Who won? Winner Determination and Robustness in Liquid Democracy

TL;DR

This paper investigates the computational complexity of determining winners in liquid democracy with multiple delegation options and analyzes the robustness of winning alternatives against limited preference or delegation changes.

Contribution

It introduces the winner determination problem for multi-option delegation in liquid democracy and studies its computational complexity and robustness properties.

Findings

Winner determination is computationally challenging in multi-option delegation settings.

Robustness analysis shows how limited changes can alter election outcomes.

The study provides complexity results and insights into the stability of winners.

Abstract

Liquid democracy is a decision-making paradigm in which each agent can either vote directly for some alternative or (transitively) delegate its vote to another agent. To mitigate the issue of delegation cycles or the concentration of power, delegating agents might be allowed to specify multiple delegation options. Then, a (cycle-free) delegation is selected in which each delegating agent has exactly one representative. We study the winner determination problem for this setting, i.e., whether we can select a delegation such that a given alternative wins (or does not win). Moreover, we study the robustness of winning alternatives in two ways: First, we consider whether we can make a limited number of changes to the preferences cast by the agents such that a given alternative becomes a winner in one/in all delegations, and second, whether we can make a limited number of changes to a selected delegation to make a given alternative a winner.