Strongly Decomposable Voting Rules on Multiattribute Domains

摘要

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 decom-posability, 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.