Measuring a Priori Voting Power in Liquid Democracy
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.
Cite
Text
Colley et al. "Measuring a Priori Voting Power in Liquid Democracy." International Joint Conference on Artificial Intelligence, 2023. doi:10.24963/IJCAI.2023/290Markdown
[Colley et al. "Measuring a Priori Voting Power in Liquid Democracy." International Joint Conference on Artificial Intelligence, 2023.](https://mlanthology.org/ijcai/2023/colley2023ijcai-measuring/) doi:10.24963/IJCAI.2023/290BibTeX
@inproceedings{colley2023ijcai-measuring,
title = {{Measuring a Priori Voting Power in Liquid Democracy}},
author = {Colley, Rachael and Delemazure, Théo and Gilbert, Hugo},
booktitle = {International Joint Conference on Artificial Intelligence},
year = {2023},
pages = {2607-2615},
doi = {10.24963/IJCAI.2023/290},
url = {https://mlanthology.org/ijcai/2023/colley2023ijcai-measuring/}
}