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35
Budgeted Social Choice: From Consensus to Personalized Decision Making
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2011
"... We develop a general framework for social choice problems in which a limited number of alternatives can be recommended to an agent population. In our budgeted social choice model, this limit is determined by a budget, capturing problems that arise naturally in a variety of contexts, and spanning the ..."
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Cited by 31 (6 self)
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We develop a general framework for social choice problems in which a limited number of alternatives can be recommended to an agent population. In our budgeted social choice model, this limit is determined by a budget, capturing problems that arise naturally in a variety of contexts, and spanning the continuum from pure consensus decision making (i.e., standard social choice) to fully personalized recommendation. Our approach applies a form of segmentation to social choice problems— requiring the selection of diverse options tailored to different agent types—and generalizes certain multiwinner election schemes. We show that standard rank aggregation methods perform poorly, and that optimization in our model is NPcomplete; but we develop fast greedy algorithms with some theoretical guarantees. Experiments on realworld datasets demonstrate the effectiveness of our algorithms.
On the computation of fully proportional representation
 JOURNAL OF AI RESEARCH
, 2013
"... We investigate two systems of fully proportional representation suggested by Chamberlin & Courant and Monroe. Both systems assign a representative to each voter so that the “sum of misrepresentations” is minimized. The winner determination problem for both systems is known to be NPhard, hence t ..."
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Cited by 20 (6 self)
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We investigate two systems of fully proportional representation suggested by Chamberlin & Courant and Monroe. Both systems assign a representative to each voter so that the “sum of misrepresentations” is minimized. The winner determination problem for both systems is known to be NPhard, hence this work aims at investigating whether there are variants of the proposed rules and/or specific electorates for which these problems can be solved efficiently. As a variation of these rules, instead of minimizing the sum of misrepresentations, we considered minimizing the maximalmisrepresentationintroducingeffectively two new rules. In the general case these “minimax ” versions of classical rules appeared to be still NPhard. We investigated the parameterized complexity of winner determination of the two classical and two new rules with respect to several parameters. Here we have a mixture of positive and negative results: e.g., we proved fixedparameter tractability for the parameter the number of candidates but fixedparameter intractability for the number of winners. For singlepeaked electorates our results are overwhelmingly positive: we provide polynomialtime algorithms for most of the considered problems. The only rule that remains NPhard for singlepeaked electorates is the classical Monroe rule. 1.
Multiwinner elections: Complexity of manipulation, control and winnerdetermination
 In Preproceedings of the Eighth Trading Agent Design and Analysis & Agent Mediated Electronic Commerce Joint International Workshop (TADA/AMEC 2006
, 2007
"... Abstract. Although recent years have seen a surge of interest in the computational aspects of social choice, no attention has previously been devoted to elections with multiple winners, e.g., elections of an assembly or committee. In this paper, we fully characterize the worstcase complexity of man ..."
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Cited by 18 (4 self)
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Abstract. Although recent years have seen a surge of interest in the computational aspects of social choice, no attention has previously been devoted to elections with multiple winners, e.g., elections of an assembly or committee. In this paper, we fully characterize the worstcase complexity of manipulation and control in the context of four prominent multiwinner voting systems. Additionally, we show that several tailormade multiwinner voting schemes are impractical, as it is N Phard to select the winners in these schemes. 1
Characterizations of scoring methods for preference aggregation
 Annals of Operations Research
, 1998
"... The paper surveys more than forty characterizations of scoring methods for preference aggregation and contains one new result. A general scoring operator is selfconsistent if alternative i is assigned a greater score than j whenever i gets no worse (better) results of comparisons and its ‘opponents ..."
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Cited by 11 (1 self)
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The paper surveys more than forty characterizations of scoring methods for preference aggregation and contains one new result. A general scoring operator is selfconsistent if alternative i is assigned a greater score than j whenever i gets no worse (better) results of comparisons and its ‘opponents ’ are assigned respectively greater (no smaller) scores than those of j. We prove that selfconsistency is satisfied if and only if the application of a scoring operator reduces to the solution of a homogeneous system of algebraic equations with a monotone function on the lefthand side.
