Strongly Decomposable Voting Rules on Multiattribute Domains

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 strongly decomposable to unify the sequential compositions of all orders. 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 orderindependent 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.