The Fluid Mechanics of Liquid Democracy

TL;DR

This paper explores a novel approach to liquid democracy by allowing multiple delegation options, aiming to balance influence among agents and prevent concentration of power, supported by theoretical analysis and empirical simulations.

Contribution

It introduces a multi-delegation model inspired by fluid mechanics principles and connects it to confluent flow theory to improve influence distribution in liquid democracy.

Findings

Multi-delegation reduces influence concentration.

The model balances votes effectively in theoretical scenarios.

Empirical results show improved influence distribution.

Abstract

Liquid democracy is the principle of making collective decisions by letting agents transitively delegate their votes. Despite its significant appeal, it has become apparent that a weakness of liquid democracy is that a small subset of agents may gain massive influence. To address this, we propose to change the current practice by allowing agents to specify multiple delegation options instead of just one. Much like in nature, where --- fluid mechanics teaches us --- liquid maintains an equal level in connected vessels, so do we seek to control the flow of votes in a way that balances influence as much as possible. Specifically, we analyze the problem of choosing delegations to approximately minimize the maximum number of votes entrusted to any agent, by drawing connections to the literature on confluent flow. We also introduce a random graph model for liquid democracy, and use it to demonstrate the benefits of our approach both theoretically and empirically.