly decomposable rules for both sequential composition and order-independent sequential composition, which leads us to defining and studying decomposable permutations. We prove that any sequential composition of neutral local rules and any order-independent sequential composition of neutral local rules satisfying a necessary condition are nearly neutral.