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30
28 Are the Hard Manipulation Problems
 Eds.), Proceedings of the 17th National Conference on AI (AAAI 2002
, 2002
"... Voting is a simple mechanism to combine together the preferences of multiple agents. Unfortunately, agents may try to manipulate the result by misreporting their preferences. One barrier that might exist to such manipulation is computational complexity. In particular, it has been shown that it is N ..."
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Cited by 17 (5 self)
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Voting is a simple mechanism to combine together the preferences of multiple agents. Unfortunately, agents may try to manipulate the result by misreporting their preferences. One barrier that might exist to such manipulation is computational complexity. In particular, it has been shown that it is NPhard to compute how to manipulate a number of different voting rules. However, NPhardness only bounds the worstcase complexity. Recent theoretical results suggest that manipulation may often be easy in practice. In this paper, we show that empirical studies are useful in improving our understanding of this issue. We consider two settings which represent the two types of complexity results that have been identified in this area: manipulation with unweighted votes by a single agent, and manipulation with weighted votes by a coalition of agents. In the first case, we consider Single Transferable Voting (STV), and in the second case, we consider veto voting. STV is one of the few voting rules used in practice where it is NPhard to compute how a single agent can manipulate the result when votes are unweighted. It also appears one of the harder voting rules to manipulate since it involves multiple rounds. On the other hand, veto voting is one of the simplest representatives of voting rules where it is NPhard to compute how a coalition of weighted agents can manipulate the result. In our experiments, we sample a number of distributions of votes including uniform, correlated and real world elections. In many of the elections in our experiments, it was easy to compute how to manipulate the result or to prove that manipulation was impossible. Even when we were able to identify a situation in which manipulation was hard to compute (e.g. when votes are highly correlated and the election is “hung”), we found that the computational difficulty of computing manipulations was somewhat precarious (e.g. with such “hung ” elections, even a single uncorrelated voter was enough to make manipulation easy to compute). 1.
L.: Manipulation of Nanson’s and Baldwin’s rules
 Proceedings of the TwentyFifth AAAI Conference on Artificial Intelligence (AAAI 2011
, 2011
"... Nanson’s and Baldwin’s voting rules select a winner by successively eliminating candidates with low Borda scores. We show that these rules have a number of desirable computational properties. In particular, with unweighted votes, it is NPhard to manipulate either rule with one manipulator, whilst w ..."
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Cited by 12 (8 self)
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Nanson’s and Baldwin’s voting rules select a winner by successively eliminating candidates with low Borda scores. We show that these rules have a number of desirable computational properties. In particular, with unweighted votes, it is NPhard to manipulate either rule with one manipulator, whilst with weighted votes, it is NPhard to manipulate either rule with a small number of candidates and a coalition of manipulators. As only a couple of other voting rules are known to be NPhard to manipulate with a single manipulator, Nanson’s and Baldwin’s rules appear to be particularly resistant to manipulation from a theoretical perspective. We also propose a number of approximation methods for manipulating these two rules. Experiments demonstrate that both rules are often difficult to manipulate in practice. These results suggest that elimination style voting rules deserve further study.
New Candidates Welcome! Possible Winners with respect to the Addition of New Candidates
, 2010
"... In some voting contexts, some new candidates may show up in the course of the process. In this case, we may want to determine which of the initial candidates are possible winners, given that a fixed number k of new candidates will be added. We give a computational study of the latter problem, focusi ..."
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Cited by 11 (5 self)
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In some voting contexts, some new candidates may show up in the course of the process. In this case, we may want to determine which of the initial candidates are possible winners, given that a fixed number k of new candidates will be added. We give a computational study of the latter problem, focusing on scoring rules, and we give a formal comparison with related problems such as control via adding candidates or cloning.
Computational Aspects of MultiWinner Approval Voting
 In Proceedings of the 8th Multidisciplinary Workshop on Advances in Preference Handling. 7
, 2014
"... We study computational aspects of three prominent voting rules that use approval ballots to select multiple winners. These rules are proportional approval voting, reweighted approval voting, and satisfaction approval voting. Each rule is designed with the intention to compute a representative winni ..."
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We study computational aspects of three prominent voting rules that use approval ballots to select multiple winners. These rules are proportional approval voting, reweighted approval voting, and satisfaction approval voting. Each rule is designed with the intention to compute a representative winning set. We show that computing the winner for proportional approval voting is NPhard, closing an open problem (Kilgour, 2010). As none of the rules we examine are strategyproof, we study various strategic aspects of the rules. In particular, we examine the computational complexity of computing a best response for both a single agent and a group of agents. In many settings, we show that it is NPhard for an agent or agents to compute how best to vote given a fixed set of approval ballots of the other agents.
