Copeland Voting Fully Resists Constructive Control

TL;DR

This paper demonstrates that Copeland voting, especially the Copeland^0.5 system, is fully resistant to constructive control, extending resistance results across all rational tie-value parameters and various control scenarios.

Contribution

It establishes the full resistance of Copeland^0.5 to constructive control and extends resistance and tractability results to all rational alpha in Copeland^alpha.

Findings

Copeland^0.5 provides full resistance to constructive control.

Resistance results are extended to all rational alpha between 0 and 1.

The paper includes analysis of bribery and fixed-parameter tractability for Copeland^alpha.

Abstract

Control and bribery are settings in which an external agent seeks to influence the outcome of an election. Faliszewski et al. [FHHR07] proved that Llull voting (which is here denoted by Copeland^1) and a variant (here denoted by Copeland^0) of Copeland voting are computationally resistant to many, yet not all, types of constructive control and that they also provide broad resistance to bribery. We study a parameterized version of Copeland voting, denoted by Copeland^alpha where the parameter alpha is a rational number between 0 and 1 that specifies how ties are valued in the pairwise comparisons of candidates in Copeland elections. We establish resistance or vulnerability results, in every previously studied control scenario, for Copeland^alpha, for each rational alpha, 0 <alpha < 1. In particular, we prove that Copeland^0.5, the system commonly referred to as ``Copeland voting,'' provides full resistance to constructive control. Among the systems with a polynomial-time winner problem, this is the first natural election system proven to have full resistance to constructive control. Results on bribery and fixed-parameter tractability of bounded-case control proven for Copeland^0 and Copeland^1 in [FHHR07] are extended to Copeland^alpha for each rational alpha, 0 < alpha < 1; we also give results in more flexible models such as microbribery and extended control.