Mattei, Nicholas

Strategyproof Peer Selection using Randomization, Partitioning, and Apportionment Artificial Intelligence

Peer review, evaluation, and selection is a fundamental aspect of modern science. Funding bodies the world over employ experts to review and select the best proposals of those submitted for funding. The problem of peer selection, however, is much more general: a professional society may want to give a subset of its members awards based on the opinions of all members; an instructor for a MOOC or online course may want to crowdsource grading; or a marketing company may select ideas from group brainstorming sessions based on peer evaluation. We make three fundamental contributions to the study of procedures or mechanisms for peer selection, a specific type of group decision-making problem, studied in computer science, economics, and political science. First, we propose a novel mechanism that is strategyproof, i.e., agents cannot benefit by reporting insincere valuations. Second, we demonstrate the effectiveness of our mechanism by a comprehensive simulation-based comparison with a suite of mechanisms found in the literature. Finally, our mechanism employs a randomized rounding technique that is of independent interest, as it solves the apportionment problem that arises in various settings where discrete resources such as parliamentary representation slots need to be divided proportionally.

Strategyproof Peer Selection: Mechanisms, Analyses, and Experiments

AAAI Conferences

We study an important crowdsourcing setting where agents evaluate one another and, based on these evaluations, a subset of agents are selected. This setting is ubiquitous when peer review is used for distributing awards in a team, allocating funding to scientists, and selecting publications for conferences. The fundamental challenge when applying crowdsourcing in these settings is that agents may misreport their reviews of others to increase their chances of being selected. We propose a new strategyproof (impartial) mechanism called Dollar Partition that satisfies desirable axiomatic properties. We then show, using a detailed experiment with parameter values derived from target real world domains, that our mechanism performs better on average, and in the worst case, than other strategyproof mechanisms in the literature.

Equilibria Under the Probabilistic Serial Rule

AAAI Conferences

The probabilistic serial (PS) rule is a prominent randomized rule for assigning indivisible goods to agents. Although it is well known for its good fairness and welfare properties, it is not strategyproof. In view of this, we address several fundamental questions regarding equilibria under PS. Firstly, we show that Nash deviations under the PS rule can cycle. Despite the possibilities of cycles, we prove that a pure Nash equilibrium is guaranteed to exist under the PS rule. We then show that verifying whether a given profile is a pure Nash equilibrium is coNP-complete, and computing a pure Nash equilibrium is NP-hard. For two agents, we present a linear-time algorithm to compute a pure Nash equilibrium which yields the same assignment as the truthful profile. Finally, we conduct experiments to evaluate the quality of the equilibria that exist under the PS rule, finding that the vast majority of pure Nash equilibria yield social welfare that is at least that of the truthful profile.

How Hard Is It to Control an Election by Breaking Ties? Artificial Intelligence

We study the computational complexity of controlling the result of an election by breaking ties strategically. This problem is equivalent to the problem of deciding the winner of an election under parallel universes tie-breaking. When the chair of the election is only asked to break ties to choose between one of the co-winners, the problem is trivially easy. However, in multi-round elections, we prove that it can be NP-hard for the chair to compute how to break ties to ensure a given result. Additionally, we show that the form of the tie-breaking function can increase the opportunities for control. Indeed, we prove that it can be NP-hard to control an election by breaking ties even with a two-stage voting rule.

On the Complexity of Bribery and Manipulation in Tournaments with Uncertain Information

AAAI Conferences

We study the computational complexity of optimal bribery and manipulation schemes for sports tournaments with uncertain information: cup; challenge or caterpillar; and round robin. Our results carry over to the equivalent voting rules: sequential pair-wise elections, cup, and Copeland, when the set of candidates is exactly the set of voters. This restriction creates new difficulties for most existing algorithms. The complexity of bribery and manipulation are well studied, almost always assuming deterministic information about votes and results. We assume that for candidates i and j the probability that i beats j and the costs of lowering each probability by fixed increments are known to the manipulators. We provide complexity analyses for cup, challenge, and round robin competitions ranging from polynomial time to NP^PP. This shows that the introduction of uncertainty into the reasoning process drastically increases the complexity of bribery problems in some instances.