Publication
Beyond Lower Quota: Avoiding Overrepresentation in Multi-Winner Voting
Anton Baychkov; Martin Lackner; Jan Maly; Oliviero Nardi; Jan Peters
In: Computing Research Repository eprint Journal (CoRR), Vol. abs/2606.19968, Pages 1-36, arXiv, 2026.
Abstract
In the recent social choice literature on proportional representation, much attention has been given to the
question of avoiding underrepresentation in approval-based multi-winner voting. In this paper, we explore
the largely overlooked complementary question of avoiding overrepresentation. This has not been explored
systematically, despite being a desirable property with concrete applications. Intuitively, overrepresentation
happens when a group determines a disproportionately large part of the committee, thereby exceeding the
group’s quota.
We formulate a strong and appealing axiom for avoiding overrepresentation, called justified upper quota
(JUQ). We introduce a generalization of Thiele rules, composite Thiele rules, and characterize the unique rule in
this class satisfying our axiom. This rule, Adams-AV, which naturally extends Adams’ apportionment method,
has not been studied before. Additionally, we introduce a polynomial-time rule that satisfies JUQ.
Furthermore, we introduce justified near quota, an axiom that balances avoiding under- and overrepresenta-
tion. It characterizes the unique Thiele rule extending the Sainte-Laguë apportionment method. Finally, we
analyze the compatibility of our axioms with established proportionality notions such as EJR+.