Campaign Management under Approval-Driven Voting Rules

TL;DR

This paper analyzes the computational complexity of campaign management strategies under approval-like voting rules, identifying cases that are computationally easy or hard, and proposing fixed-parameter tractable algorithms for certain scenarios.

Contribution

It provides a detailed complexity analysis of campaign management under approval-driven voting rules and introduces fixed-parameter algorithms for challenging cases.

Findings

Optimizing candidate promotion by moving candidates up in preferences is computationally easy for Bucklin and Fallback.

Changing the number of approved candidates is computationally hard even with small modifications.

Fixed-parameter algorithms are effective in a broad class of scenarios.

Abstract

Approval-like voting rules, such as Sincere-Strategy Preference-Based Approval voting (SP-AV), the Bucklin rule (an adaptive variant of $k$-Approval voting), and the Fallback rule (an adaptive variant of SP-AV) have many desirable properties: for example, they are easy to understand and encourage the candidates to choose electoral platforms that have a broad appeal. In this paper, we investigate both classic and parameterized computational complexity of electoral campaign management under such rules. We focus on two methods that can be used to promote a given candidate: asking voters to move this candidate upwards in their preference order or asking them to change the number of candidates they approve of. We show that finding an optimal campaign management strategy of the first type is easy for both Bucklin and Fallback. In contrast, the second method is computationally hard even if the degree to which we need to affect the votes is small. Nevertheless, we identify a large class of scenarios that admit fixed-parameter tractable algorithms.