In cooperative multiagent systems an alternative that maximizes the social welfare — the sum of utilities — can only be selected if each agent reports its full utility function. This may be infeasible in environments where communication is restricted. Employing a voting rule to choose an alternative greatly reduces the communication burden, but leads to a possible gap between the social welfare of the optimal alternative and the social welfare of the one that is ultimately elected. Procaccia and Rosenschein have introduced the concept of distortion to quantify this gap. In this paper, we present the notion of embeddings into voting rules: functions that receive an agent's utility function and return the agent's vote. We establish that very low distortion can be obtained using randomized embeddings, especially when the number of agents is large compared to the number of alternatives. We investigate our ideas in the context of three prominent voting rules with low communication costs: Plurality, Approval, and Veto. Our results arguably provide a compelling reason for employing voting in cooperative multiagent systems.

Cake cutting is a common metaphor for the division of a heterogeneous divisible good. There are numerous papers that study the problem of fairly dividing a cake; a small number of them also take into account self-interested agents and consequent strategic issues, but these papers focus on fairness and consider a strikingly weak notion of truthfulness. In this paper we investigate the problem of cutting a cake in a way that is truthful and fair, where for the first time our notion of dominant strategy truthfulness is the ubiquitous one in social choice and computer science. We design both deterministic and randomized cake cutting algorithms that are truthful and fair under different assumptions with respect to the valuation functions of the agents.

The Gibbard-Satterthwaite Theorem asserts that any reasonable voting rule cannot be strategyproof. A large body of research in AI deals with circumventing this theorem via computational considerations; the goal is to design voting rules that are computationally hard, in the worst-case, to manipulate. However, recent work indicates that the prominent voting rules are usually easy to manipulate. In this paper, we suggest a new CS-oriented approach to circumventing Gibbard-Satterthwaite, using randomization and approximation. Specifically, we wish to design strategyproof randomized voting rules that are close, in a standard approximation sense, to prominent score-based (deterministic) voting rules. We give tight lower and upper bounds on the approximation ratio achievable via strategyproof randomized rules with respect to positional scoring rules, Copeland, and Maximin.

We consider directed graphs over a set of n agents, where an edge (i,j) is taken to mean that agent i supports or trusts agent j. Given such a graph and an integer k\leq n, we wish to select a subset of k agents that maximizes the sum of indegrees, i.e., a subset of k most popular or most trusted agents. At the same time we assume that each individual agent is only interested in being selected, and may misreport its outgoing edges to this end. This problem formulation captures realistic scenarios where agents choose among themselves, which can be found in the context of Internet search, social networks like Twitter, or reputation systems like Epinions. Our goal is to design mechanisms without payments that map each graph to a k-subset of agents to be selected and satisfy the following two constraints: strategyproofness, i.e., agents cannot benefit from misreporting their outgoing edges, and approximate optimality, i.e., the sum of indegrees of the selected subset of agents is always close to optimal. Our first main result is a surprising impossibility: for k \in {1,...,n-1}, no deterministic strategyproof mechanism can provide a finite approximation ratio. Our second main result is a randomized strategyproof mechanism with an approximation ratio that is bounded from above by four for any value of k, and approaches one as k grows.

Understanding the computational complexity of manipulation in elections is arguably the most central agenda in Computational Social Choice. One of the influential variations of the the problem involves a coalition of manipulators trying to make a favorite candidate win the election. Although the complexity of the problem is well-studied under the assumption that the voters are weighted, there were very few successful attempts to abandon this strong assumption. In this paper, we study the complexity of the unweighted coalitional manipulation problem (UCM) under several prominent voting rules. Our main result is that UCM is NP-complete under the maximin rule; this resolves an enigmatic open question. We then show that UCM is NP-complete under the ranked pairs rule, even with respect to a single manipulator. Furthermore, we provide an extreme hardness-of-approximation result for an optimization version of UCM under ranked pairs. Finally, we show that UCM under the Bucklin rule is in P.