# Iterative Delegations in Liquid Democracy with Restricted Preferences

arXiv: https://arxiv.org/abs/1809.04362 · HTML: https://mlsanity.com/paper/1809.04362/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2018.

## Built on by (most cited first, 5 of 5)

- [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)
- [Measuring a Priori Voting Power -- Taking Delegations Seriously](https://mlsanity.com/paper/2301.02462/) (2023)
- [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)

## Abstract (arXiv)

In this paper, we study liquid democracy, a collective decision making paradigm which lies between direct and representative democracy. One main feature of liquid democracy is that voters can delegate their votes in a transitive manner so that: A delegates to B and B delegates to C leads to A delegates to C. Unfortunately, this process may not converge as there may not even exist a stable state (also called equilibrium). In this paper, we investigate the stability of the delegation process in liquid democracy when voters have restricted types of preference on the agent representing them (e.g., single-peaked preferences). We show that various natural structures of preferences guarantee the existence of an equilibrium and we obtain both tractability and hardness results for the problem of computing several equilibria with some desirable properties.