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62
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 58 (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.
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 55 (8 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.
A Multivariate Complexity Analysis of Determining Possible Winners Given Incomplete Votes
"... The POSSIBLE WINNER problem asks whether some distinguished candidate may become the winner of an election when the given incomplete votes are extended into complete ones in a favorable way. POSSIBLE WINNER is NPcomplete for common voting rules such as Borda, many other positional scoring rules, Bu ..."
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Cited by 35 (9 self)
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The POSSIBLE WINNER problem asks whether some distinguished candidate may become the winner of an election when the given incomplete votes are extended into complete ones in a favorable way. POSSIBLE WINNER is NPcomplete for common voting rules such as Borda, many other positional scoring rules, Bucklin, Copeland etc. We investigate how three different parameterizations influence the computational complexity of POSSIBLE WINNER for a number of voting rules. We show fixedparameter tractability results with respect to the parameter “number of candidates ” but intractability results with respect to the parameter “number of votes”. Finally, we derive fixedparameter tractability results with respect to the parameter “total number of undetermined candidate pairs ” and identify an interesting polynomialtime solvable special case for Borda. 1
Swap bribery
, 2009
"... Abstract. In voting theory, bribery is a form of manipulative behavior in which an external actor (the briber) offers to pay the voters to change their votes in order to get her preferred candidate elected. We investigate a model of bribery where the price of each vote depends on the amount of chang ..."
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Cited by 30 (12 self)
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Abstract. In voting theory, bribery is a form of manipulative behavior in which an external actor (the briber) offers to pay the voters to change their votes in order to get her preferred candidate elected. We investigate a model of bribery where the price of each vote depends on the amount of change that the voter is asked to implement. Specifically, in our model the briber can change a voter’s preference list by paying for a sequence of swaps of consecutive candidates. Each swap may have a different price; the price of a bribery is the sum of the prices of all swaps that it involves. We prove complexity results for this model, which we call swap bribery, for a broad class of voting rules, including variants of approval and kapproval, Borda, Copeland, and maximin. 1
Robust Approximation and Incremental Elicitation in Voting Protocols
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
"... While voting schemes provide an effective means for aggregating preferences, methods for the effective elicitation of voter preferences have received little attention. We address this problem by first considering approximate winner determination when incomplete voter preferences are provided. Exploi ..."
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Cited by 29 (13 self)
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While voting schemes provide an effective means for aggregating preferences, methods for the effective elicitation of voter preferences have received little attention. We address this problem by first considering approximate winner determination when incomplete voter preferences are provided. Exploiting natural scoring metrics, we use max regret to measure the quality or robustness of proposed winners, and develop polynomial time algorithms for computing the alternative with minimax regret for several popular voting rules. We then show how minimax regret can be used to effectively drive incremental preference/vote elicitation and devise several heuristics for this process. Despite worstcase theoretical results showing that most voting protocols require nearly complete voter preferences to determine winners, we demonstrate the practical effectiveness of regretbased elicitation for determining both approximate and exact winners on several realworld data sets.
A Maximum Likelihood Approach towards Aggregating Partial Orders
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
"... In many of the possible applications as well as the theoretical models of computational social choice, the agents ’ preferences are represented as partial orders. In this paper, we extend the maximum likelihood approach for defining “optimal ” voting rules to this setting. We consider distributions ..."
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Cited by 22 (10 self)
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In many of the possible applications as well as the theoretical models of computational social choice, the agents ’ preferences are represented as partial orders. In this paper, we extend the maximum likelihood approach for defining “optimal ” voting rules to this setting. We consider distributions in which the pairwise comparisons/incomparabilities between alternatives are drawn i.i.d. We call such models pairwiseindependent models and show that they correspond to a class of voting rules that we call pairwise scoring rules. This generalizes rules such as Kemeny and Borda. Moreover, we show that Borda is the only pairwise scoring rule that satisfies neutrality, when the outcome space is the set of all alternatives. We then study which voting rules defined for linear orders can be extended to partial orders via our MLE model. We show that any weakly neutral outcome scoring rule (including any ranking/candidate scoring rule) based on the weighted majority graph can be represented as the MLE of a weakly neutral pairwiseindependent model. Therefore, all such rules admit natural extensions to profiles of partial orders. Finally, we propose a specific MLE model πk for generating a set of k winning alternatives, and study the computational complexity of winner determination for the MLE of πk.
