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32
The price of neutrality for the ranked pairs method
 In Proc. of AAAI2012
, 2012
"... The complexity of the winner determination problem has been studied for almost all common voting rules. A notable exception, possibly caused by some confusion regarding its exact definition, is the method of ranked pairs. The original version of the method, due to Tideman, yields a social preference ..."
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The complexity of the winner determination problem has been studied for almost all common voting rules. A notable exception, possibly caused by some confusion regarding its exact definition, is the method of ranked pairs. The original version of the method, due to Tideman, yields a social preference function that is irresolute and neutral. A variant introduced subsequently uses an exogenously given tiebreaking rule and therefore fails neutrality. The latter variant is the one most commonly studied in the area of computational social choice, and it is easy to see that its winner determination problem is computationally tractable. We show that by contrast, computing the set of winners selected by Tideman’s original ranked pairs method is NPcomplete, thus revealing a tradeoff between tractability and neutrality. In addition, several known results concerning the hardness of manipulation and the complexity of computing possible and necessary winners are shown to follow as corollaries from our findings. 1
Weighted Electoral Control
"... www.cs.rochester.edu/∼lane Although manipulation and bribery have been extensively studied under weighted voting, there has been almost no work done on election control under weighted voting. This is unfortunate, since weighted voting appears in many important natural settings. In this paper, we stu ..."
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Cited by 10 (6 self)
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www.cs.rochester.edu/∼lane Although manipulation and bribery have been extensively studied under weighted voting, there has been almost no work done on election control under weighted voting. This is unfortunate, since weighted voting appears in many important natural settings. In this paper, we study the complexity of controlling the outcome of weighted elections through adding and deleting voters. We obtain polynomialtime algorithms, NPcompleteness results, and for many NPcomplete cases, approximation algorithms. Our work shows that for quite a few important cases, either polynomialtime exact algorithms or polynomialtime approximation algorithms exist.
Computational aspects of nearly singlepeaked electorates
 In Proceedings of the 26th AAAI Conference on Artificial Intelligence
, 2013
"... Manipulation, bribery, and control are wellstudied ways of changing the outcome of an election. Many voting systems are, in the general case, computationally resistant to some of these manipulative actions. However when restricted to singlepeaked electorates, these systems suddenly become easy to ..."
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Cited by 10 (6 self)
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Manipulation, bribery, and control are wellstudied ways of changing the outcome of an election. Many voting systems are, in the general case, computationally resistant to some of these manipulative actions. However when restricted to singlepeaked electorates, these systems suddenly become easy to manipulate. Recently, Faliszewski, Hemaspaandra, and Hemaspaandra (2011b) studied the complexity of dishonest behavior in nearly singlepeaked electorates. These are electorates that are not singlepeaked but close to it according to some distance measure. In this paper we introduce several new distance measures regarding singlepeakedness. We prove that determining whether a given profile is nearly singlepeaked is NPcomplete in many cases. For one case we present a polynomialtime algorithm. Furthermore, we explore the relations between several notions of nearly singlepeakedness.
Complexity of Judgment Aggregation
"... We analyse the computational complexity of three problems in judgment aggregation: (1) computing a collective judgment from a profile of individual judgments (the winner determination problem); (2) deciding whether a given agent can influence the outcome of a judgment aggregation procedure in her fa ..."
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Cited by 7 (3 self)
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We analyse the computational complexity of three problems in judgment aggregation: (1) computing a collective judgment from a profile of individual judgments (the winner determination problem); (2) deciding whether a given agent can influence the outcome of a judgment aggregation procedure in her favour by reporting insincere judgments (the strategic manipulation problem); and (3) deciding whether a given judgment aggregation scenario is guaranteed to result in a logically consistent outcome, independently from what the judgments supplied by the individuals are (the problem of the safety of the agenda). We provide results both for specific aggregation procedures (the quota rules, the premisebased procedure, and a distancebased procedure) and for classes of aggregation procedures characterised in terms of fundamental axioms. 1.
Parameterized algorithmics for computational social choice: nine research challenges
 Tsinghua Science and Technology
, 2014
"... Computational Social Choice is an interdisciplinary research area involving Economics, Political Science, and Social Science on the one side, and Mathematics and Computer Science (including Artificial Intelligence and Multiagent Systems) on the other side. Typical computational problems studied in ..."
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Cited by 6 (3 self)
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Computational Social Choice is an interdisciplinary research area involving Economics, Political Science, and Social Science on the one side, and Mathematics and Computer Science (including Artificial Intelligence and Multiagent Systems) on the other side. Typical computational problems studied in this field include the vulnerability of voting procedures against attacks, or preference aggregation in multiagent systems. Parameterized Algorithmics is a subfield of Theoretical Computer Science seeking to exploit meaningful problemspecific parameters in order to identify tractable special cases of in general computationally hard problems. In this paper, we propose nine of our favorite research challenges concerning the parameterized complexity of problems appearing in this context.
