Approval-based multiwinner voting rules have recently received much attention in the Computational Social Choice literature. Such rules aggregate approval ballots and determine a winning committee of alternatives. To assess effectiveness, we propose to employ new noise models that are specifically tailored for approval votes and committees. These models take as input a ground truth committee and return random approval votes to be thought of as noisy estimates of the ground truth. A minimum robustness requirement for an approval-based multiwinner voting rule is to return the ground truth when applied to profiles with sufficiently many noisy votes. Our results indicate that approval-based multiwinner voting is always robust to reasonable noise. We further refine this finding by presenting a hierarchy of rules in terms of how robust to noise they are.
To choose a suitable multiwinner voting rule is a hard and ambiguous task. Depending on the context, it varies widely what constitutes the choice of an ``optimal'' subset of alternatives. In this paper, we provide a quantitative analysis of multiwinner voting rules using methods from the theory of approximation algorithms---we estimate how well multiwinner rules approximate two extreme objectives: a representation criterion defined via the Approval Chamberlin--Courant rule and a utilitarian criterion defined via Multiwinner Approval Voting. With both theoretical and experimental methods, we cl…
Fairness in multiwinner elections, a growing line of research in computational social choice, primarily concerns the use of constraints to ensure fairness. Recent work proposed a model to find a diverse \emph{and} representative committee and studied the model's computational aspects. However, the work gave complexity results under major assumptions on how the candidates and the voters are grouped. Here, we close this gap and classify the complexity of finding a diverse and representative committee using a monotone, separable positional multiwinner voting rule, conditioned \emph{only} on the a…
Social choice is replete with various settings including single-winner voting, multi-winner voting, probabilistic voting, multiple referenda, and public decision making. We study a general model of social choice called Sub-Committee Voting (SCV) that simultaneously generalizes these settings. We then focus on sub-committee voting with approvals and propose extensions of the justified representation axioms that have been considered for proportional representation in approval-based committee voting. We study the properties and relations of these axioms. For each of the axioms, we analyse whether…
Multiwinner voting rules are used to select a small representative subset of candidates or items from a larger set given the preferences of voters. However, if candidates have sensitive attributes such as gender or ethnicity (when selecting a committee), or specified types such as political leaning (when selecting a subset of news items), an algorithm that chooses a subset by optimizing a multiwinner voting rule may be unbalanced in its selection -- it may under or over represent a particular gender or political orientation in the examples above. We introduce an algorithmic framework for multi…
Epistemic social choice aims at unveiling a hidden ground truth given votes, which are interpreted as noisy signals about it. We consider here a simple setting where votes consist of approval ballots: each voter approves a set of alternatives which they believe can possibly be the ground truth. Based on the intuitive idea that more reliable votes contain fewer alternatives, we define several noise models that are approval voting variants of the Mallows model. The likelihood-maximizing alternative is then characterized as the winner of a weighted approval rule, where the weight of a ballot decr…
NICTA（国家信息与通信技术研究院）；UNSW（新南威尔士大学）；University of Sydney（悉尼大学）
We study computational aspects of three prominent voting rules that use approval ballots to elect multiple winners. These rules are satisfaction approval voting, proportional approval voting, and reweighted approval voting. We first show that computing the winner for proportional approval voting is NP-hard, closing a long standing open problem. As none of the rules are strategyproof, even for dichotomous preferences, we study various strategic aspects of the rules. In particular, we examine the computational complexity of computing a best response for both a single agent and a group of agents.…
Tulane University（杜兰大学）；Louisiana State University（路易斯安那州立大学）；University of West Florida（西佛罗里达大学）；Institute for Human and Machine Cognition（人机认知研究所）
In many real world situations, collective decisions are made using voting and, in scenarios such as committee or board elections, employing voting rules that return multiple winners. In multi-winner approval voting (AV), an agent submits a ballot consisting of approvals for as many candidates as they wish, and winners are chosen by tallying up the votes and choosing the top-$k$ candidates receiving the most approvals. In many scenarios, an agent may manipulate the ballot they submit in order to achieve a better outcome by voting in a way that does not reflect their true preferences. In complex…
