A Quantitative Analysis of Multi-Winner Rules

Lackner, Martin; Skowron, Piotr

doi:10.24963/ijcai.2019/58

Cited by 16 publications

(10 citation statements)

References 24 publications

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“…The next theorem gives a generic tool for calculating the utilitarian efficiency for a large subclass of Thiele methods. In particular, Theorem 3 generalizes some known results from the literaturean asymptotically tight utilitarian efficiency guarantee is already known for PAV and for the pgeometric rule [18]. Theorem 3.…”

Section: The Tradeoff Between Proportionality and Utilitarian Efficiencysupporting

confidence: 70%

“…We consider the following open question particularly interesting and important: can we find a rule that combines the virtues of Phragmén's Sequential Rule and of PAV? Such a rule should in particular (i) satisfy Pareto efficiency (which PAV satisfies and the Phragmén's rule violates [18]), (ii) satisfy strong unanimity (which Phragmén's Sequential Rule satisfies and PAV violates), and (iii) have a high proportionality degree. It is tempting to suggest a rule that first takes all unanimously approved candidates and complements the committee by running PAV, yet such rule looks a bit artificial, and its definition is specifically tailored for strong unanimity 7 .…”

Section: Discussionmentioning

confidence: 99%

“…We establish asymptotically tight bounds on the loss of the utilitarian efficiency for convex Thiele methods. For Sequential PAV and for Phragmén's Sequential Rule such bounds are already known [18]. Together with the aforementioned proportionality guarantees, this allows to quantify the tradeoff between the level of proportionality and utilitarian efficiency, that is to estimate the price of fairness for particular (classes of) rules.…”

Section: Introductionmentioning

confidence: 99%

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Proportionality Degree of Multiwinner Rules

Skowron¹

2018

Preprint

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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 considered rules are proportional. This allows us to arrange the rules in a clear hierarchy. For example, we find out that Proportional Approval Voting (PAV) has better proportionality guarantees than its sequential counterpart, and that Phragmén's Sequential Rule is worse than Sequential PAV. Yet, the loss of proportionality for the two sequential rules is moderate and in some contexts can be outweighed by their other appealing properties. Finally, we measure the tradeoff between proportionality and utilitarian efficiency for a broad subclass of committee election rules.1 Other basic axioms describing fairness requirements are, for instance, anonymity or solid coalitions property [10]. 2 Indeed, proportional representation (PR) electoral systems are often argued to be more fair than non-proportional

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Section: The Tradeoff Between Proportionality and Utilitarian Efficiencysupporting

confidence: 70%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Proportionality Degree of Multiwinner Rules

Skowron¹

2018

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“…Our PFC model relies on approval ballots in order to elicit agents' preferences. Dichotomous preferences have been considered in several important setting including committee voting (Lackner andSkowron, 2019, Aziz, Brill, Conitzer, Elkind, Freeman, andWalsh, 2017) and discrete participatory budgeting (Aziz et al, 2018, Fluschnik, Skowron, Triphaus, andWilker, 2019).…”

Section: Related Workmentioning

confidence: 99%

Participatory Funding Coordination: Model, Axioms and Rules

Aziz¹,

Ganguly²

2021

Preprint

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We present a new model of collective decision making that captures important crowd-funding and donor coordination scenarios. In the setting, there is a set of projects (each with its own cost) and a set of agents (that have their budgets as well as preferences over the projects). An outcome is a set of projects that are funded along with the specific contributions made by the agents. For the model, we identify meaningful axioms that capture concerns including fairness, efficiency, and participation incentives. We then propose desirable rules for the model and study, which sets of axioms can be satisfied simultaneously. An experimental study indicates the relative performance of different rules as well as the price of enforcing fairness axioms.

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“…In this section, we analyze the voting rules introduced in Section 2, to obtain guarantees on their normalized social welfare. Formally, for each number m of alternatives, we calculate the rules' efficiency guarantee (Lackner and Skowron 2019)…”

Section: Guarantees For Voting Rulesmentioning

confidence: 99%

Price of Fairness in Budget Division and Probabilistic Social Choice

Michorzewski

Peters

Skowron

2020

AAAI

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A group of agents needs to divide a divisible common resource (such as a monetary budget) among several uses or projects. We assume that agents have approval preferences over projects, and their utility is the fraction of the budget spent on approved projects. If we maximize utilitarian social welfare, the entire budget will be spent on a single popular project, even if a substantial fraction of the agents disapprove it. This violates the individual fair share axiom (IFS) which requires that for each agent, at least 1/n of the budget is spent on approved projects. We study the price of imposing such fairness axioms on utilitarian social welfare. We show that no division rule satisfying IFS can guarantee to achieve more than an O(1/√m) fraction of maximum utilitarian welfare, in the worst case. However, imposing stronger group fairness conditions (such as the core) does not come with an increased price, since both the conditional utilitarian rule and the Nash rule match this bound and guarantee an Ώ(1/√m) fraction. The same guarantee is attained by the rule under which the spending on a project is proportional to its approval score. We also study a family of rules interpolating between the utilitarian and the Nash rule, quantifying a trade-off between welfare and group fairness. An experimental analysis by sampling using several probabilistic models shows that the conditional utilitarian rule achieves very high welfare on average.

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A Quantitative Analysis of Multi-Winner Rules

Cited by 16 publications

References 24 publications

Proportionality Degree of Multiwinner Rules

Proportionality Degree of Multiwinner Rules

Participatory Funding Coordination: Model, Axioms and Rules

Price of Fairness in Budget Division and Probabilistic Social Choice

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