Measuring a Priori Voting Power in Liquid Democracy

Colley, R. , Delemazure, T. and Gilbert, H. (2023) Measuring a Priori Voting Power in Liquid Democracy. In: Thirty-Second International Joint Conference on Artificial Intelligence (IJCAI 2023), Macao, S.A.R, 19-25 August 2023, pp. 2607-2615. ISBN 9781956792034 (doi: 10.24963/ijcai.2023/290)

Abstract

We introduce new power indices to measure the a priori voting power of voters in liquid democracy elections where an underlying network restricts delegations. We argue that our power indices are natural extensions of the standard Penrose-Banzhaf index in simple voting games. We show that computing the criticality of a voter is #P-hard even in weighted games with weights polynomially-bounded in the size of the instance. However, for specific settings, such as when the underlying network is a bipartite or complete graph, recursive formulas can compute these indices for weighted voting games in pseudo-polynomial time. We highlight their theoretical properties and provide numerical results to illustrate how restricting the possible delegations can alter voters' voting power.

• Item Type: Conference Proceedings
• Additional Information: Rachael Colley acknowledges the support of the ANR JCJC project SCONE (ANR 18-CE23-0009-01). Theo Delemazure ´ was supported by the PRAIRIE 3IA Institute under grant ANR-19-P3IA-0001 (e). Hugo Gilbert acknowledges the support from the project THEMIS ANR-20-CE23-0018 of the French National Research Agency (ANR).
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Colley, Dr Rachael
• Authors: Colley, R., Delemazure, T., and Gilbert, H.
• College/School: College of Science and Engineering > School of Computing Science
• ISBN: 9781956792034