Eliminating the Weakest Link: Making Manipulation Intractable
 In: Proceedings of the National Conference on Artificial Intelligence (AAAI
, 2012
"... Successive elimination of candidates is often a route to making manipulation intractable to compute. We prove that eliminating candidates does not necessarily increase the computational complexity of manipulation. However, for many voting rules used in practice, the computational complexity increase ..."
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Cited by 7 (2 self)
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Successive elimination of candidates is often a route to making manipulation intractable to compute. We prove that eliminating candidates does not necessarily increase the computational complexity of manipulation. However, for many voting rules used in practice, the computational complexity increases. For example, it is already known that it is NPhard to compute how a single voter can manipulate the result of single transferable voting(the elimination version of plurality voting). We show here that it is NPhard to compute how a single voter can manipulate the result of the elimination version of veto voting, of the closely related Coombs ’ rule, and of the elimination versions of a general class of scoring rules.
Control complexity in Bucklin and fallback voting
 Computing Research Repository
, 2011
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Coalitional Manipulation for Schulze’s Rule
"... Schulze’s rule is used in the elections of a large number of organizations including Wikimedia and Debian. Part of the reason for its popularity is the large number of axiomatic properties, like monotonicity and Condorcet consistency, which it satisfies. We identify a potential shortcoming of Schulz ..."
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Cited by 5 (0 self)
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Schulze’s rule is used in the elections of a large number of organizations including Wikimedia and Debian. Part of the reason for its popularity is the large number of axiomatic properties, like monotonicity and Condorcet consistency, which it satisfies. We identify a potential shortcoming of Schulze’s rule: it is computationally vulnerable to manipulation. In particular, we prove that computing an unweighted coalitional manipulation (UCM) is polynomial for any number of manipulators. This result holds for both the unique winner and the cowinner versions of UCM. This resolves an open question in [14]. We also prove that computing a weighted coalitional manipulation (WCM) is polynomial for a bounded number of candidates. Finally, we discuss the relation between the unique winner UCM problem and the cowinner UCM problem and argue that they have substantially different necessary and sufficient conditions for the existence of a successful manipulation.
Ties Matter: Complexity of Manipulation when Tiebreaking with a Random Vote
"... We study the impact on strategic voting of tiebreaking by means of considering the order of tied candidates within a random vote. We compare this to another nondeterministic tiebreaking rule where we simply choose candidate uniformly at random. In general, we demonstrate that there is no connecti ..."
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We study the impact on strategic voting of tiebreaking by means of considering the order of tied candidates within a random vote. We compare this to another nondeterministic tiebreaking rule where we simply choose candidate uniformly at random. In general, we demonstrate that there is no connection between the computational complexity of computing a manipulating vote with the two different types of tiebreaking. However, we prove that for some scoring rules, the computational complexity of computing a manipulation can increase from polynomial to NPhard. We also discuss the relationship with the computational complexity of computing a manipulating vote when we ask for a candidate to be the unique winner, or to be among the set of cowinners.
How to Change a Group’s Collective Decision?
"... Persuasion is a common social and economic activity. It usually arises when conflicting interests among agents exist, and one of the agents wishes to sway the opinions of others. This paper considers the problem of an automated agent that needs to influence the decision of a group of selfinterested ..."
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Cited by 4 (2 self)
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Persuasion is a common social and economic activity. It usually arises when conflicting interests among agents exist, and one of the agents wishes to sway the opinions of others. This paper considers the problem of an automated agent that needs to influence the decision of a group of selfinterested agents that must reach an agreement on a joint action. For example, consider an automated agent that aims to reduce the energy consumption of a nonresidential building, by convincing a group of people who share an office to agree on an economy mode of the airconditioning and low light intensity. In this paper we present four problems that address issues of minimality and safety of the persuasion process. We discuss the relationships to similar problems from social choice, and show that if the agents are using Plurality or Veto as their voting rule all of our problems are in P. We also show that with KApproval, Bucklin and Borda voting rules some problems become intractable. We thus present heuristics for efficient persuasion with Borda, and evaluate them through simulations. 1
Combining voting rules together
 In: Proceedings of the 20th European Conference on Artificial Intelligence (ECAI
, 2012
"... Abstract. We propose a simple method for combining together voting rules that performs a runoff between the different winners of each voting rule. We prove that this combinator has several good properties. For instance, even if just one of the base voting rules has a desirable property like Condorc ..."
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Abstract. We propose a simple method for combining together voting rules that performs a runoff between the different winners of each voting rule. We prove that this combinator has several good properties. For instance, even if just one of the base voting rules has a desirable property like Condorcet consistency, the combination inherits this property. On the other hand, some important properties can be lost by the introduction of a runoff, including monotonicity and consistency. In addition, we prove that combining voting rules together in this way can make finding a manipulation more computationally difficult. 1