Haris Aziz, Barton E. Lee
A well-known axiom for proportional representation is Proportionality of Solid Coalitions (PSC). We characterize committees satisfying PSC as possible outcomes of the Minimal Demand rule, which generalizes an approach pioneered by Michael Dummett.
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We study a class of elections in which the input format is trichotomous and allows voters to elicit their negative feelings explicitly. In particular, we study multiwinner elections with a special proclivity to elect proportionally representative committees. That is, we design various axioms to deal with negative feelings and suggest some structures to these preferences that allow better preference aggregation rules. We propose two different classes of axioms designed to aggregate trichotomous preferences more efficiently. We propose trichotomous versions of some well known multiwinner voting …
A population of voters must elect representatives among themselves to decide on a sequence of possibly unforeseen binary issues. Voters care only about the final decision, not the elected representatives. The disutility of a voter is proportional to the fraction of issues, where his preferences disagree with the decision. While an issue-by-issue vote by all voters would maximize social welfare, we are interested in how well the preferences of the population can be approximated by a small committee. We show that a k-sortition (a random committee of k voters with the majority vote within the com…
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…
We present a new model that describes the process of electing a group of representatives (e.g., a parliament) for a group of voters. In this model, called the voting committee model, the elected group of representatives runs a number of ballots to make final decisions regarding various issues. The satisfaction of voters comes from the final decisions made by the elected committee. Our results suggest that depending on a decision system used by the committee to make these final decisions, different multi-winner election rules are most suitable for electing the committee. Furthermore, we show th…
Low Cost, Fair, and Representative Committees in a Metric Space
研究度量空间中代表性委员会选择问题，提出同时满足低成本、公平性及新公理NORP的算法，证明此类委员会总是存在。
Participatory budgeting is one of the exciting developments in deliberative grassroots democracy. We concentrate on approval elections and propose proportional representation axioms in participatory budgeting, by generalizing relevant axioms for approval-based multi-winner elections. We observe a rich landscape with respect to the computational complexity of identifying proportional budgets and computing such, and present budgeting methods that satisfy these axioms by identifying budgets that are representative to the demands of vast segments of the voters.
We study multiwinner elections with approval-based preferences. An instance of a multiwinner election consists of a set of alternatives, a population of voters---each voter approves a subset of alternatives, and the desired committee size $k$; the goal is to select a committee (a~subset) of $k$ alternatives according to the preferences of the voters. We investigate a number of election rules and ask whether the committees that they return represent the voters proportionally. In contrast to the classic literature, we employ quantitative techniques that allow to measure the extent to which the c…
Proportionally Representative Clustering
聚焦无监督机器学习的质心聚类，提出‘比例代表性公平’公理，现有算法不满足该公理，设计高效算法在无约束和离散聚类问题中实现此公理，无约束算法是首个多项式时间近似算法，离散算法匹配已知最佳近似因子。
Participatory budgeting (PB) is a democratic paradigm whereby voters decide on a set of projects to fund with a limited budget. We consider PB in a setting where voters report ordinal preferences over projects and have (possibly) asymmetric weights. We propose proportional representation axioms and clarify how they fit into other preference aggregation settings, such as multi-winner voting and approval-based multi-winner voting. As a result of our study, we also discover a new solution concept for approval-based multi-winner voting, which we call Inclusion PSC (IPSC). IPSC is stronger than pro…
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…
