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

  • Benno Kuckuck
  • Jörg RotheEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11327)

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].

Keywords

Computational social choice Fair division Scoring allocation rule Duplication monotonicity 

Notes

Acknowledgments

This work was supported in part by DFG grant RO 1202/14-2.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Mathematisches InstitutHeinrich-Heine-Universität DüsseldorfDüsseldorfGermany
  2. 2.Institut für InformatikHeinrich-Heine-Universität DüsseldorfDüsseldorfGermany

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