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Rank Aggregation Methods for the Web
, 2010
"... We consider the problem of combining ranking results from various sources. In the context of the Web, the main applications include building metasearch engines, combining ranking functions, selecting documents based on multiple criteria, and improving search precision through word associations. Wed ..."
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Cited by 478 (6 self)
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We consider the problem of combining ranking results from various sources. In the context of the Web, the main applications include building metasearch engines, combining ranking functions, selecting documents based on multiple criteria, and improving search precision through word associations. Wedevelop a set of techniques for the rank aggregation problem and compare their performance to that of wellknown methods. A primary goal of our work is to design rank aggregation techniques that can effectively combat "spam," a serious problem in Web searches. Experiments show that our methods are simple, efficient, and effective.
Learning to Order Things
 Journal of Artificial Intelligence Research
, 1998
"... There are many applications in which it is desirable to order rather than classify instances. Here we consider the problem of learning how to order, given feedback in the form of preference judgments, i.e., statements to the effect that one instance should be ranked ahead of another. We outline a ..."
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Cited by 409 (12 self)
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There are many applications in which it is desirable to order rather than classify instances. Here we consider the problem of learning how to order, given feedback in the form of preference judgments, i.e., statements to the effect that one instance should be ranked ahead of another. We outline a twostage approach in which one first learns by conventional means a preference function, of the form PREF(u; v), which indicates whether it is advisable to rank u before v. New instances are then ordered so as to maximize agreements with the learned preference function. We show that the problem of finding the ordering that agrees best with a preference function is NPcomplete, even under very restrictive assumptions. Nevertheless, we describe a simple greedy algorithm that is guaranteed to find a good approximation. We then discuss an online learning algorithm, based on the "Hedge" algorithm, for finding a good linear combination of ranking "experts." We use the ordering algorith...
When are elections with few candidates hard to manipulate?
 JOURNAL OF THE ACM
, 2007
"... In multiagent settings where the agents have different 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 158 (18 self)
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In multiagent settings where the agents have different 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 beneficial 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
The Complexity of Computing Medians of Relations
, 1998
"... Let N be a finite set and R be the set of all binary relations on N . Consider R endowed with a metric d, the symmetric difference distance. For a given mtuple = (R 1 ; : : : ; Rm ) 2 R m , a relation R 2 R that minimizes the function P m k=1 d(R k ; R) is called a median relation of . In the socia ..."
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Cited by 22 (0 self)
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Let N be a finite set and R be the set of all binary relations on N . Consider R endowed with a metric d, the symmetric difference distance. For a given mtuple = (R 1 ; : : : ; Rm ) 2 R m , a relation R 2 R that minimizes the function P m k=1 d(R k ; R) is called a median relation of . In the social sciences, in qualitative data analysis and in multicriteria decision making, problems occur in which the mtuple represents collected data (preferences, similarities, games) and the objective is that of finding a median relation of with some special feature (representing for example, consensus of preferences, clustering of similar objects, ranking of teams, etc.). In this paper we analyse the computational complexity of all such problems in which the median is required to satisfy one or more of the properties: reexitivity, symmetry, antisymmetry, transitivity and completeness. We prove that whenever transitivity is required (except when symmetry and completeness are also si...
Feasibility and Approximability of Dodgson's rule
 Auckland University
, 2006
"... It is known that Dodgson's rule is computationally very demanding. Tideman [15] suggested an approximation to it but did not investigate how often his approximation selects the Dodgson winner. We show that under the Impartial Culture assumption the probability that the Tideman winner is the Do ..."
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Cited by 17 (2 self)
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It is known that Dodgson's rule is computationally very demanding. Tideman [15] suggested an approximation to it but did not investigate how often his approximation selects the Dodgson winner. We show that under the Impartial Culture assumption the probability that the Tideman winner is the Dodgson winner tends to 1. However we show that the convergence of this probability to 1 is slow. We suggest another approximation  we call it Dodgson Quick  for which this convergence is exponentially fast. 1
Computational Politics: Electoral Systems
 In Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
, 2000
"... This paper discusses three computationrelated results in the study of electoral systems: 1. Determining the winner in Lewis Carroll's 1876 electoral system is complete for parallel access to NP [22]. 2. For any electoral system that is neutral, consistent, and Condorcet, determining the winner ..."
