Parameterized Control Complexity in Fallback Voting

TL;DR

This paper analyzes the computational complexity of influencing fallback voting outcomes through candidate and voter modifications, revealing significant hardness results and fixed-parameter tractability in certain cases.

Contribution

It provides the first detailed parameterized complexity analysis of control problems in fallback voting, identifying W[2]-hardness and fixed-parameter tractability results.

Findings

Adding/deleting candidates are W[2]-hard for both cases.

Adding/deleting voters are W[2]-hard for constructive case.

Adding/deleting voters are in FPT for destructive case.

Abstract

We study the parameterized control complexity of fallback voting, a voting system that combines preference-based with approval voting. Electoral control is one of many different ways for an external agent to tamper with the outcome of an election. We show that adding and deleting candidates in fallback voting are W[2]-hard for both the constructive and destructive case, parameterized by the amount of action taken by the external agent. Furthermore, we show that adding and deleting voters in fallback voting are W[2]-hard for the constructive case, parameterized by the amount of action taken by the external agent, and are in FPT for the destructive case.