The Complexity of Losing Voters
"... We consider the scenario of a parliament that is going to vote on a specific important issue. The voters are grouped in parties, and all voters of a party vote in the same way. The expected winner decision is known, because parties declare their intentions to vote, but before the actual vote takes p ..."
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We consider the scenario of a parliament that is going to vote on a specific important issue. The voters are grouped in parties, and all voters of a party vote in the same way. The expected winner decision is known, because parties declare their intentions to vote, but before the actual vote takes place some voters may leave the leading party to join other parties. We investigate the computational complexity of the problem of determining how many voters need to leave the leading party before the winner changes. We consider both positional scoring rules (plurality, veto, kapproval, kveto, Borda) and Condorcetconsistent methods (maximin, Copeland), and we study two versions of the problem: a pessimistic one, where we want to determine the maximal number of voters that can leave the leading party without changing the winner; and an optimistic one, where we want the minimal number of voters that must leave the leading party to be sure the winner will change. These two numbers provide a measure of the threat to the expected winner, and thus to the leading party, given by losing some voters. We show that for many positional scoring rules these problems are easy (except for the optimistic version with kapproval, for k at least 3, and Borda). Instead, for Condorcetconsistent rules, they are both computationally difficult, with both Maximin and Copeland.
Multivariate Algorithmics for NPHard String Problems
, 2014
"... String problems arise in various applications ranging from text mining to biological sequence analysis. Many string problems are NPhard. This motivates the search for (fixedparameter) tractable special cases of these problems. We survey parameterized and multivariate algorithmics results for NPha ..."
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String problems arise in various applications ranging from text mining to biological sequence analysis. Many string problems are NPhard. This motivates the search for (fixedparameter) tractable special cases of these problems. We survey parameterized and multivariate algorithmics results for NPhard string problems and identify challenges for future research.
It Only Takes a Few: On the Hardness of Voting With a Constant Number of Agents
, 2013
"... Many hardness results in computational social choice make use of the fact that every directed graph may be induced by the pairwise majority relation. However, this fact requires that the number of voters is almost linear in the number of alternatives. It is therefore unclear whether existing hardnes ..."
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Many hardness results in computational social choice make use of the fact that every directed graph may be induced by the pairwise majority relation. However, this fact requires that the number of voters is almost linear in the number of alternatives. It is therefore unclear whether existing hardness results remain intact when the number of voters is bounded, as is for example typically the case in search engine aggregation settings. In this paper, we provide sufficient conditions for majority graphs to be obtainable using a constant number of voters and leverage these conditions to show that winner determination for the Banks set, the tournament equilibrium set, Slater’s rule, and ranked pairs remains hard even when there is only a small constant number of voters.
On the Discriminative Power of Tournament Solutions
, 2014
"... Tournament solutions constitute an important class of social choice functions that only depend on the pairwise majority comparisons between alternatives. Recent analytical results have shown that several concepts with appealing axiomatic properties such as the Banks set or the minimal covering set t ..."
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Cited by 1 (1 self)
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Tournament solutions constitute an important class of social choice functions that only depend on the pairwise majority comparisons between alternatives. Recent analytical results have shown that several concepts with appealing axiomatic properties such as the Banks set or the minimal covering set tend to not discriminate at all when the tournaments are chosen from the uniform distribution. This is in sharp contrast to empirical studies which have found that realworld preference profiles often exhibit Condorcet winners, i.e., alternatives that all tournament solutions select as the unique winner. In this work, we aim to fill the gap between these extremes by examining the distribution of the number of alternatives returned by common tournament solutions for empirical data as well as data generated according to stochastic preference models such as impartial culture, impartial anonymous culture, Mallows mixtures, spatial models, and PólyaEggenberger urn models.
Strategic Abstention based on Preference Extensions: Positive Results and ComputerGenerated Impossibilities
, 2015
"... Voting rules are powerful tools that allow multiple agents to aggregate their preferences in order to reach joint decisions. A common flaw of some voting rules, known as the noshow paradox, is that agents may obtain a more preferred outcome by abstaining an election. We study strategic abstention ..."
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Voting rules are powerful tools that allow multiple agents to aggregate their preferences in order to reach joint decisions. A common flaw of some voting rules, known as the noshow paradox, is that agents may obtain a more preferred outcome by abstaining an election. We study strategic abstention for setvalued voting rules based on Kelly’s and Fishburn’s preference extensions. Our contribution is twofold. First, we show that, whenever there are at least five alternatives, every Paretooptimal majoritarian voting rule suffers from the noshow paradox with respect to Fishburn’s extension. This is achieved by reducing the statement to a finite—yet very large—problem, which is encoded as a formula in propositional logic and then shown to be unsatisfiable by a SAT solver. We also provide a humanreadable proof which we extracted from a minimal unsatisfiable core of the formula. Secondly, we prove that every voting rule that satisfies two natural conditions cannot be manipulated by strategic abstention with respect to Kelly’s extension. We conclude by giving examples of wellknown Paretooptimal majoritarian voting rules that meet these requirements. 1