We study the computational complexity of committee selection problem for several approval-based voting rules in the presence of outliers. Our first result shows that outlier consideration makes committee selection problem intractable for approval, net approval, and minisum approval voting rules. We then study parameterized complexity of this problem with five natural parameters, namely the target score, the size of the committee (and its dual parameter, the number of candidates outside the committee), the number of outliers (and its dual parameter, the number of non-outliers). For net approval…
AGH University（AGH大学）；TU Berlin（柏林工业大学）；Weizmann Institute of Science（魏茨曼科学研究所）
We study the problem of bribery in multiwinner elections, for the case where the voters cast approval ballots (i.e., sets of candidates they approve) and the bribery actions are limited to: adding an approval to a vote, deleting an approval from a vote, or moving an approval within a vote from one candidate to the other. We consider a number of approval-based multiwinner rules (AV, SAV, GAV, RAV, approval-based Chamberlin--Courant, and PAV). We find the landscape of complexity results quite rich, going from polynomial-time algorithms through NP-hardness with constant-factor approximations, to …
Proportional representation (PR) is often discussed in voting settings as a major desideratum. For the past century or so, it is common both in practice and in the academic literature to jump to single transferable vote (STV) as the solution for achieving PR. Some of the most prominent electoral reform movements around the globe are pushing for the adoption of STV. It has been termed a major open problem to design a voting rule that satisfies the same PR properties as STV and better monotonicity properties. In this paper, we first present a taxonomy of proportional representation axioms for ge…
In many real world situations, collective decisions are made using voting. Moreover, scenarios such as committee or board elections require voting rules that return multiple winners. In multi-winner approval voting (AV), an agent may vote for as many candidates as they wish. Winners are chosen by tallying up the votes and choosing the top-$k$ candidates receiving the most votes. An agent may manipulate the vote to achieve a better outcome by voting in a way that does not reflect their true preferences. In complex and uncertain situations, agents may use heuristics to strategize, instead of inc…
Technische Universität Berlin（柏林工业大学）；Paris School of Economics（巴黎经济学院）；University of Warsaw（华沙大学）
We establish a link between multiwinner elections and apportionment problems by showing how approval-based multiwinner election rules can be interpreted as methods of apportionment. We consider several multiwinner rules and observe that they induce apportionment methods that are well-established in the literature on proportional representation. For instance, we show that Proportional Approval Voting induces the D'Hondt method and that Monroe's rule induces the largest reminder method. We also consider properties of apportionment methods and exhibit multiwinner rules that induce apportionment m…
On the Complexity of Winner Determination and Strategic Control in Conditional Approval Voting
Athens University of Economics and Business（雅典经济与商业大学）；Archimedes, Athena Research Center（阿基米德、雅典研究中心）；Input Output Global (IOG)（输入输出全球（IOG））；University of Warsaw（华沙大学）
The study of fairness in multiwinner elections focuses on settings where candidates have attributes. However, voters may also be divided into predefined populations under one or more attributes (e.g., "California" and "Illinois" populations under the "state" attribute), which may be same or different from candidate attributes. The models that focus on candidate attributes alone may systematically under-represent smaller voter populations. Hence, we develop a model, DiRe Committee WinnerDetermination (DRCWD), which delineates candidate and voter attributes to select a committee by specifying di…
TU Berlin（柏林工业大学）；AGH University of Science and Technology（AGH科技大学）；Ben-Gurion University（本-古里安大学）
Given an election, a preferred candidate p, and a budget, the SHIFT BRIBERY problem asks whether p can win the election after shifting p higher in some voters' preference orders. Of course, shifting comes at a price (depending on the voter and on the extent of the shift) and one must not exceed the given budget. We study the (parameterized) computational complexity of S HIFT BRIBERY for multiwinner voting rules where winning the election means to be part of some winning committee. We focus on the well-established SNTV, Bloc, k-Borda, and Chamberlin-Courant rules, as well as on approximate vari…
Université de Lyon（里昂大学）；Université Lumière Lyon 2（里昂第二大学）；INSA de Lyon（里昂国立应用科学学院）；Institut Camille Jordan（卡米尔·若尔当研究所）
Voting rules based on evaluation inputs rather than preference orders have been recently proposed, like majority judgement, range voting or approval voting. Traditionally, probabilistic analysis of voting rules supposes the use of simulation models to generate preferences data, like the Impartial Culture (IC) or Impartial and Anonymous Culture (IAC) models. But these simulation models are not suitable for the analysis of evaluation-based voting rules as they generate preference orders instead of the needed evaluations. We propose in this paper several simulation models for generating evaluatio…
