Mini Workshop on Social Choice Theory

Location: Academie Gebouw, Economics Faculty Room (1st Floor)

Time: 15:00 to 17:00, 13th November 2023. NOTE: the workshop starts after the reception following the defense, so a slight delay might occur. 

Edith Elkind (University of Oxford)

Title: Fairness in temporal slot assignment.

Abstract: We investigate settings where projects need to be assigned to time slots based on preferences of multiple agents. We consider a variety of objectives, including utilitarian social welfare, egalitarian social welfare, Nash social welfare, Pareto optimality, equitability, and proportionality. We introduce a general-purpose randomized algorithm, which, for each of these objectives, can decide whether it is achievable for a given instance; the running time of this algorithm is in the complexity class XP with respect to the number of agents. We also provide complexity results for the case where the number of agents is large, and identify special cases that admit efficient algorithms. 

(Joint work with Sonja Kraiczy and Nicholas Teh (SAGT'22))

Hans Peters (Maastricht University)

Title: Mechanisms and axiomatics for division problems with single-dipped preferences

Abstract: A mechanism allocates one unit of an infinitely divisible commodity among agents reporting a number between zero and one. Nash, Pareto optimal Nash, and strong equilibria are analyzed for the case where the agents have single-dipped preferences. One main result is that when the mechanism satisfies anonymity, monotonicity, the zero-one property, and order preservation, then the Pareto optimal Nash and strong equilibria coincide and assign Pareto optimal allocations that are characterized by so-called maximal coalitions: members of a maximal coalition prefer an equal coalition share over obtaining zero, whereas the outside agents prefer zero over obtaining an equal share from joining the coalition. A second main result is an axiomatic characterization of the associated social choice correspondence as the maximal correspondence satisfying minimal envy Pareto optimality, equal division lower bound, and sharing index order preservation.

(Joint work with Bas Dietzenbacher and Doudou Gong)

Ulle Endriss (University of Amsterdam)

Title: Characterisation and Impossibility Results for Interval Aggregation

Abstract: In the context of aggregating intervals reflecting the views of several agents into a single interval, we investigate the impact of the form of representation chosen for the intervals involved. Specifically, we ask whether there are natural rules we can define both as rules that aggregate separately the left and right endpoints of intervals and as rules that aggregate separately the left endpoints and the interval widths. We show that on discrete scales it is essentially impossible to do so, while on continuous scales we can characterise the rules meeting these requirements as those that compute a weighted average of the endpoints of the individual intervals.

(Joint work with Arianna Novaro and Zoi Terzopoulou)