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47
Single transferable vote resists strategic voting
, 2003
"... We give evidence that Single Tranferable Vote (STV) is computationally resistant to manipulation: It is NPcomplete to determine whether there exists a (possibly insincere) preference that will elect a favored candidate, even in an election for a single seat. Thus strategic voting under STV is qual ..."
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Cited by 141 (0 self)
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We give evidence that Single Tranferable Vote (STV) is computationally resistant to manipulation: It is NPcomplete to determine whether there exists a (possibly insincere) preference that will elect a favored candidate, even in an election for a single seat. Thus strategic voting under STV is qualitatively more difficult than under other commonlyused voting schemes. Furthermore, this resistance to manipulation is inherent to STV and does not depend on hopeful extraneous assumptions like the presumed difficulty of learning the preferences of the other voters. We also prove that it is NPcomplete to recognize when an STV election violates monotonicity. This suggests that nonmonotonicity in STV elections might be perceived as less threatening since it is in effect “hidden” and hard to exploit for strategic advantage.
How hard is it to control an election
 Mathematical and Computer Modeling
, 1992
"... Some voting schemes that are in principle susceptible to control are nevertheless resistant in practice due to excessive computational costs; others are vulnerable. We illustrate this in detail for plurality voting and for Condorcet voting. 1 ..."
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Cited by 79 (0 self)
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Some voting schemes that are in principle susceptible to control are nevertheless resistant in practice due to excessive computational costs; others are vulnerable. We illustrate this in detail for plurality voting and for Condorcet voting. 1
Nonexistence of Voting Rules That Are Usually Hard to Manipulate
, 2006
"... ... problem for multiagent systems, and one general method for doing so is to vote over the alternatives (candidates). Unfortunately, the GibbardSatterthwaite theorem shows that when there are three or more candidates, all reasonable voting rules are manipulable (in the sense that there exist s ..."
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Cited by 76 (6 self)
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... problem for multiagent systems, and one general method for doing so is to vote over the alternatives (candidates). Unfortunately, the GibbardSatterthwaite theorem shows that when there are three or more candidates, all reasonable voting rules are manipulable (in the sense that there exist situations in which a voter would benefit from reporting its preferences insincerely). To circumvent this impossibility result, recent research has investigated whether it is possible to make finding a beneficial manipulation computationally hard. This approach has had some limited success, exhibiting rules under which the problem of finding a beneficial manipulation is NP hard, #Phard, or even PSPACEhard. Thus, under these rules, it is unlikely that a computationally efficient algorithm can be constructed that always finds a beneficial manipulation (when it exists). However, this still does not preclude the existence of an efficient algorithm that often finds a successful manipulation (when it exists). There have been attempts to design a rule under which finding a beneficial manipulation is usually hard, but they have failed. To explain this failure, in this paper, we show that it is in fact impossible to design such a rule, if the rule is also required to satisfy another property: a large fraction of the manipulable instances are both weakly monotone, and allow the manipulators to make either of exactly two candidates win. We argue why one should expect voting rules to have this property, and show experimentally that common voting rules clearly satisfy it. We also discuss approaches for potentially circumventing this impossibility result.
Computing Shapley values, manipulating value division schemes, and checking core membership in multiissue domains
 IN PROCEEDINGS OF THE NATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE (AAAI
, 2004
"... Coalition formation is a key problem in automated negotiation among selfinterested agents. In order for coalition formation to be successful, a key question that must be answered is how the gains from cooperation are to be distributed. Various solution concepts have been proposed, but the computati ..."
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Cited by 53 (7 self)
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Coalition formation is a key problem in automated negotiation among selfinterested agents. In order for coalition formation to be successful, a key question that must be answered is how the gains from cooperation are to be distributed. Various solution concepts have been proposed, but the computational questions around these solution concepts have received little attention. We study a concise representation of characteristic functions which allows for the agents to be concerned with a number of independent issues that each coalition of agents can address. For example, there may be a set of tasks that the capacityunconstrained agents could undertake, where accomplishing a task generates a certain amount of value (possibly depending on how well the task is accomplished). Given this representation, we show how to quickly compute the Shapley value—a seminal value division scheme that distributes the gains from cooperation fairly in a certain sense. We then show that in (distributed) marginalcontribution based value division schemes, which are known to be vulnerable to manipulation of the order in which the agents are added to the coalition, this manipulation is NPcomplete. Thus, computational complexity serves as a barrier to manipulating the joining order. Finally, we show that given a value division, determining whether some subcoalition has an incentive to break away (in which case we say the division is not in the core) is NPcomplete. So, computational complexity serves to increase the stability of the coalition.
