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56
Compilation complexity of common voting rules
, 2010
"... In computational social choice, one important problem is to take the votes of a subelectorate (subset of the voters), and summarize them using a small number of bits. This needs to be done in such a way that, if all that we know is the summary, as well as the votes of voters outside the subelectorat ..."
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Cited by 41 (12 self)
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In computational social choice, one important problem is to take the votes of a subelectorate (subset of the voters), and summarize them using a small number of bits. This needs to be done in such a way that, if all that we know is the summary, as well as the votes of voters outside the subelectorate, we can conclude which of the m alternatives wins. This corresponds to the notion of compilation complexity, the minimum number of bits required to summarize the votes for a particular rule, which was introduced by Chevaleyre et al. [IJCAI09]. We study three different types of compilation complexity. The first, studied by Chevaleyre et al., depends on the size of the subelectorate but not on the size of the complement (the voters outside the subelectorate). The second depends on the size of the complement but not on the size of the subelectorate. The third depends on both. We first investigate the relations among the three types of compilation complexity. Then, we give upper and lower bounds on all three types of compilation complexity for the most prominent voting rules. We show that for lapproval (when l ≤ m/2), Borda, and Bucklin, the bounds for all three types are asymptotically tight, up to a multiplicative constant; for lapproval (when l> m/2), plurality with runoff, all Condorcet consistent rules that are based on unweighted majority graphs (including Copeland and voting trees), and all Condorcet consistent rules that are based on the order of pairwise elections (including ranked pairs and maximin), the bounds for all three types are asymptotically tight up to a multiplicative constant when the sizes of the subelectorate and its complement are both larger than m 1+ǫ for some ǫ> 0.
Preference Functions That Score Rankings and Maximum Likelihood Estimation
"... A preference function (PF) takes a set of votes (linear orders over a set of alternatives) as input, and produces one or more rankings (also linear orders over the alternatives) as output. Such functions have many applications, for example, aggregating the preferences of multiple agents, or merging ..."
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Cited by 38 (14 self)
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A preference function (PF) takes a set of votes (linear orders over a set of alternatives) as input, and produces one or more rankings (also linear orders over the alternatives) as output. Such functions have many applications, for example, aggregating the preferences of multiple agents, or merging rankings (of, say, webpages) into a single ranking. The key issue is choosing a PF to use. One natural and previously studied approach is to assume that there is an unobserved “correct ” ranking, and the votes are noisy estimates of this. Then, we can use the PF that always chooses the maximum likelihood estimate (MLE) of the correct ranking. In this paper, we define simple ranking scoring functions (SRSFs) and show that the class of neutral SRSFs is exactly the class of neutral PFs that are MLEs for some noise model. We also define extended ranking scoring functions (ERSFs) and show a condition under which these coincide with SRSFs. We study key properties such as consistency and continuity, and consider some example PFs. In particular, we study Single Transferable Vote (STV), a commonly used PF, showing that it is an ERSF but not an SRSF, thereby clarifying the extent to which it is an MLE function. This also gives a new perspective on how ties should be broken under STV. We leave some open questions. 1
AI’s war on manipulation: Are we winning
 AI Magazine
"... We provide an overview of more than two decades of work, mostly in AI, that studies computational complexity as a barrier against manipulation in elections. ..."
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Cited by 34 (6 self)
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We provide an overview of more than two decades of work, mostly in AI, that studies computational complexity as a barrier against manipulation in elections.
Llull and Copeland voting computationally resist bribery and control
, 2009
"... Control and bribery are settings in which an external agent seeks to influence the outcome of an election. Constructive control of elections refers to attempts by an agent to, via such actions as addition/deletion/partition of candidates or voters, ensure that a given candidate wins. Destructive con ..."
