Computational Complexity Characterization of Protecting Elections from Bribery

TL;DR

This paper investigates the computational complexity of protecting elections from bribery by modeling a bi-level decision problem where a protector can safeguard voters, revealing that protection is often computationally harder than bribery, with some cases solvable efficiently.

Contribution

It provides a comprehensive complexity analysis of election protection problems, establishing that they are generally more complex than bribery problems, including some being -complete.

Findings

Protection problems are ^2-complete even in restricted cases.

Most bribery problems are in NP, while protection problems are often harder.

Some protection problems can be solved in polynomial time.

Abstract

The bribery problem in election has received considerable attention in the literature, upon which various algorithmic and complexity results have been obtained. It is thus natural to ask whether we can protect an election from potential bribery. We assume that the protector can protect a voter with some cost (e.g., by isolating the voter from potential bribers). A protected voter cannot be bribed. Under this setting, we consider the following bi-level decision problem: Is it possible for the protector to protect a proper subset of voters such that no briber with a fixed budget on bribery can alter the election result? The goal of this paper is to give a full picture on the complexity of protection problems. We give an extensive study on the protection problem and provide algorithmic and complexity results. Comparing our results with that on the bribery problems, we observe that the protection problem is in general significantly harder. Indeed, it becomes $\sum_{p}^2$-complete even for very restricted special cases, while most bribery problems lie in NP. However, it is not necessarily the case that the protection problem is always harder. Some of the protection problems can still be solved in polynomial time, while some of them remain as hard as the bribery problem under the same setting.