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Related papers: On Multi-Level Apportionment

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Inspired by multigrid methods for linear systems of equations, multilevel optimization methods have been proposed to solve structured optimization problems. Multilevel methods make more assumptions regarding the structure of the…

Optimization and Control · Mathematics 2019-11-27 Chin Pang Ho , Michal Kocvara , Panos Parpas

The apportionment problem asks how to assign representation to states based on their populations. That is, given census data and a fixed number of seats, how many seats should each state be assigned? Various algorithms exist to solve the…

Probability · Mathematics 2026-03-26 Joseph Cutrone , Tyler C. Wunder

The class of assignment problems is a fundamental and well-studied class in the intersection of Social Choice, Computational Economics and Discrete Allocation. In a general assignment problem, a group of agents expresses preferences over a…

Data Structures and Algorithms · Computer Science 2021-05-25 Barak Steindl , Meirav Zehavi

Judgment aggregation problems form a class of collective decision-making problems represented in an abstract way, subsuming some well known problems such as voting. A collective decision can be reached in many ways, but a direct one-step…

Artificial Intelligence · Computer Science 2016-08-30 Marija Slavkovik , Wojciech Jamroga

We consider the notions of agreement, diversity, and polarization in ordinal elections (that is, in elections where voters rank the candidates). While (computational) social choice offers good measures of agreement between the voters, such…

Computer Science and Game Theory · Computer Science 2023-05-18 Piotr Faliszewski , Andrzej Kaczmarczyk , Krzysztof Sornat , Stanisław Szufa , Tomasz Wąs

Over the last few years, researchers have put significant effort into understanding of the notion of proportional representation in committee election. In particular, recently they have proposed the notion of proportionality degree. We…

Computer Science and Game Theory · Computer Science 2022-07-11 Łukasz Janeczko , Piotr Faliszewski

Approval voting is a common method of preference aggregation where voters vote by ``approving'' of a subset of candidates and the winner(s) are those who are approved of by the largest number of voters. In approval voting, the degree to…

Computer Science and Game Theory · Computer Science 2023-07-19 Hari Sarang Nathan

While proportionality is frequently named as a desirable property of voting rules, its interpretation in multiwinner voting differs significantly from that in apportionment. We aim to bridge these two distinct notions of proportionality by…

Computer Science and Game Theory · Computer Science 2026-02-11 Daria Boratyn , Dariusz Stolicki

Like many other voting systems, Majority Judgement suffers from the weaknesses of the underlying mathematical model: Elections as problem of choice or ranking. We show how the model can be enhanced to take into account the complete process…

Computer Science and Game Theory · Computer Science 2023-07-07 Friedemann Kemm

In this paper we extend the principle of proportional representation to rankings. We consider the setting where alternatives need to be ranked based on approval preferences. In this setting, proportional representation requires that…

Computer Science and Game Theory · Computer Science 2016-12-06 Piotr Skowron , Martin Lackner , Markus Brill , Dominik Peters , Edith Elkind

In approval-based multiwinner voting, voters express approval preferences over a set of candidates, and the goal is to return a winning committee. This model captures a broad range of subset selection problems under preferences. Prior work…

Computer Science and Game Theory · Computer Science 2026-04-28 Niclas Boehmer , Luca Kreisel , Jannik Peters

We prove that under the Jefferson--D'Hondt method of apportionment, given certain distributional assumptions regarding mean rounding residuals, as well as absence of correlations between party vote shares, district sizes (in votes), and…

Physics and Society · Physics 2025-10-16 Daria Boratyn , Wojciech Słomczyński , Dariusz Stolicki

We consider multi-agent systems where agents' preferences are aggregated via sequential majority voting: each decision is taken by performing a sequence of pairwise comparisons where each comparison is a weighted majority vote among the…

Artificial Intelligence · Computer Science 2012-04-18 Maria Pini , Francesca Rossi , Brent Venable , Toby Walsh

The hierarchical topology is a common property of many complex systems. Here we introduce a simple but generic model of hierarchy growth from the bottom to the top. Therein, two dynamical processes are accounted for: agent's promotions to…

Physics and Society · Physics 2025-03-06 Agnieszka Czaplicka , Janusz A. Hołyst

We introduce the concept of multilevel fair allocation of resources with tree-structured hierarchical relations among agents. While at each level it is possible to consider the problem locally as an allocation of an agent to its children,…

Computer Science and Game Theory · Computer Science 2026-05-13 Maxime Lucet , Nawal Benabbou , Aurélie Beynier , Nicolas Maudet

The Assignment problem is a fundamental and well-studied problem in the intersection of Social Choice, Computational Economics and Discrete Allocation. In the Assignment problem, a group of agents expresses preferences over a set of items,…

Data Structures and Algorithms · Computer Science 2021-05-24 Barak Steindl , Meirav Zehavi

Democracies employ elections at various scales to select officials at the corresponding levels of administration. The geographical distribution of political opinion, the policy issues delegated to each level, and the multilevel interactions…

Applications · Statistics 2022-11-03 Sihao Huang , Alexander F. Siegenfeld , Andrew Gelman

Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…

Data Structures and Algorithms · Computer Science 2026-05-05 Samuel Boardman

We consider a model where a subset of candidates must be selected based on voter preferences, subject to general constraints that specify which subsets are feasible. This model generalizes committee elections with diversity constraints,…

Computer Science and Game Theory · Computer Science 2026-02-10 Piotr Skowron

Peer reviews, evaluations, and selections are a fundamental aspect of modern science. Funding bodies the world over employ experts to review and select the best proposals from those submitted for funding. The problem of peer selection,…

Computer Science and Game Theory · Computer Science 2019-05-01 Haris Aziz , Omer Lev , Nicholas Mattei , Jeffrey S. Rosenschein , Toby Walsh