Generalizing Liquid Democracy to multi-agent delegation: A Voting Weight Measure and Equilibrium Analysis

TL;DR

This paper extends liquid democracy to allow fractional delegation and analyzes the existence of equilibrium states, showing that chain length penalties promote stable voting configurations with pure strategy Nash equilibria.

Contribution

It introduces a fractional delegation model with chain length penalties and proves the existence of pure strategy Nash equilibria in this generalized setting.

Findings

Smaller penalties improve model properties.

Pure strategy Nash equilibria exist with chain length penalties.

The model generalizes classic liquid democracy to fractional delegation.

Abstract

In this study, we propose a generalization of the classic model of liquid democracy that allows fractional delegation of voting weight, while simultaneously allowing for the existence of equilibrium states. Our approach empowers agents to partition and delegate their votes to multiple representatives, all while retaining a fraction of the voting power for themselves. We introduce a penalty mechanism for the length of delegation chains. We discuss the desirable properties of a reasonable generalization of the classic model, and prove that smaller penalty factors bring the model closer to satisfying these properties. In the subsequent section, we explore the presence of equilibrium states in a general delegation game utilizing the proposed voting measure. In contrast to the classical model, we demonstrate that this game exhibits pure strategy Nash equilibria, contingent upon the imposition of a penalty on the length of delegation chains.