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47
When are elections with few candidates hard to manipulate?
 JOURNAL OF THE ACM
, 2007
"... In multiagent settings where the agents have di®erent preferences, preference aggregation is a central issue. Voting is a general method for preference aggregation, but seminal results have shown that all general voting protocols are manipulable. One could try to avoid manipulation by using protoco ..."
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Cited by 160 (18 self)
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In multiagent settings where the agents have di®erent preferences, preference aggregation is a central issue. Voting is a general method for preference aggregation, but seminal results have shown that all general voting protocols are manipulable. One could try to avoid manipulation by using protocols where determining a bene¯cial manipulation is hard. Especially among computational agents, it is reasonable to measure this hardness by computational complexity. Some earlier work has been done in this area, but it was assumed that the number of voters and candidates is unbounded. Such hardness results lose relevance when the number of candidates is small, because manipulation algorithms that are exponential only in the number of candidates (and only slightly so) might be available. We give such an algorithm for an individual agent to manipulate the Single Transferable Vote (STV) protocol, which has been shown hard to manipulate in the above sense. This motivates the core of this paper, which derives hardness results for realistic elections where the number of candidates is a small constant (but the number of voters can be large). The main manipulation question we study is that of coalitional manipulation by weighted voters. (We show that for simpler manipulation problems, manipulation cannot be hard with few candidates.) We study both constructive manipulation (making a given candidate win) and de
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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Eliciting singlepeaked preferences using comparison queries
 In Proceedings of the International Conference on Autonomous Agents and Multiagent Systems
, 2007
"... Voting is a general method for aggregating the preferences of multiple agents. Each agent ranks all the possible alternatives, and based on this, an aggregate ranking of the alternatives (or at least a winning alternative) is produced. However, when there are many alternatives, it is impractical to ..."
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Cited by 37 (5 self)
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Voting is a general method for aggregating the preferences of multiple agents. Each agent ranks all the possible alternatives, and based on this, an aggregate ranking of the alternatives (or at least a winning alternative) is produced. However, when there are many alternatives, it is impractical to simply ask agents to report their complete preferences. Rather, the agents’ preferences, or at least the relevant parts thereof, need to be elicited. This is done by asking the agents a (hopefully small) number of simple queries about their preferences, such as comparison queries, which ask an agent to compare two of the alternatives. Prior work on preference elicitation in voting has focused on the case of unrestricted preferences. It has been shown that in this setting, it is sometimes necessary to ask each agent (almost) as many queries as would be required to determine an arbitrary ranking of the alternatives. In contrast, in this paper, we focus on singlepeaked preferences. We show that such preferences can be elicited using only a linear number of comparison queries, if either the order with respect to which preferences are singlepeaked is known, or at least one other agent’s complete preferences are known. We show that using a sublinear number of queries does not suffice. We also consider the case of cardinally singlepeaked preferences. For this case, we show that if the alternatives ’ cardinal positions are known, then an agent’s preferences can be elicited using only a logarithmic number of queries; however, we also show that if the cardinal positions are not known, then a sublinear number of queries does not suffice. We present experimental results for all elicitation algorithms. We also consider the problem of only eliciting enough information to determine the aggregate ranking, and show that even for this more modest objective, a sublinear number of queries per agent does not suffice for known ordinal or unknown cardinal positions. Finally, we discuss whether and how these techniques can be applied when preferences are almost singlepeaked. 1 1
Deterministic pivoting algorithms for constrained ranking and Clustering Problems
, 2007
"... We consider ranking and clustering problems related to the aggregation of inconsistent information, in particular, rank aggregation, (weighted) feedback arc set in tournaments, consensus and correlation clustering, and hierarchical clustering. Ailon, Charikar, and Newman [4], Ailon and Charikar [3], ..."
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Cited by 32 (4 self)
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We consider ranking and clustering problems related to the aggregation of inconsistent information, in particular, rank aggregation, (weighted) feedback arc set in tournaments, consensus and correlation clustering, and hierarchical clustering. Ailon, Charikar, and Newman [4], Ailon and Charikar [3], and Ailon [2] proposed randomized constant factor approximation algorithms for these problems, which recursively generate a solution by choosing a random vertex as “pivot ” and dividing the remaining vertices into two groups based on the pivot vertex. In this paper, we answer an open question in these works by giving deterministic approximation algorithms for these problems. The analysis of our algorithms is simpler than the analysis of the randomized algorithms in [4], [3] and [2]. In addition, we consider the problem of finding minimumcost rankings and clusterings which must obey certain constraints (e.g. an input partial order in the case of ranking problems), which were introduced by Hegde and Jain [25] (see also [34]). We show that the first type of algorithms we propose can also handle these constrained problems. In addition, we show that in the case of a rank aggregation or consensus clustering problem, if the input rankings or clusterings obey the constraints, then we can always ensure that the output of
Better human computation through principled voting
 In Proceedings of the 27th AAAI Conference on Artificial Intelligence (AAAI). Forthcoming
, 2013
"... Designers of human computation systms often face the need to aggregate noisy information provided by multiple people. While voting is often used for this purpose, the choice of voting method is typically not principled. We conduct extensive experiments on Amazon Mechanical Turk to better understand ..."
