The Complexity of Online Voter Control in Sequential Elections

TL;DR

This paper introduces a framework for online voter control in sequential elections, revealing that such problems are often computationally harder than traditional models, with some cases being PSPACE-complete or coNP-complete.

Contribution

It models online voter control in sequential elections and establishes complexity results, including PSPACE-completeness and coNP-completeness, for various control actions and election systems.

Findings

Online control problems can be PSPACE-complete even with two candidates.

Certain control problems are coNP-complete with bounded limits.

For plurality, online control by deleting or adding voters is in P.

Abstract

Previous work on voter control, which refers to situations where a chair seeks to change the outcome of an election by deleting, adding, or partitioning voters, takes for granted that the chair knows all the voters' preferences and that all votes are cast simultaneously. However, elections are often held sequentially and the chair thus knows only the previously cast votes and not the future ones, yet needs to decide instantaneously which control action to take. We introduce a framework that models online voter control in sequential elections. We show that the related problems can be much harder than in the standard (non-online) case: For certain election systems, even with efficient winner problems, online control by deleting, adding, or partitioning voters is PSPACE-complete, even if there are only two candidates. In addition, we obtain (by a new characterization of coNP in terms of weight-bounded alternating Turing machines) completeness for coNP in the deleting/adding cases with a bounded deletion/addition limit, and we obtain completeness for NP in the partition cases with an additional restriction. We also show that for plurality, online control by deleting or adding voters is in P, and for partitioning voters is coNP-hard.