Proportional Representation as Resource Allocation: Approximability Results
, 2012
"... We model Monroe’s and Chamberlin and Courant’s multiwinner voting systems as a certain resource allocation problem. We show that for many restricted variants of this problem, under standard complexitytheoretic assumptions, there are no constantfactor approximation algorithms. Yet, we also show case ..."
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Cited by 8 (1 self)
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We model Monroe’s and Chamberlin and Courant’s multiwinner voting systems as a certain resource allocation problem. We show that for many restricted variants of this problem, under standard complexitytheoretic assumptions, there are no constantfactor approximation algorithms. Yet, we also show cases where good approximation algorithms exist (briefly put, these variants correspond to optimizing total voter satisfaction under Borda scores, within Monroe’s and Chamberlin and Courant’s voting systems). 1
Fully Proportional Representation as Resource Allocation: Approximability Results
 PROCEEDINGS OF THE TWENTYTHIRD INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2013
"... We study the complexity of (approximate) winner determination under Monroe’s and ChamberlinCourant’s multiwinner voting rules, where we focus on the total (dis)satisfaction of the voters (the utilitarian case) or the (dis)satisfaction of the worstoff voter (the egalitarian case). We show good appro ..."
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Cited by 8 (6 self)
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We study the complexity of (approximate) winner determination under Monroe’s and ChamberlinCourant’s multiwinner voting rules, where we focus on the total (dis)satisfaction of the voters (the utilitarian case) or the (dis)satisfaction of the worstoff voter (the egalitarian case). We show good approximation algorithms for the satisfactionbased utilitarian cases, and inapproximability results for the remaining settings.
Achieving Fully Proportional Representation is Easy in Practice
"... We provide experimental evaluation of a number of known and new algorithms for approximate computation of Monroe’s and ChamberlinCourant’s rules. Our experiments, conducted both on reallife preferenceaggregation data and on synthetic data, show that even very simple and fast algorithms can in man ..."
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Cited by 7 (3 self)
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We provide experimental evaluation of a number of known and new algorithms for approximate computation of Monroe’s and ChamberlinCourant’s rules. Our experiments, conducted both on reallife preferenceaggregation data and on synthetic data, show that even very simple and fast algorithms can in many cases find nearperfect solutions. Our results confirm and complement very recenttheoreticalanalysisofSkowronetal.,whohaveshowngood lower bounds on the quality of (some of) the algorithms that we study. Categories andSubject Descriptors
Multiwinner Social Choice with Incomplete Preferences
"... Multiwinner social choice considers the problem of selecting a slate of K options to realize some social objective. It has found application in the construction of political legislatures and committees, product recommendation, and related problems, and has recently attracted attention from a comput ..."
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Cited by 6 (0 self)
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Multiwinner social choice considers the problem of selecting a slate of K options to realize some social objective. It has found application in the construction of political legislatures and committees, product recommendation, and related problems, and has recently attracted attention from a computational perspective. We address the multiwinner problem when facing incomplete voter preferences, using the notion of minimax regret to determine a robust slate of options in the presence of preference uncertainty. We analyze the complexity of this problem and develop new exact and greedy robust optimization algorithms for its solution. Using these techniques, we also develop preference elicitation heuristics which, in practice, allow us to find nearoptimal slates with considerable savings in the preference information required visàvis complete votes. 1
Choosing Collectively Optimal Sets of Alternatives Based on the Condorcet Criterion
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
"... In elections, an alternative is said to be a Condorcet winner if it is preferred to any other alternative by a majority of voters. While this is a very attractive solution concept, many elections do not have a Condorcet winner. In this paper, we propose a setvalued relaxation of this concept, which ..."
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Cited by 6 (2 self)
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In elections, an alternative is said to be a Condorcet winner if it is preferred to any other alternative by a majority of voters. While this is a very attractive solution concept, many elections do not have a Condorcet winner. In this paper, we propose a setvalued relaxation of this concept, which we call a Condorcet winning set: such sets consist of alternatives that collectively dominate any other alternative. We also consider a more general version of this concept, where instead of domination by a majority of voters we require domination by a given fraction θ of voters; we refer to this concept as θwinning set. We explore social choicetheoretic and algorithmic aspects of these solution concepts, both theoretically and empirically.