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We study situations where a group of voters need to take a collective decision over a number of public issues, with the goal of getting a result that reflects the voters' opinions in a proportional manner. Our focus is on interconnected…

Computer Science and Game Theory · Computer Science 2025-09-25 Julian Chingoma , Umberto Grandi , Arianna Novaro

Permanent citizens' assemblies are ongoing deliberative bodies composed of randomly selected citizens, organized into panels that rotate over time. Unlike one-off panels, which represent the population in a single snapshot, permanent…

Computer Science and Game Theory · Computer Science 2026-02-19 Yusuf Hakan Kalayci , Evi Micha

A most debated topic of the last years is whether simple statistical physics models can explain collective features of social dynamics. A necessary step in this line of endeavour is to find regularities in data referring to large scale…

Physics and Society · Physics 2009-11-13 Santo Fortunato , Claudio Castellano

We describe an electoral system for distributing seats in a parliament. It gives proportionality for the political parties and close to proportionality for constituencies. The system suggested here is a version of the system used in Sweden…

Optimization and Control · Mathematics 2013-10-31 Svante Linusson , Gustav Ryd

Election data represent a precious source of information to study human behavior at a large scale. In proportional elections with open lists, the number of votes received by a candidate, rescaled by the average performance of all…

Physics and Society · Physics 2013-01-25 Arnab Chatterjee , Marija Mitrović , Santo Fortunato

We consider a voting model, where a number of candidates need to be selected subject to certain feasibility constraints. The model generalises committee elections (where there is a single constraint on the number of candidates that need to…

Computer Science and Game Theory · Computer Science 2025-09-24 Tomáš Masařík , Grzegorz Pierczyński , Piotr Skowron

In parliamentary elections, parties compete for a limited, typically fixed number of seats. Most parliaments are assembled using apportionment methods that distribute the seats based on the parties' vote counts. Common apportionment methods…

Mechanism design is concerned with settings where a policymaker (or social planner) faces the problem of aggregating the announced preferences of multiple agents into a collective (or social), system-wide decision. One of the most important…

Multiagent Systems · Computer Science 2020-03-02 Mohammad Ali Javidian , Pooyan Jamshidi , Marco Valtorta , Rasoul Ramezanian

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

Apportionment is the task of assigning resources to entities with different entitlements in a fair manner, and specifically a manner that is as proportional as possible. The best-known application is the assignment of parliamentary seats to…

Computer Science and Game Theory · Computer Science 2025-10-14 Julian Chingoma , Ulle Endriss , Ronald de Haan , Adrian Haret , Jan Maly

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

The Constitutionally mandated task of assigning Congressional seats to the various U.S. States proportional to their represented populations ("according to their numbers") has engendered much contention, but rather less consensus. Using the…

Physics and Society · Physics 2021-07-06 A. E. Charman

Proportional representation plays a crucial role in electoral systems. In ordinal elections, where voters rank candidates based on their preferences, the Single Transferable Vote (STV) is the most widely used proportional voting method. STV…

Computer Science and Game Theory · Computer Science 2025-05-02 Tuva Bardal , Markus Brill , David McCune , Jannik Peters

Computational social choice and algorithmic decision theory offer rich aggregation theory but no comprehensive process for egalitarian self-governance: aggregation, deliberation, amendment, and consensus are each considered in isolation,…

Multiagent Systems · Computer Science 2026-05-15 Ehud Shapiro , Nimrod Talmon

Every representative democracy must specify a mechanism under which voters choose their representatives. The most common mechanism in the United States -- Winner takes all single-member districts -- both enables substantial partisan…

Computer Science and Game Theory · Computer Science 2026-02-23 Nikhil Garg , Wes Gurnee , David Rothschild , David Shmoys

Distribution of seats in The European Parliament postulated by Treaty of Lisbon should be degressively proportional. The meaning of degressively proportional concept can be found in two principles annexed to the draft of European Parliament…

Physics and Society · Physics 2011-04-29 Jan Florek

In recent years, the study of various models and questions related to Liquid Democracy has been of growing interest among the community of Computational Social Choice. A concern that has been raised, is that current academic literature…

Computer Science and Game Theory · Computer Science 2023-07-25 Evangelos Markakis , Georgios Papasotiropoulos

Proportional representation (PR) is one of the central principles in voting. Elegant rules with compelling PR axiomatic properties have the potential to be adopted for several important collective decision making settings. I survey some…

Computer Science and Game Theory · Computer Science 2018-02-06 Haris Aziz

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…

Computer Science and Game Theory · Computer Science 2021-01-14 Nimrod Talmon , Rutvik Page

Voting methods are instrumental design elements of democracies. Citizens use them to express and aggregate their preferences to reach a collective decision. However, voting outcomes can be as sensitive to voting rules as they are to…