Rupert Freeman

Fair Public Decision Making

We generalize the classic problem of fairly allocating indivisible goods to the problem of fair public decision making, in which a decision must be made on several social issues simultaneously, and, unlike the classic setting, a decision can provide positive utility to multiple players. We extend the popular fairness notion of proportionality (which is not guaranteeable) to our more general setting, and introduce three novel relaxations --- proportionality up to one issue, round robin share, and pessimistic proportional share --- that are also interesting in the classic goods allocation setting. We show that the Maximum Nash Welfare solution, which is known to satisfy appealing fairness properties in the classic setting, satisfies or approximates all three relaxations in our framework. We also provide polynomial time algorithms and hardness results for finding allocations satisfying these axioms, with or without insisting on Pareto optimality.

The Double Clinching Auction for Wagering

We develop the first incentive compatible and near-Pareto-optimal wagering mechanism. Wagering mechanisms can be used to elicit predictions from agents who reveal their beliefs by placing bets. Lambert et al. [20, 21] introduced weighted score wagering mechanisms, a class of budget-balanced wagering mechanisms under which agents with immutable beliefs truthfully report their predictions. However, we demonstrate that these and other existing incentive compatible wagering mechanisms are not Pareto optimal: agents have significant budget left over even when additional trade would be mutually beneficial. Motivated by this observation, we design a new wagering mechanism, the double clinching auction, a two-sided version of the adaptive clinching auction [9]. We show that no wagering mechanism can simultaneously satisfy weak budget balance, individual rationality, weak incentive compatibility, and Pareto optimality. However, we prove that the double clinching auction attains the first three and show in a series of simulations using real contest data that it comes much closer to Pareto optimality than previously known incentive compatible wagering mechanisms, in some cases almost matching the efficiency of the Pareto optimal (but not incentive compatible) parimutuel consensus mechanism. When the goal of wagering is to crowdsource probabilities, Pareto optimality drives participation and incentive compatibility drives accuracy, making the double clinching auction an attractive and practical choice. Our mechanism may be of independent interest as the first two-sided version of the adaptive clinching auction.

Fair and Efficient Social Choice in Dynamic Settings

We study a dynamic social choice problem in which an alternative is chosen at each round according to the reported valuations of a set of agents. In the interests of obtaining a solution that is both efficient and fair, we aim to maximize the long-term Nash welfare, which is the product of all agents’ utilities. We present and analyze two greedy algorithms for this problem, including the classic Proportional Fair (PF) algorithm. We analyze several versions of the algorithms and how they relate, and provide an axiomatization of PF. Finally, we evaluate the algorithms on data gathered from a computer systems application.

On the Price of Stability of Undirected Multicast Games

In multicast network design games, a set of agents choose paths from their source locations to a common sink with the goal of minimizing their individual costs, where the cost of an edge is divided equally among the agents using it. Since the work of Anshelevich et al. FOCS 2004 that introduced network design games, the main open problem in this field has been the price of stability PoS of multicast games. For the special case of broadcast games every vertex is a terminal, i.e., has an agent, a series of works has culminated in a constant upper bound on the PoS Bilo et al., FOCS 2013. However, no significantly sub-logarithmic bound is known for multicast games. In this paper, we make progress toward resolving this question by showing a constant upper bound on the PoS of multicast games for quasi-bipartite graphs. These are graphs where all edges are between two terminals as in broadcast games or between a terminal and a nonterminal, but there is no edge between nonterminals. This represents a natural class of intermediate generality between broadcast and multicast games. In addition to the result itself, our techniques overcome some of the fundamental difficulties of analyzing the PoS of general multicast games, and are a promising step toward resolving this major open problem.