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Cited by 31 (11 self)
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Designers of human computation systms often face the need to aggregate noisy information provided by multiple people. While voting is often used for this purpose, the choice of voting method is typically not principled. We conduct extensive experiments on Amazon Mechanical Turk to better understand how different voting rules perform in practice. Our empirical conclusions show that noisy human voting can differ from what popular theoretical models would predict. Our shortterm goal is to motivate the design of better human computation systems; our longterm goal is to spark an interaction between researchers in (computational) social choice and human computation. 1
On the approximability of Dodgson and Young elections
, 2008
"... The voting rules proposed by Dodgson and Young are both designed to find the alternative closest to being a Condorcet winner, according to two different notions of proximity; the score of a given alternative is known to be hard to compute under either rule. In this paper, we put forward two algorith ..."
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Cited by 27 (10 self)
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The voting rules proposed by Dodgson and Young are both designed to find the alternative closest to being a Condorcet winner, according to two different notions of proximity; the score of a given alternative is known to be hard to compute under either rule. In this paper, we put forward two algorithms for approximating the Dodgson score: an LPbased randomized rounding algorithm and a deterministic greedy algorithm, both of which yield an O(log m) approximation ratio, where m is the number of alternatives; we observe that this result is asymptotically optimal, and further prove that our greedy algorithm is optimal up to a factor of 2, unless problems in N P have quasipolynomial time algorithms. Although the greedy algorithm is computationally superior, we argue that
Anonymityproof voting rules
 In Computational Social Systems and the Internet #07271, Dagstuhl Workshop
, 2007
"... In open, anonymous environments such as the Internet, mechanism design must be extended to take new types of manipulation into account—especially, the possibility that an agent participates in the mechanism multiple times. General social choice or voting settings lie at the heart of mechanism design ..."
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Cited by 24 (13 self)
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In open, anonymous environments such as the Internet, mechanism design must be extended to take new types of manipulation into account—especially, the possibility that an agent participates in the mechanism multiple times. General social choice or voting settings lie at the heart of mechanism design and provide a natural starting point. A (randomized, anonymous) voting rule maps any multiset of total orders of (aka. votes over) a fixed set of alternatives to a probability distribution over these alternatives. A voting rule f is neutral if it treats all alternatives symmetrically. It satisfies participation if no voter ever benefits from not casting her vote. It is falsenameproof if no voter ever benefits from casting additional (potentially different) votes. It is anonymityproof if it satisfies participation and it is falsenameproof. We show that the class of anonymityproof neutral voting rules consists exactly of the rules of the following form.
FixedParameter Algorithms for Kemeny Rankings
, 2009
"... The computation of Kemeny rankings is central to many applications in the context of rank aggregation. Given a set of permutations (votes) over a set of candidates, one searches for a “consensus permutation” that is “closest” to the given set of permutations. Unfortunately, the problem is NPhard. W ..."
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Cited by 23 (9 self)
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The computation of Kemeny rankings is central to many applications in the context of rank aggregation. Given a set of permutations (votes) over a set of candidates, one searches for a “consensus permutation” that is “closest” to the given set of permutations. Unfortunately, the problem is NPhard. We provide a broad study of the parameterized complexity for computing optimal Kemeny rankings. Beside the three obvious parameters “number of votes”, “number of candidates”, and solution size (called Kemeny score), we consider further structural parameterizations. More specifically, we show that the Kemeny score (and a corresponding Kemeny ranking) of an election can be computed efficiently whenever the average pairwise distance between two input votes is not too large. In other words, Kemeny Score is fixedparameter tractable with respect to the parameter “average pairwise KendallTau distance da”. We describe a fixedparameter algorithm with running time 16 ⌈da ⌉ · poly. Moreover, we extend our studies to the parameters “maximum range ” and “average range ” of positions a candidate takes in the input votes. Whereas Kemeny