Journal of the ACM

In multiagent settings where the agents have different preferences, preference aggregation is a central issue. Voting is a general method for preference aggregation, but seminal results have shown that all general voting protocols are manipulable. One could try to avoid manipulation by using protocols where determining a beneficial manipulation is hard. Especially among computational agents, it is reasonable to measure this hardness by computational complexity. Some earlier work has been done in this area, but it was assumed that the number of voters and candidates is unbounded. Such hardness results lose relevance when the number of candidates is small, because manipulation algorithms that are exponential only in the number of candidates (and only slightly so) might be available. We give such an algorithm for an individual agent to manipulate the Single Transferable Vote (STV) protocol, which has been shown hard to manipulate in the above sense. This motivates the core of this article, which derives hardness results for realistic elections where the number of candidates is a small constant (but the number of voters can be large).The main manipulation question we study is that of coalitional manipulation by weighted voters. (We show that for simpler manipulation problems, manipulation cannot be hard with few candidates.) We study both constructive manipulation (making a given candidate win) and destructive manipulation (making a given candidate not win). We characterize the exact number of candidates for which manipulation becomes hard for the plurality, Borda, STV, Copeland, maximin, veto, plurality with runoff, regular cup, and randomized cup protocols. We also show that hardness of manipulation in this setting implies hardness of manipulation by an individual in unweighted settings when there is uncertainty about the others' votes (but not vice-versa). To our knowledge, these are the first results on the hardness of manipulation when there is uncertainty about the others' votes.

/pdf/when-are-elections-with-few-candidates-hard-to-manipulate-qnd849b3g9.pdf

When are elections with few candidates hard to manipulate

The rapidly growing field of computational social choice, at the intersection of computer science and economics, deals with the computational aspects of collective decision making. This handbook, written by thirty-six prominent members of the computational social choice community, covers the field comprehensively. Chapters devoted to each of the field's major themes offer detailed introductions. Topics include voting theory (such as the computational complexity of winner determination and manipulation in elections), fair allocation (such as algorithms for dividing divisible and indivisible goods), coalition formation (such as matching and hedonic games), and many more. Graduate students, researchers, and professionals in computer science, economics, mathematics, political science, and philosophy will benefit from this accessible and self-contained book.

/pdf/handbook-of-computational-social-choice-12i1xbv1b8.pdf

Handbook of Computational Social Choice

The theory of cooperative games provides a rich mathematical framework with which to understand the interactions between self-interested agents in settings where they can benefit from cooperation, and where binding agreements between agents can be made. Our aim in this talk is to describe the issues that arise when we consider cooperative game theory through a computational lens. We begin by introducing basic concepts from cooperative game theory, and in particular the key solution concepts: the core and the Shapley value. We then introduce the key issues that arise if one is to consider the cooperative games in a computational setting: in particular, the issue of representing games, and the computational complexity of cooperative solution concepts.

/pdf/computational-aspects-of-cooperative-game-theory-22sw4t9fz8.pdf

Computational Aspects of Cooperative Game Theory

The literature on algorithmic mechanism design is mostly concerned with game-theoretic versions of optimization problems to which standard economic money-based mechanisms cannot be applied efficiently. Recent years have seen the design of various truthful approximation mechanisms that rely on payments. In this article, we advocate the reconsideration of highly structured optimization problems in the context of mechanism design. We explicitly argue for the first time that, in such domains, approximation can be leveraged to obtain truthfulness without resorting to payments. This stands in contrast to previous work where payments are almost ubiquitous and (more often than not) approximation is a necessary evil that is required to circumvent computational complexity.We present a case study in approximate mechanism design without money. In our basic setting, agents are located on the real line and the mechanism must select the location of a public facility; the cost of an agent is its distance to the facility. We establish tight upper and lower bounds for the approximation ratio given by strategyproof mechanisms without payments, with respect to both deterministic and randomized mechanisms, under two objective functions: the social cost and the maximum cost. We then extend our results in two natural directions: a domain where two facilities must be located and a domain where each agent controls multiple locations.

/pdf/approximate-mechanism-design-without-money-2pt91l4prf.pdf

Approximate mechanism design without money

We study the complexity of influencing elections through bribery: How computationally complex is it for an external actor to determine whether by a certain amount of bribing voters a specified candidate can be made the election's winner? We study this problem for election systems as varied as scoring protocols and Dodgson voting, and in a variety of settings regarding homogeneous-vs.-nonhomogeneous electorate bribability, bounded-size-vs.-arbitrary-sized candidate sets, weighted-vs.-unweighted voters, and succinct-vs.-nonsuccinct input specification. We obtain both polynomial-time bribery algorithms and proofs of the intractability of bribery, and indeed our results show that the complexity of bribery is extremely sensitive to the setting. For example, we find settings in which bribery is NP-complete but manipulation (by voters) is in P, and we find settings in which bribing weighted voters is NP-complete but bribing voters with individual bribe thresholds is in P. For the broad class of elections (including plurality, Borda, k-approval, and veto) known as scoring protocols, we prove a dichotomy result for bribery of weighted voters: We find a simple-to-evaluate condition that classifies every case as either NP-complete or in P.

/pdf/the-complexity-of-bribery-in-elections-38nylt6ihi.pdf

The complexity of bribery in elections

In 1992, Bartholdi, Tovey, and Trick [1992] opened the study of control attacks on elections--attempts to improve the election outcome by such actions as adding/deleting candidates or voters. That work has led to many results on how algorithms can be used to find attacks on elections and how complexity-theoretic hardness results can be used as shields against attacks. However, all the work in this line has assumed that the attacker employs just a single type of attack. In this paper, we model and study the case in which the attacker launches a multipronged (i.e., multimode) attack. We do so to more realistically capture the richness of reallife settings. For example, an attacker might simultaneously try to suppress some voters, attract new voters into the election, and introduce a spoiler candidate. Our model provides a unified framework for such varied attacks, and by constructing polynomial-time multiprong attack algorithms we prove that for various election systems even such concerted, flexible attacks can be perfectly planned in deterministic polynomial time.

/pdf/multimode-control-attacks-on-elections-4g3reil5nd.pdf

Multimode control attacks on elections

We study elections in which voters may submit partial ballots consisting of truncated lists: each voter ranks some of her top candidates (and possibly some of her bottom candidates) and is indifferent among the remaining ones. Holding elections with such votes requires adapting classical voting rules (which expect complete rankings as input) and these adaptations create various opportunities for candidates who want to increase their chances of winning. We provide complexity results regarding planning various kinds of campaigns in such settings, and we study the complexity of the possible winner problem for the case of truncated votes.

/pdf/campaigns-for-lazy-voters-truncated-ballots-1ssaf3qz7l.pdf

Campaigns for lazy voters: truncated ballots

Achieving fully proportional representation

In elections, a set of candidates ranked consecutively (though possibly in different order) by all voters is called a clone set, and its members are called clones. A clone structure is the family of all clone sets of a given election. In this paper we study properties of clone structures. In particular, we give an axiomatic characterization of clone structures, show that they are organized hierarchically, and analyze clone structures in single-peaked and single-crossing elections. We describe a polynomial-time algorithm that finds a minimal collection of clones that need to be collapsed for an election to become single-peaked, and we show that this problem is NP-hard for single-crossing elections.

/pdf/clone-structures-in-voters-preferences-11thm6pbny.pdf

Piotr Faliszewski

Papers

The complexity of bribery in elections

Multimode control attacks on elections

Campaigns for lazy voters: truncated ballots

Achieving fully proportional representation

Clone structures in voters' preferences