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52
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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Preference Functions That Score Rankings and Maximum Likelihood Estimation
"... A preference function (PF) takes a set of votes (linear orders over a set of alternatives) as input, and produces one or more rankings (also linear orders over the alternatives) as output. Such functions have many applications, for example, aggregating the preferences of multiple agents, or merging ..."
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Cited by 60 (20 self)
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A preference function (PF) takes a set of votes (linear orders over a set of alternatives) as input, and produces one or more rankings (also linear orders over the alternatives) as output. Such functions have many applications, for example, aggregating the preferences of multiple agents, or merging rankings (of, say, webpages) into a single ranking. The key issue is choosing a PF to use. One natural and previously studied approach is to assume that there is an unobserved “correct ” ranking, and the votes are noisy estimates of this. Then, we can use the PF that always chooses the maximum likelihood estimate (MLE) of the correct ranking. In this paper, we define simple ranking scoring functions (SRSFs) and show that the class of neutral SRSFs is exactly the class of neutral PFs that are MLEs for some noise model. We also define extended ranking scoring functions (ERSFs) and show a condition under which these coincide with SRSFs. We study key properties such as consistency and continuity, and consider some example PFs. In particular, we study Single Transferable Vote (STV), a commonly used PF, showing that it is an ERSF but not an SRSF, thereby clarifying the extent to which it is an MLE function. This also gives a new perspective on how ties should be broken under STV. We leave some open questions. 1
Consensus ranking under the exponential model
 UAI
, 2007
"... We analyze the generalized Mallows model, a popular exponential model over rankings. Estimating the central (or consensus) ranking from data is NPhard. We obtain the following new results: (1) We show that search methods can estimate both the central ranking π0 and the model parameters θ exactly. T ..."
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Cited by 34 (5 self)
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We analyze the generalized Mallows model, a popular exponential model over rankings. Estimating the central (or consensus) ranking from data is NPhard. We obtain the following new results: (1) We show that search methods can estimate both the central ranking π0 and the model parameters θ exactly. The search is n! in the worst case, but is tractable when the true distribution is concentrated around its mode; (2) We show that the generalized Mallows model is jointly exponential in (π0, θ), and introduce the conjugate prior for this model class; (3) The sufficient statistics are the pairwise marginal probabilities that item i is preferred to item j. Preliminary experiments confirm the theoretical predictions and compare the new algorithm and existing heuristics.
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
Making Decisions Based on the Preferences of Multiple Agents
"... People often have to reach a joint decision even though they have conflicting preferences over the alternatives. Examples range from the mundane—such as allocating chores among the members of a household—to the sublime—such as electing a government and thereby charting the course for a country. The ..."
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Cited by 29 (8 self)
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People often have to reach a joint decision even though they have conflicting preferences over the alternatives. Examples range from the mundane—such as allocating chores among the members of a household—to the sublime—such as electing a government and thereby charting the course for a country. The joint decision can be reached by an informal negotiating process or by a carefully specified protocol. Philosophers, mathematicians, political scientists, economists, and others have studied the merits of various protocols for centuries. More recently, especially over the course of the past decade or so, computer scientists have also become deeply involved in this study. The perhaps surprising arrival of computer scientists on this scene is due to a variety of reasons, including the following. 1. Computer networks provide a new platform for communicating
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 Scores
"... Abstract. The Kemeny Score problem 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. Computing an optimal consensus permutat ..."
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Cited by 23 (7 self)
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Abstract. The Kemeny Score problem 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. Computing an optimal consensus permutation is NPhard. We provide first, encouraging fixedparameter tractability results for computing optimal scores (that is, the overall distance of an optimal consensus permutation). Our fixedparameter algorithms employ the parameters “score of the consensus”, “maximum distance between two input permutations”, and “number of candidates”. We extend our results to votes with ties and incomplete votes, thus, in both cases having no longer permutations as input. 1