Determining Possible and Necessary Winners under Common Voting Rules Given Partial Orders
"... Usually a voting rule or correspondence 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 profile of part ..."
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Cited by 48 (13 self)
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Usually a voting rule or correspondence 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 profile of partial orders and a candidate c, two important questions arise: first, is c guaranteed to win, and second, is it still possible for c to win? These are the necessary winner and possible winner problems, respectively. We consider the setting where the number of alternatives is unbounded and the votes are unweighted. We prove that for Copeland, maximin, Bucklin, and ranked pairs, the possible winner problem is NPcomplete; also, we give a sufficient condition on scoring rules for the possible winner problem to be NPcomplete (Borda satisfies this condition). We also prove that for Copeland and ranked pairs, the necessary winner problem is coNPcomplete. All the hardness results hold even when the number of undetermined pairs in each vote is no more than a constant. We also present polynomialtime algorithms for the necessary winner problem for scoring rules, maximin, and Bucklin.
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.
Approximability of manipulating elections
 In Proceedings of the 23rd AAAI Conference on Artificial Intelligence
, 2008
"... In this paper, we set up a framework to study approximation of manipulation, control, and bribery in elections. We show existence of approximation algorithms (even fully polynomial time approximation schemes) as well as obtain inapproximability results. ..."
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Cited by 15 (8 self)
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In this paper, we set up a framework to study approximation of manipulation, control, and bribery in elections. We show existence of approximation algorithms (even fully polynomial time approximation schemes) as well as obtain inapproximability results.
Preference Handling in Combinatorial Domains: From AI to Social Choice
"... In both individual and collective decision making, the space of alternatives from which the agent (or the group of agents) has to choose often has a combinatorial (or multiattribute) structure. We give an introduction to preference handling in combinatorial domains in the context of collective deci ..."
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Cited by 14 (9 self)
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In both individual and collective decision making, the space of alternatives from which the agent (or the group of agents) has to choose often has a combinatorial (or multiattribute) structure. We give an introduction to preference handling in combinatorial domains in the context of collective decision making, and show that the considerable body of work on preference representation and elicitation that AI researchers have been working on for several years is particularly relevant. After giving an overview of languages for compact representation of preferences, we discuss problems in voting in combinatorial domains, and then focus on multiagent resource allocation and fair division. These issues belong to a larger field, known as computational social choice, that brings together ideas from AI and social choice theory, to investigate mechanisms for collective decision making from a computational point of view. We conclude by briefly describing some of the other research topics studied in computational social choice.
Dealing with Incomplete Agents ’ Preferences and an Uncertain Agenda in Group Decision Making via Sequential Majority Voting
"... We consider multiagent systems where agents ’ preferences are aggregated via sequential majority voting: each decision is taken by performing a sequence of pairwise comparisons where each comparison is a weighted majority vote among the agents. Incompleteness in the agents ’ preferences is common i ..."
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Cited by 13 (8 self)
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We consider multiagent systems where agents ’ preferences are aggregated via sequential majority voting: each decision is taken by performing a sequence of pairwise comparisons where each comparison is a weighted majority vote among the agents. Incompleteness in the agents ’ preferences is common in many reallife settings due to privacy issues or an ongoing elicitation process. In addition, there may be uncertainty about how the preferences are aggregated. For example, the agenda (a tree whose leaves are labelled with the decisions being compared) may not yet be known or fixed. We therefore study how to determine collectively optimal decisions (also called winners) when preferences may be incomplete, and when the agenda may be uncertain. We show that it is computationally easy to determine if a candidate decision always wins, or may win, whatever the agenda. On the other hand, it is computationally hard to know whether a candidate decision wins in at least one agenda for at least one completion of the agents ’ preferences. These results hold even if the agenda must be balanced so that each candidate decision faces the same number of majority votes. Such results are useful for reasoning about preference elicitation. They help understand the complexity of tasks such as determining if a decision can be taken collectively, as well as knowing if the winner can be manipulated by appropriately ordering the agenda.