Representation in Peer Selection: A Liquid Democracy Perspective

2026-08-13

AI Summary

This study addresses the problem of selecting a fixed-size committee from a peer group while ensuring both representativeness and proportionality. To this end, it introduces a “liquid preferences” model, wherein each voter delegates trust to a single agent, and preferences propagate transitively along chains of trust, thereby inducing a structured preference domain. Building on this novel preference framework, the paper designs voting rules tailored to its structure and systematically evaluates their performance within an approval voting setting by integrating delegation graph analysis with axiomatic proportionality guarantees. The results demonstrate that the proposed rules substantially enhance proportionality under liquid preferences, offering both theoretical grounding and practical potential for real-world peer-based selection mechanisms.

Abstract

We study the peer selection problem in which a group of peers must select a fixed-size committee from among themselves. To this end, we introduce a class of approval-based preference profiles, inspired by delegation graphs in liquid democracy and the transitivity of trust therein, which we call ``liquid profiles''. Under this new domain restriction, each voter designates a single trusted agent and, in turn, approves all those trusted by that individual. After establishing relationships to standard restricted preference profiles and examining computational properties of liquid profiles, we focus on understanding how novel and established proportionality axioms behave in this domain and how they relate to one another. Then, we study their satisfaction under various voting rules, including new ones that are directly inspired by the structure of liquid profiles. Our findings reveal that particularly strong proportionality guarantees are attainable in this new domain, showing promise for applications to real-world peer selection problems via transitive delegations.

Problem

• peer selection
• liquid democracy
• proportionality
• approval voting
• delegation

Innovation

• liquid democracy
• peer selection
• approval voting
• proportionality axioms
• delegation graphs