Proportionality Variations in Repeated Fair Division of Indivisible Goods

Karl Jochen Micheel, Anaëlle Wilczynski

Keywords: Computational social choice, Fair division, Proportionality, Fairness over time

Abstract: This article deals with fair division of indivisible goods under additive utilities in a repeated context where the same allocation problem is decided multiple times. We focus on the well-established proportionality criterion imposing, in the traditional non-repeated setting, that each agent should get a satisfaction at least equal to her valuation for the whole bundle of goods divided by the number of agents. In the repeated setting, we propose several variations of proportionality by requiring that proportionality should be satisfied on average over specified periods of time. While proportionality can be rarely achieved in a one-shot decision, we identify some configurations where considering several rounds helps reach fairness over time via particular proportionality variations. From a computational point of view, we show that most decision problems related to the existence of allocation sequence satisfying variations of proportionality are hard, but we nevertheless highlight several restrictions where the problems can be solved efficiently and show through experiments that our proposed variations can make fairness more achievable.

Area: Game Theory and Economic Paradigms (GTEP)

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Submission Number: 899