There has been much recent work on multiwinner voting systems. However, sometimes a committee is highly structured, and if we want to vote for such a committee, our voting method should be more structured as well. We consider committees consisting of representatives for disjoint parts of a collective; for instance, n departments of an organization might each have m possible representatives to choose from. However, in our model the entire population still gets to vote on the committee, and we need to respect that symmetry, which we do by building on earlier work of Barcelo et al. using represen…
Finding Representative and Approximately Efficient Committees
针对PAV计算NP困难问题，提出多项式时间算法，通过凹松弛管道舍入初始化局部PAV，同时满足EJR+、α*-fPO、弱帕累托最优及0.79近似最优PAV分数。
Proportionality and Strategyproofness in Multiwinner Elections
该研究针对基于认可票的多胜者选举规则，通过命题逻辑建模与SAT求解证明，弱比例性与弱策略防伪性无法同时满足，并讨论了相关公理问题。
Full Proportional Justified Representation
本文提出并研究完全比例正当代表（FPJR），结合两种凝聚力和代表定义，发现其具有PJR的优点且被高效规则满足，但PAV可能违反，与EJR互不蕴含。
We consider the problem of committee selection from a fixed set of candidates where each candidate has multiple quantifiable attributes. To select the best possible committee, instead of voting for a candidate, a voter is allowed to approve the preferred attributes of a given candidate. Though attribute based preference is addressed in several contexts, committee selection problem with attribute approval of voters has not been attempted earlier. A committee formed on attribute preferences is more likely to be a better representative of the qualities desired by the voters and is less likely to …
Learning Proportional Committees from Violation Feedback
该研究针对PJR+和EJR+两种比例代表概念，分析了全见证与仅候选者两种违规反馈下的提案拒绝复杂度，给出了确定性与随机化场景下的拒绝界及对应算法。
Committee scoring rules form a rich class of aggregators of voters' preferences for the purpose of selecting subsets of objects with desired properties, e.g., a shortlist of candidates for an interview, a representative collective body such as a parliament, or a set of locations for a set of public facilities. In the spirit of celebrated Young's characterization result that axiomatizes single-winner scoring rules, we provide an axiomatic characterization of multiwinner committee scoring rules. We show that committee scoring rules---despite forming a remarkably general class of rules---are char…
Differentially Private Approval-Based Committee Voting
本文研究了差分隐私与基于批准的委员会投票中多个代表性公理的权衡，证明了公理与DP的不兼容性并建立了双向和三方权衡的上下界，量化了DP对公理满足度的影响。
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 …
Diverse Representation in Approval-Based Committee Voting
本文提出审批制委员会投票中多元代表的更全面理论，加强合理代表公理，引入独特代表及其局部优化变体，并证明相关公理的可满足性与计算复杂性，实验显示局部DR在多元性度量上表现良好。
Proportional Representation in Metric Spaces and Low-Distortion Committee Selection
该研究提出度量空间中集合代表性的新定义，在资源扩增框架和序数模型下证明EAR规则的代表性边界，还得到比例公平、核心公平及单胜者投票规则的相关衍生结果。
Explanation Systems for Approval-Based Multiwinner Voting
本文研究了基于批准投票的多赢家投票中的解释系统，旨在量化委员会对选民的代表性，分析选民影响力分配及候选人支持情况，并提出价格系统框架及多项公理。
We consider the following problem in which a given number of items has to be chosen from a predefined set. Each item is described by a vector of attributes and for each attribute there is a desired distribution that the selected set should have. We look for a set that fits as much as possible the desired distributions on all attributes. Examples of applications include choosing members of a representative committee, where candidates are described by attributes such as sex, age and profession, and where we look for a committee that for each attribute offers a certain representation, i.e., a sin…
Individual Representation in Approval-Based Committee Voting
本文形式化了个体代表性概念，证明其判定计算难解，并揭示常见批准投票规则可能无法实现个体代表性，同时通过领域限制和实验分析了可实现性条件。
Proportional Selection in Networks
本文研究了如何从网络中选择k个代表性节点，旨在识别最有影响力节点并确保选择比例反映网络的多样性，提出了两种方法并进行了理论分析和实验验证。
A Generalised Theory of Proportionality in Collective Decision Making
本文提出集体决策中比例性的一般化理论，将委员会选举、多样性约束选举、公共决策和集体调度统一建模，提出不依赖预定义群体的比例性公理，并将PAV和Phragmén规则推广到拟阵约束下满足公理。
Proportional Representation in Rank Aggregation
提出比例序列博达规则和流调整博达规则，确保每个输入排名在输出排名中得到比例代表，解决经典社会福利函数多数决问题。
Metritocracy: Representative Metrics for Lite Benchmarks
针对大语言模型评估中指标子集“代表性”定义模糊的问题，研究基于社会选择理论形式化两种代表性概念，证明了所需最少指标数的上下界，并通过真实案例实现理论与实践结合。
Optimally Selecting Representative Agents from a Metric Space
本文针对度量空间中的比例公平聚类问题，证明了Droop核心下界的紧致性，提出仅选智能体位置作中心的2-Droop核心聚类方法，解决了β-多数问题，其结果由ChatGPT-5.6-Sol生成并经作者验证。
Social Choice Foundations for Simulation-Augmented Generation
针对模拟增强生成（SAGE）的效率问题，提出基于度量比例公正表示+（mPJR+）公理的首次形式化，证明双重缩减模拟与路由仍保近似比例表示，并在两个领域验证算法优于基线。
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