# Protecting Elections by Recounting Ballots

## TL;DR

This paper models a two-stage election manipulation and recount process as a Stackelberg game, analyzing the computational complexity for attackers and defenders under different voting rules.

## Contribution

It provides a comprehensive complexity analysis of manipulation and recount strategies in plurality voting, highlighting the computational challenges faced by both attackers and defenders.

## Key findings

- Complexity results for manipulation and recount under different scenarios.
- Almost complete complexity landscape for attacker and defender strategies.
- Insights into the computational difficulty of protecting election integrity.

## Abstract

Complexity of voting manipulation is a prominent topic in computational social choice. In this work, we consider a two-stage voting manipulation scenario. First, a malicious party (an attacker) attempts to manipulate the election outcome in favor of a preferred candidate by changing the vote counts in some of the voting districts. Afterwards, another party (a defender), which cares about the voters' wishes, demands a recount in a subset of the manipulated districts, restoring their vote counts to their original values. We investigate the resulting Stackelberg game for the case where votes are aggregated using two variants of the Plurality rule, and obtain an almost complete picture of the complexity landscape, both from the attacker's and from the defender's perspective.