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Cited by 13 (2 self)
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This paper discusses three computationrelated results in the study of electoral systems: 1. Determining the winner in Lewis Carroll's 1876 electoral system is complete for parallel access to NP [22]. 2. For any electoral system that is neutral, consistent, and Condorcet, determining the winner is complete for parallel access to NP [21]. 3. For each census in US history, a simulated annealing algorithm yields provably fairer (in a mathematically rigorous sense) congressional apportionments than any of the classic algorithms  even the algorithm currently used in the United States [24].
Range Voting
, 2000
"... The "range voting" system is as follows. In a ccandidate election, you select a vector of c real numbers, each of absolute value 1, as your vote. E.g. you could vote (+1; 1; +:3; :9; +1) in a 5candidate election. The votevectors are summed to get a vector ~x and the winner is the i su ..."
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Cited by 1 (0 self)
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The "range voting" system is as follows. In a ccandidate election, you select a vector of c real numbers, each of absolute value 1, as your vote. E.g. you could vote (+1; 1; +:3; :9; +1) in a 5candidate election. The votevectors are summed to get a vector ~x and the winner is the i such that x i is maximum. Previously the area of voting systems lay under the dark cloud of "impossibility theorems" showing that no voting system can satisfy certain seemingly reasonable sets of axioms. But I now prove theorems advancing the thesis that range voting is uniquely best among all possible "Compactset based, One time, Additive, Fair" (COAF) voting systems in the limit of a large number of voters. ("Best" here roughly means that each voter has both the incentive and the opportunity to provide more information about more candidates in his vote than in any other COAF system.) I then describe the rst utilitybased large Monte Carlo comparison of 22 different voting systems. The conclusio...
Vote Trading in Public Elections (updated version)
, 2008
"... During the 2000 U.S. Presidential race an apparently new idea, called vote trading, was introduced to help one of the two majorparty candidates (Gore) win. The idea was, through an Internet mechanism, to induce voters who supported a minorparty candidate (Nader) to vote for Gore in states where thi ..."
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During the 2000 U.S. Presidential race an apparently new idea, called vote trading, was introduced to help one of the two majorparty candidates (Gore) win. The idea was, through an Internet mechanism, to induce voters who supported a minorparty candidate (Nader) to vote for Gore in states where this would help Gore and to induce an equal number of voters who supported Gore to vote for Nader in states where this would not hurt Gore. Thus Nader would receive the same number of popular votes as he would have received without the trading (providing an incentive for Nader voters to participate). Vote trading was implemented at a number of Web sites in 2000 (and again in 2004); it illustrates how information technology can be used to exploit the electoral college system; and it has the potential to alter the outcome of Presidential elections. In this paper, we formalize this idea, present several variations, and present an optimal way for Web sites to implement it (so as to best help the majorparty candidate get elected) in both deterministic and stochastic settings.
Computing Spanning Trees in a Social Choice Context
, 2008
"... This paper combines social choice theory with discrete optimization. We assume that individuals have preferences over edges of a graph that need to be aggregated. The goal is to nd a socially best spanning tree in the graph. As ranking all spanning trees is becoming infeasible even for small numbers ..."
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This paper combines social choice theory with discrete optimization. We assume that individuals have preferences over edges of a graph that need to be aggregated. The goal is to nd a socially best spanning tree in the graph. As ranking all spanning trees is becoming infeasible even for small numbers of vertices and/or edges of a graph, our interest lies in nding algorithms that determine a socially "best" spanning tree in a simple manner. This problem is closely related to the minimum (or maximum) spanning tree problem in combinatorial optimization. Our main result shows that for the various underlying ranking rules on the set of spanning trees discussed in this paper the sets of best spanning trees coincide. Moreover, a greedy algorithm based on a transitive group ranking on the set of edges will always provide such a "best" spanning tree.