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Cited by 34 (17 self)
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Control and bribery are settings in which an external agent seeks to influence the outcome of an election. Constructive control of elections refers to attempts by an agent to, via such actions as addition/deletion/partition of candidates or voters, ensure that a given candidate wins. Destructive control refers to attempts by an agent to, via the same actions, preclude a given candidate’s victory. An election system in which an agent can sometimes affect the result and it can be determined in polynomial time on which inputs the agent can succeed is said to be vulnerable to the given type of control. An election system in which an agent can sometimes affect the result, yet in which it is NPhard to recognize the inputs on which the agent can succeed, is said to be resistant to the given type of control. Aside from election systems with an NPhard winner problem, the only systems previously known to be resistant to all the standard control types were highly artificial election systems created by hybridization. This paper studies a parameterized version of Copeland voting, denoted by Copeland α, where the parameter α is a rational number between 0 and 1 that specifies how ties are valued in the pairwise comparisons of candidates. In every previously studied constructive or destructive
A Scheduling Approach to Coalitional Manipulation
"... The coalitional manipulation problem is one of the central problems in computational social choice. In this paper we focus on solving the problem under the important family of positional scoring rules, in an approximate sense that was advocated by Zuckerman et al. [SODA 2008]. Our main result is a p ..."
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Cited by 28 (12 self)
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The coalitional manipulation problem is one of the central problems in computational social choice. In this paper we focus on solving the problem under the important family of positional scoring rules, in an approximate sense that was advocated by Zuckerman et al. [SODA 2008]. Our main result is a polynomialtime algorithm with (roughly speaking) the following theoretical guarantee: given a manipulable instance with m alternatives the algorithm finds a successful manipulation with at most m − 2 additional manipulators. Our technique is based on a reduction to the scheduling problem known as QpmtnCmax, along with a novel rounding procedure. We demonstrate that our analysis is tight by establishing a new type of integrality gap. We also resolve a known open question in computational social choice by showing that the coalitional manipulation problem remains (strongly) NPcomplete for positional scoring rules even when votes are unweighted. Finally, we discuss the implications of our results with respect to the question: “Is there a prominent voting rule that is usually hard to manipulate?”
Unweighted coalitional manipulation under the Borda rule is NPhard
 In IJCAI11
, 2011
"... The Borda voting rule is a positional scoring rule where, for m candidates, for every vote the first candidate receives m − 1 points, the second m − 2 points and so on. A Borda winner is a candidate with highest total score. It has been a prominent open problem to determine the computational complex ..."
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Cited by 18 (0 self)
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The Borda voting rule is a positional scoring rule where, for m candidates, for every vote the first candidate receives m − 1 points, the second m − 2 points and so on. A Borda winner is a candidate with highest total score. It has been a prominent open problem to determine the computational complexity of UNWEIGHTED COALITIONAL MANIPULATION UNDER BORDA: Can one add a certain number of additional votes (called manipulators) to an election such that a distinguished candidate becomes a winner? We settle this open problem by showing NPhardness even for two manipulators and three input votes. Moreover, we discuss extensions and limitations of this hardness result. 1
Finite local consistency characterizes generalized scoring rules
 IJCAI
, 2009
"... An important problem in computational social choice concerns whether it is possible to prevent manipulation of voting rules by making it computationally intractable. To answer this, a key question is how frequently voting rules are manipulable. We [Xia and Conitzer, 2008] recently defined the class ..."
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Cited by 17 (9 self)
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An important problem in computational social choice concerns whether it is possible to prevent manipulation of voting rules by making it computationally intractable. To answer this, a key question is how frequently voting rules are manipulable. We [Xia and Conitzer, 2008] recently defined the class of generalized scoring rules (GSRs) and characterized the frequency of manipulability for such rules. We showed, by examples, that most common rules seem to fall into this class. However, no natural axiomatic characterization of the class was given, leaving the possibility that there are natural rules to which these results do not apply. In this paper, we characterize the class of GSRs based on two natural properties: it is equal to the class of rules that are anonymous and finitely locally consistent. Generalized scoring rules also have other uses in computational social choice. For these uses, the order of the GSR (the dimension of its score vector) is important. Our characterization result implies that the order of a GSR is related to the minimum number of locally consistent components of the rule. We proceed to bound the minimum number of locally consistent components for some common rules. 1
Multimode Control Attacks on 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 complexi ..."
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Cited by 17 (4 self)
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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 complexitytheoretic 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 polynomialtime multiprong attack algorithms we prove that for various election systems even such concerted, flexible attacks can be perfectly planned in deterministic polynomial time. 1