When Can Liquid Democracy Unveil the Truth?
Ruben Becker, Gianlorenzo D'Angelo, Esmaeil Delfaraz, Hugo Gilbert

TL;DR
This paper analyzes the computational complexity of the ODP problem in liquid democracy, demonstrating hardness results, proposing approximation algorithms under certain conditions, and showing through simulations that liquid democracy can outperform direct democracy.
Contribution
It provides new hardness bounds for ODP, introduces conditions for effective approximation, and empirically compares liquid democracy with direct democracy.
Findings
Hardness of approximation for ODP under certain conditions
Connectivity of social networks influences algorithm efficiency
Simple algorithms outperform direct democracy in simulations
Abstract
In this paper, we investigate the so-called ODP-problem that has been formulated by Caragiannis and Micha [10]. Here, we are in a setting with two election alternatives out of which one is assumed to be correct. In ODP, the goal is to organise the delegations in the social network in order to maximize the probability that the correct alternative, referred to as ground truth, is elected. While the problem is known to be computationally hard, we strengthen existing hardness results by providing a novel strong approximation hardness result: For any positive constant , we prove that, unless , there is no polynomial-time algorithm for ODP that achieves an approximation guarantee of , where is the number of voters. The reduction designed for this result uses poorly connected social networks in which some voters suffer from misinformation. Interestingly,…
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Internet Traffic Analysis and Secure E-voting · Game Theory and Voting Systems
