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95
A short introduction to computational social choice
 Proc. 33rd Conference on Current Trends in Theory and Practice of Computer Science
, 2007
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Determining possible and necessary winners under common voting rules given partial orders.
 In Proceedings of the National Conference on Artificial Intelligence (AAAI),
, 2008
"... Abstract Usually a voting rule requires agents to give their preferences as linear orders. However, in some cases it is impractical for an agent to give a linear order over all the alternatives. It has been suggested to let agents submit partial orders instead. Then, given a voting rule, a profile ..."
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Cited by 63 (11 self)
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Abstract Usually a voting rule requires agents to give their preferences as linear orders. However, in some cases it is impractical for an agent to give a linear order over all the alternatives. It has been suggested to let agents submit partial orders instead. Then, given a voting rule, a profile of partial orders, and an alternative (candidate) c, two important questions arise: first, is it still possible for c to win, and second, is c guaranteed to win? These are the possible winner and necessary winner problems, respectively. Each of these two problems is further divided into two subproblems: determining whether c is a unique winner (that is, c is the only winner), or determining whether c is a cowinner (that is, c is in the set of winners). We consider the setting where the number of alternatives is unbounded and the votes are unweighted. We completely characterize the complexity of possible/necessary winner problems for the following common voting rules: a class of positional scoring rules (including Borda), Copeland, maximin, Bucklin, ranked pairs, voting trees, and plurality with runoff.
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 (13 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 57 (9 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.
Uncertainty in preference elicitation and aggregation
 In AAAI’07
, 2007
"... Uncertainty arises in preference aggregation in several ways. There may, for example, be uncertainty in the votes or the voting rule. Such uncertainty can introduce computational complexity in determining which candidate or candidates can or must win the election. In this paper, we survey recent wor ..."
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Cited by 51 (13 self)
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Uncertainty arises in preference aggregation in several ways. There may, for example, be uncertainty in the votes or the voting rule. Such uncertainty can introduce computational complexity in determining which candidate or candidates can or must win the election. In this paper, we survey recent work in this area and give some new results. We argue, for example, that the set of possible winners can be computationally harder to compute than the necessary winner. As a second example, we show that, even if the unknown votes are assumed to be singlepeaked, it remains computationally hard to compute the possible and necessary winners, or to manipulate the election.
Winner determination in sequential majority voting
 In Proceedings of the ECAI2006 Multidisciplinary Workshop on Advances in Preference Handling
, 2007
"... Preferences can be aggregated using a voting rule. Each agent gives their preference orderings over a set of candidates, and a voting rule is used to compute the winner. We consider voting rules which perform a sequence of pairwise comparisons between two candidates, where the result of each is comp ..."
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Cited by 45 (14 self)
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Preferences can be aggregated using a voting rule. Each agent gives their preference orderings over a set of candidates, and a voting rule is used to compute the winner. We consider voting rules which perform a sequence of pairwise comparisons between two candidates, where the result of each is computed by a majority vote. The winner thus depends on the chosen sequence of comparisons, which can be represented by a binary tree. There are candidates that will win in some trees (called possible winners) or in all trees (called Condorcet winners). While it is easy to find the possible and Condorcet winners, we prove that it is difficult if we insist that the tree is balanced. This restriction is therefore enough to make voting difficult for the chair to manipulate. We also consider the situation where we lack complete informations about preferences, and determine the computational complexity of computing possible and Condorcet winners in this extended case. 1
Incompleteness and Incomparability in Preference Aggregation
 In Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI 2007
, 2007
"... We consider how to combine the preferences of multiple agents despite the presence of incompleteness and incomparability in their preference orderings. An agent’s preference ordering may be incomplete because, for example, there is an ongoing preference elicitation process. It may also contain incom ..."
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Cited by 43 (16 self)
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We consider how to combine the preferences of multiple agents despite the presence of incompleteness and incomparability in their preference orderings. An agent’s preference ordering may be incomplete because, for example, there is an ongoing preference elicitation process. It may also contain incomparability as this is useful, for example, in multicriteria scenarios. We focus on the problem of computing the possible and necessary winners, that is, those outcomes which can be or always are the most preferred for the agents. Possible and necessary winners are useful in many scenarios including preference elicitation. First we show that computing the sets of possible and necessary winners is in general a difficult problem as is providing a good approximation of such sets. Then we identify general properties of the preference aggregation function which are sufficient for such sets to be computed in polynomial time. Finally, we show how possible and necessary winners can be used to focus preference elicitation. 1
Bypassing Combinatorial Protections: PolynomialTime Algorithms for Singlepeaked Electorates
, 2010
"... For many election systems, bribery (and related) attacks have been shown NPhard using constructions on combinatorially rich structures such as partitions and covers. It is important to learn how robust these hardness protection results are, in order to find whether they can be relied on in practice ..."
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Cited by 35 (5 self)
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For many election systems, bribery (and related) attacks have been shown NPhard using constructions on combinatorially rich structures such as partitions and covers. It is important to learn how robust these hardness protection results are, in order to find whether they can be relied on in practice. This paper shows that for voters who follow the most central politicalscience model of electorates—singlepeaked preferences—those protections vanish. By using singlepeaked preferences to simplify combinatorial covering challenges, we show that NPhard bribery problems—including those for Kemeny and Llull elections—fall to polynomial time. By using singlepeaked preferences to simplify combinatorial partition challenges, we show that NPhard partitionofvoters problems fall to polynomial time. We furthermore show that for singlepeaked electorates, the winner problems for Dodgson and Kemeny elections, though Θ p 2complete in the general case, fall to polynomial time. And we completely classify the complexity of weighted coalition manipulation for scoring protocols in singlepeaked electorates.
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 32 (8 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 32 (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