27 March 2019, Computational Social Choice Seminar, Dominik Peters

Abstract

We consider a participatory budgeting problem in which each voter submits a proposal for how to divide a single divisible resource (such as money or time) among several possible alternatives (such as public projects or activities) and these proposals must be aggregated into a single consensus division. Under ℓ_1 preferences---for which a voter's disutility is given by the ℓ_1 distance between the consensus division and the division he or she most prefers---the social welfare-maximizing mechanism, which minimizes the average ℓ_1 distance between the outcome and each voter's proposal, is incentive compatible [Goel et al. 2016]. However, it fails to satisfy a natural fairness notion of proportionality, placing too much weight on majority preferences. Leveraging a connection between market prices and the generalized median rules of Moulin [1980], we introduce the independent markets mechanism, which is both incentive compatible and proportional. We unify the social welfare-maximizing mechanism and the independent markets mechanism by defining a broad class of moving phantom mechanisms that includes both. We show that every moving phantom mechanism is incentive compatible. Finally, we characterize the social welfare-maximizing mechanism as the unique Pareto-optimal mechanism in this class, suggesting an inherent tradeoff between Pareto optimality and proportionality. (This is joint work with Rupert Freeman, David Pennock, and Jenn Wortman Vaughan.)

For more information on the Computational Social Choice Seminar, please consult https://staff.science.uva.nl/u.endriss/seminar/.