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 _1 preferences—for which a voter’s disutility is given by the _1 distance between the consensus division and the division he or she most prefers—the social welfare-maximizing mechanism, which minimizes the average _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.

(joint work with Rupert Freeman, David Pennock, Jenn Wortman Vaughan)

]]>**BIO**

Marijn Heule is a Research Assistant Professor at the University of Texas at Austin whose research focuses on major challenges in automated reasoning. Marijn Heule´s current research focusses on two major challenges for SAT solving. The first challenge is the exploitation of the potential of high-performance computing. The second is validating the results of SAT solvers and related tools. His computer-aided solutions of long-standing mathematical problems such as the Pythagorean Triples Problem and the computation of the fifth Schur Number have received substantial media coverage.

**In 2018 Marijn Heule, and Benjamin Kiesl and Adrian Rebola-Pardo** (PhD students of the FWF-funded doctoral college Logical Methods in Computer Science – LogiCS at TU Wien) received the Best Paper Award at the **premier international conference on all topics in automated reasoning**, IJCAR 2018 in Oxford, UK. The best paper award recognizes the originality and significance of the awarded paper “Extended Resolution Simulates DRAT”, which for the first time provides a mathematical argument showing that Tseitin’s old system of proof checking was actually already powerful enough to do everything that can be done by modern approaches. The paper finally bridges the gap between proofs of the present and of the past, thereby helping the humans to actually better understand computer-generated proofs.

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