As Time Goes By: Adding a Temporal Dimension Towards Resolving Delegations in Liquid Democracy

TL;DR

This paper introduces a temporal dimension to Liquid Democracy, allowing voters to change their delegation choices over time, which can improve participation and reduce delegation issues.

Contribution

It is the first to incorporate a time horizon into Liquid Democracy decision-making, analyzing its computational complexity using temporal graph theory.

Findings

Adding a temporal dimension increases delegation paths.

Temporal modeling can reduce delegation cycles.

Complexity analysis reveals computational challenges.

Abstract

In recent years, the study of various models and questions related to Liquid Democracy has been of growing interest among the community of Computational Social Choice. A concern that has been raised, is that current academic literature focuses solely on static inputs, concealing a key characteristic of Liquid Democracy: the right for a voter to change her mind as time goes by, regarding her options of whether to vote herself or delegate her vote to other participants, till the final voting deadline. In real life, a period of extended deliberation preceding the election-day motivates voters to adapt their behaviour over time, either based on observations of the remaining electorate or on information acquired for the topic at hand. By adding a temporal dimension to Liquid Democracy, such adaptations can increase the number of possible delegation paths and reduce the loss of votes due to delegation cycles or delegating paths towards abstaining agents, ultimately enhancing participation. Our work takes a first step to integrate a time horizon into decision-making problems in Liquid Democracy systems. Our approach, via a computational complexity analysis, exploits concepts and tools from temporal graph theory which turn out to be convenient for our framework.