Existence of Core-Stable Outcomes on Liquid Profiles

Establish whether a core-stable committee always exists for liquid profiles, or characterize the liquid profiles and related variants of core stability for which such outcomes are guaranteed to exist.

Background

Core Stability is presented as a strong fairness requirement from cooperative game theory and approval-based committee voting. The paper notes that, even in the general multiwinner setting, it remains unresolved whether a core-stable committee always exists and that no voting rule is known to guarantee one. Although the paper studies the relationship between Core Stability and the strong representation axioms on liquid profiles, it proves only independence results and does not settle existence. The conclusion therefore explicitly identifies existence of core-stable outcomes, including possible variants, as an open technical problem in the liquid-profile setting.