Using Weighted Matching to Solve 2-Approval/Veto Control and Bribery
Abstract
Determining the complexity of election attack problems is a major research direction in the computational study of voting problems. The paper "Towards completing the puzzle: complexity of control by replacing, adding, and deleting candidates or voters" by Erd\'elyi et al. (JAAMAS 2021) provides a comprehensive study of the complexity of control problems. The sole open problem is constructive control by replacing voters for 2-Approval. We show that this case is in P, strengthening the recent RP (randomized polynomial-time) upper bound due to Fitzsimmons and Hemaspaandra (IJCAI 2022). We show this by transforming 2-Approval CCRV to weighted matching. We also use this approach to show that priced bribery for 2-Veto elections is in P. With this result, and the accompanying (unsurprising) result that priced bribery for 3-Veto elections is NP-complete, this settles the complexity for -Approval and -Veto standard control and bribery cases.
Cite
@article{arxiv.2305.16889,
title = {Using Weighted Matching to Solve 2-Approval/Veto Control and Bribery},
author = {Zack Fitzsimmons and Edith Hemaspaandra},
journal= {arXiv preprint arXiv:2305.16889},
year = {2023}
}