Strengthening Proportionality in Temporal Voting

TL;DR

This paper explores advanced proportionality axioms in temporal approval voting, proposing stronger variants and analyzing their existence and relationships, thus enriching the theoretical framework of fair representation over time.

Contribution

It introduces and studies new, stronger proportionality axioms in temporal voting, extending the hierarchy of fairness concepts beyond existing standards.

Findings

EJR+ and FJR strengthen EJR and are always satisfiable in temporal elections.

The paper establishes a hierarchy of proportionality concepts in temporal voting.

It analyzes the existence and relationships of these new axioms within the framework.

Abstract

We study proportional representation in the framework of temporal voting with approval ballots. Prior work adapted basic proportional representation concepts -- justified representation (JR), proportional JR (PJR), and extended JR (EJR) -- from the multiwinner setting to the temporal setting. Our work introduces and examines ways of going beyond EJR. Specifically, we consider stronger variants of JR, PJR, and EJR, and introduce temporal adaptations of more demanding multiwinner axioms, such as EJR+, full JR (FJR), full proportional JR (FPJR), and the Core. For each of these concepts, we investigate its existence and study its relationship to existing notions, thereby establishing a rich hierarchy of proportionality concepts. Notably, we show that two of our proposed axioms -- EJR+ and FJR -- strengthen EJR while remaining satisfiable in every temporal election.