# The Fluid Mechanics of Liquid Democracy

arXiv: https://arxiv.org/abs/1808.01906 · HTML: https://mlsanity.com/paper/1808.01906/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Aug 2018.

## Built on by (most cited first, 10 of 10)

- [Unravelling multi-agent ranked delegations](https://mlsanity.com/paper/2111.13145/) (2021)
- [When Can Liquid Democracy Unveil the Truth?](https://mlsanity.com/paper/2104.01828/) (2021)
- [The Optimal Size of an Epistemic Congress](https://mlsanity.com/paper/2107.01042/) (2021)
- [As Time Goes By: Adding a Temporal Dimension Towards Resolving Delegations in Liquid Democracy](https://mlsanity.com/paper/2307.12898/) (2023)
- [The Cost Perspective of Liquid Democracy: Feasibility and Control](https://mlsanity.com/paper/2502.02380/) (2025)
- [Artificial Delegates Resolve Fairness Issues in Perpetual Voting with Partial Turnout](https://mlsanity.com/paper/2506.21186/) (2025)
- [Fluid Democracy in Federated Data Aggregation](https://mlsanity.com/paper/2507.02710/) (2025)
- [Computation and Bribery of Voting Power in Delegative Simple Games](https://mlsanity.com/paper/2104.03692/) (2021)
- [Pandering in a Flexible Representative Democracy](https://mlsanity.com/paper/2211.09986/) (2022)
- [AgentSociety: Incentivizing Agentic Social Intelligence](https://mlsanity.com/paper/2605.26203/) (2026)

## Abstract (arXiv)

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.