The Gibbard-Satterthwaite theorem states that no unanimous and non-dictatorial voting rule is strategyproof. We revisit voting rules and consider a weaker notion of strategyproofness called not obvious manipulability that was proposed by Troyan and Morrill (2020). We identify several classes of voting rules that satisfy this notion. We also show that several voting rules including k-approval fail to satisfy this property. We characterize conditions under which voting rules are obviously manipulable. One of our insights is that certain rules are obviously manipulable when the number of alternat…
Tata Institute of Fundamental Research（塔塔基础研究所）；Weizmann Institute of Science（魏茨曼科学研究学院）
We consider elections where the voters come one at a time, in a streaming fashion, and devise space-efficient algorithms which identify an approximate winning committee with respect to common multiwinner proportional representation voting rules; specifically, we consider the Approval-based and the Borda-based variants of both the Chamberlin-- ourant rule and the Monroe rule. We complement our algorithms with lower bounds. Somewhat surprisingly, our results imply that, using space which does not depend on the number of voters it is possible to efficiently identify an approximate representative …
We investigate the problem of winner determination from computational social choice theory in the data stream model. Specifically, we consider the task of summarizing an arbitrarily ordered stream of $n$ votes on $m$ candidates into a small space data structure so as to be able to obtain the winner determined by popular voting rules. As we show, finding the exact winner requires storing essentially all the votes. So, we focus on the problem of finding an {\em $\eps$-winner}, a candidate who could win by a change of at most $\eps$ fraction of the votes. We show non-trivial upper and lower bound…
Epistemic voting interprets votes as noisy signals about a ground truth. We consider contexts where the truth consists of a set of objective winners, knowing a lower and upper bound on its cardinality. A prototypical problem for this setting is the aggre-gation of multi-label annotations with prior knowledge on the size of the ground truth. We posit noisemodels, for which we define rules that output an optimal set of winners. We report on experiments on multi-label annotations (which we collected).
University of Warsaw（华沙大学）；University of Wrocław（弗罗茨瓦夫大学）；Warsaw Center of Mathematics and Computer Science（华沙数学与计算机科学中心）
We present three results on the complexity of Minimax Approval Voting. First, we study Minimax Approval Voting parameterized by the Hamming distance $d$ from the solution to the votes. We show Minimax Approval Voting admits no algorithm running in time $\mathcal{O}^\star(2^{o(d\log d)})$, unless the Exponential Time Hypothesis (ETH) fails. This means that the $\mathcal{O}^\star(d^{2d})$ algorithm of Misra et al. [AAMAS 2015] is essentially optimal. Motivated by this, we then show a parameterized approximation scheme, running in time $\mathcal{O}^\star(\left({3}/ε\right)^{2d})$, which is essent…
CNRS（法国国家科学研究中心）；Facebook AI Research（脸书人工智能研究院）；University of Warsaw（华沙大学）
Assume $k$ candidates need to be selected. The candidates appear over time. Each time one appears, it must be immediately selected or rejected -- a decision that is made by a group of individuals through voting. Assume the voters use approval ballots, i.e., for each candidate they only specify whether they consider it acceptable or not. This setting can be seen as a voting variant of choosing $k$ secretaries. Our contribution is twofold. (1) We assess to what extent the committees that are computed online can proportionally represent the voters. (2) If a prior probability over candidate approv…
The growing need for labeled training data has made crowdsourcing an important part of machine learning. The quality of crowdsourced labels is, however, adversely affected by three factors: (1) the workers are not experts; (2) the incentives of the workers are not aligned with those of the requesters; and (3) the interface does not allow workers to convey their knowledge accurately, by forcing them to make a single choice among a set of options. In this paper, we address these issues by introducing approval voting to utilize the expertise of workers who have partial knowledge of the true answe…
Tulane University（杜兰大学）；Louisiana State University（路易斯安那州立大学）；Institute for Human & Machine Cognition（人机认知研究所）；University of West Florida（西佛罗里达大学）
In many collective decision making situations, agents vote to choose an alternative that best represents the preferences of the group. Agents may manipulate the vote to achieve a better outcome by voting in a way that does not reflect their true preferences. In real world voting scenarios, people often do not have complete information about other voter preferences and it can be computationally complex to identify a strategy that will maximize their expected utility. In such situations, it is often assumed that voters will vote truthfully rather than expending the effort to strategize. However,…
Digital Age Research Center（数字时代研究中心）；University of Klagenfurt（克拉根福大学）
This work researches the impact of including a wider range of participants in the strategy-making process on the performance of organizations which operate in either moderately or highly complex environments. Agent-based simulation demonstrates that the increased number of ideas generated from larger and diverse crowds and subsequent preference aggregation lead to rapid discovery of higher peaks in the organization's performance landscape. However, this is not the case when the expansion in the number of participants is small. The results confirm the most frequently mentioned benefit in the Op…
