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Llull and Copeland voting computationally resist bribery and control
, 2009
"... Control and bribery are settings in which an external agent seeks to influence the outcome of an election. Constructive control of elections refers to attempts by an agent to, via such actions as addition/deletion/partition of candidates or voters, ensure that a given candidate wins. Destructive con ..."
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Cited by 63 (30 self)
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Control and bribery are settings in which an external agent seeks to influence the outcome of an election. Constructive control of elections refers to attempts by an agent to, via such actions as addition/deletion/partition of candidates or voters, ensure that a given candidate wins. Destructive control refers to attempts by an agent to, via the same actions, preclude a given candidate’s victory. An election system in which an agent can sometimes affect the result and it can be determined in polynomial time on which inputs the agent can succeed is said to be vulnerable to the given type of control. An election system in which an agent can sometimes affect the result, yet in which it is NPhard to recognize the inputs on which the agent can succeed, is said to be resistant to the given type of control. Aside from election systems with an NPhard winner problem, the only systems previously known to be resistant to all the standard control types were highly artificial election systems created by hybridization. This paper studies a parameterized version of Copeland voting, denoted by Copeland α, where the parameter α is a rational number between 0 and 1 that specifies how ties are valued in the pairwise comparisons of candidates. In every previously studied constructive or destructive
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.
Sidelines: An Algorithm for Increasing Diversity in News and Opinion Aggregators
"... Aggregators rely on votes, and links to select and present subsets of the large quantity of news and opinion items generated each day. Opinion and topic diversity in the output sets can provide individual and societal benefits, but simply selecting the most popular items may not yield as much divers ..."
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Cited by 11 (0 self)
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Aggregators rely on votes, and links to select and present subsets of the large quantity of news and opinion items generated each day. Opinion and topic diversity in the output sets can provide individual and societal benefits, but simply selecting the most popular items may not yield as much diversity as is present in the overall pool of votes and links. In this paper, we define three diversity metrics that address different dimensions of diversity: inclusion, nonalienation, and proportional representation. We then present the Sidelines algorithm – which temporarily suppresses a voter’s preferences after a preferred item has been selected – as one approach to increase the diversity of result sets. In comparison to collections of the most popular items, from user votes on Digg.com and links from a panel of political blogs, the Sidelines algorithm increased inclusion while decreasing alienation. For the blog links, a set with known political preferences, we also found that Sidelines improved proportional representation. In an online experiment using blog link data as votes, readers were more likely to find something challenging to their views in the Sidelines result sets. These findings can help build news and opinion aggregators that present users with a broader range of topics and opinions.
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.