Practical voting rules with partial information
 AUTON AGENT MULTIAGENT SYST
, 2010
"... Voting is an essential mechanism that allows multiple agents to reach a joint decision. The joint decision, representing a function over the preferences of all agents, is the winner among all possible (candidate) decisions. To compute the winning candidate, previous work has typically assumed that ..."
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Cited by 20 (4 self)
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Voting is an essential mechanism that allows multiple agents to reach a joint decision. The joint decision, representing a function over the preferences of all agents, is the winner among all possible (candidate) decisions. To compute the winning candidate, previous work has typically assumed that voters send their complete set of preferences for computation, and in fact this has been shown to be required in the worst case. However, in practice, it may be infeasible for all agents to send a complete set of preferences due to communication limitations and willingness to keep as much information private as possible. The goal of this paper is to empirically evaluate algorithms to reduce communication on various sets of experiments. Accordingly, we propose an iterative algorithm that allows the agents to send only part of their preferences, incrementally. Experiments with simulated and realworld data show that this algorithm results in an average of 35 % savings in communications, while guaranteeing that the actual winning candidate is revealed. A second algorithm applies a greedy heuristic to save up to 90 % of communications. While this heuristic algorithm cannot guarantee that a true winning candidate is found, we show that in practice, close approximations are obtained.
Compiling the Votes of a Subelectorate
"... In many practical contexts where a number of agents have to find a common decision, the votes do not come all together at the same time. In such situations, we may want to preprocess the information given by the subelectorate (consisting of the voters who have expressed their votes) so as to “compil ..."
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Cited by 19 (4 self)
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In many practical contexts where a number of agents have to find a common decision, the votes do not come all together at the same time. In such situations, we may want to preprocess the information given by the subelectorate (consisting of the voters who have expressed their votes) so as to “compile” the known votes for the time when the latecomers have expressed their votes. We study the amount of space necessary for such a compilation, as a function of the voting rule, the number of candidates, and the number of votes already known. We relate our results to existing work, especially on communication complexity. 1
Towards a dichotomy of finding possible winners in elections based on scoring rules
 In Proc. 34th MFCS, volume 5734 of LNCS
, 2009
"... Abstract. To make a joint decision, agents (or voters) are often required to provide their preferences as linear orders. To determine a winner, the given linear orders can be aggregated according to a voting protocol. However, in realistic settings, the voters may often only provide partial orders. ..."
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Cited by 19 (1 self)
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Abstract. To make a joint decision, agents (or voters) are often required to provide their preferences as linear orders. To determine a winner, the given linear orders can be aggregated according to a voting protocol. However, in realistic settings, the voters may often only provide partial orders. This directly leads to the POSSIBLE WINNER problem that asks, given a set of partial votes, if a distinguished candidate can still become a winner. In this work, we consider the computational complexity of POSSIBLE WINNER for the broad class of voting protocols defined by scoring rules. A scoring rule provides a score value for every position which a candidate can have in a linear order. Prominent examples include plurality, kapproval, and Borda. Generalizing previous NPhardness results for some special cases and providing new manyone reductions, we settle the computational complexity for all but one scoring rule. More precisely, for an unbounded number of candidates and unweighted voters, we show that POSSIBLE WINNER is NPcomplete for all pure scoring rules except plurality, veto, and the scoring rule defined by the scoring vector (2,1,..., 1, 0), while it is solvable in polynomial time for plurality and veto. 1
Probabilistic possible winner determination
 In Proc. of 24th AAAI
, 2010
"... We study the computational complexity of the counting version of the POSSIBLEWINNER problem for elections. In the POSSIBLEWINNER problem we are given a profile of voters, each with a partial preference order, and ask if there are linear extensions of the votes such that a designated candidate wins ..."
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Cited by 17 (6 self)
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We study the computational complexity of the counting version of the POSSIBLEWINNER problem for elections. In the POSSIBLEWINNER problem we are given a profile of voters, each with a partial preference order, and ask if there are linear extensions of the votes such that a designated candidate wins. We also analyze a special case of POSSIBLEWINNER, the MANIPULATION problem. We provide polynomialtime algorithms for counting manipulations in a class of scoring protocols and in several other voting rules. We show #Phardness of the counting variant of POSSIBLEWINNER for plurality and veto and give a simple yet general and practically useful randomized algorithm for a variant of POSSIBLEWINNER for all voting rules for which a winner can be computed in polynomial time.