Search versus Search for Collapsing Electoral Control Types
Benjamin Carleton, Michael C. Chavrimootoo, Lane A. Hemaspaandra, David E. Narv\'aez, Conor Taliancich, Henry B. Welles

TL;DR
This paper investigates the computational complexity of search problems related to collapsing pairs of electoral control types, establishing polynomial relationships and reductions, and classifying their complexity for specific voting systems.
Contribution
It proves polynomial relationships between search versions of collapsing pairs and provides complexity classifications for key voting systems.
Findings
Search complexities of collapsing pairs are polynomially related.
Efficient reductions exist between solutions of paired search problems.
For plurality, veto, and approval, the complexity of search problems is fully classified.
Abstract
Electoral control types are ways of trying to change the outcome of elections by altering aspects of their composition and structure [BTT92]. We say two compatible (i.e., having the same input types) control types that are about the same election system E form a collapsing pair if for every possible input (which typically consists of a candidate set, a vote set, a focus candidate, and sometimes other parameters related to the nature of the attempted alteration), either both or neither of the attempted attacks can be successfully carried out. For each of the seven general (i.e., holding for all election systems) electoral control type collapsing pairs found by Hemaspaandra, Hemaspaandra, and Menton [HHM20] and for each of the additional electoral control type collapsing pairs of Carleton et al. [CCH+24] for veto and approval (and many other election systems in light of that paper's…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsInternet Traffic Analysis and Secure E-voting · Game Theory and Voting Systems · Cryptography and Data Security
