Monotonicity, Duplication Monotonicity, and Pareto Optimality in the Scoring-Based Allocation of Indivisible Goods

Abstract

We study the properties of scoring allocation correspondences and rules, due to Baumeister et al. [7], that are based on a scoring vector (e.g., Borda or lexicographic scoring) and an aggregation function (e.g., utilitarian or egalitarian social welfare) and can be used to allocate indivisible goods to agents. Extending their previous results considerably and solving some of their open questions, we show that while necessary duplication monotonicity (a notion inspired by the twin paradox [21] and false-name manipulation [1]) fails for most choices of scoring vector when using leximin social welfare, possible duplication monotonicity holds for a very wide range of scoring allocation rules. We also show that a very large family of scoring allocation rules is monotonic. Finally, we show that a large class of scoring allocation correspondences satisfies possible Pareto-optimality, which extends a result of Brams et al. [12].