Control Complexity in Fallback Voting

TL;DR

This paper investigates the complexity of controlling fallback voting elections and demonstrates its resistance to various control strategies, highlighting its robustness compared to other voting systems.

Contribution

It proves that fallback voting is resistant to all common types of candidate and constructive control, expanding understanding of its robustness against election manipulation.

Findings

Fallback voting is resistant to all common candidate control types.

Fallback voting is resistant to all common constructive control types.

Fallback voting offers a robust alternative with high resistance to election control.

Abstract

We study the control complexity of fallback voting. Like manipulation and bribery, electoral control describes ways of changing the outcome of an election; unlike manipulation or bribery attempts, control actions---such as adding/deleting/partitioning either candidates or voters---modify the participative structure of an election. Via such actions one can try to either make a favorite candidate win ("constructive control") or prevent a despised candidate from winning ("destructive control"). Computational complexity can be used to protect elections from control attempts, i.e., proving an election system resistant to some type of control shows that the success of the corresponding control action, though not impossible, is computationally prohibitive. We show that fallback voting, an election system combining approval with majority voting, is resistant to each of the common types of candidate control and to each common type of constructive control. Among natural election systems with a polynomial-time winner problem, only plurality and sincere-strategy preference-based approval voting (SP-AV) were previously known to be fully resistant to candidate control, and only Copeland voting and SP-AV were previously known to be fully resistant to constructive control. However, plurality has fewer resistances to voter control, Copeland voting has fewer resistances to destructive control, and SP-AV (which like fallback voting has 19 out of 22 proven control resistances) is arguably less natural a system than fallback voting.