On the Tractability Landscape of the Conditional Minisum Approval Voting Rule

TL;DR

This paper analyzes the computational complexity of the Conditional Minisum Approval Voting Rule, showing it is generally hard but identifying practical restrictions that make it feasible, thus clarifying its applicability in real elections.

Contribution

It provides the first practical restrictions that render the problem computationally tractable and demonstrates their tightness, advancing understanding of conditional approval voting.

Findings

No significant algorithmic improvements over brute-force under common assumptions

Two practical restrictions make the problem computationally feasible

Conditional approval voting can be applied in practice under specific conditions

Abstract

This work examines the Conditional Approval Framework for elections involving multiple interdependent issues, specifically focusing on the Conditional Minisum Approval Voting Rule. We first conduct a detailed analysis of the computational complexity of this rule, demonstrating that no approach can significantly outperform the brute-force algorithm under common computational complexity assumptions and various natural input restrictions. In response, we propose two practical restrictions (the first in the literature) that make the problem computationally tractable and show that these restrictions are essentially tight. Overall, this work provides a clear picture of the tractability landscape of the problem, contributing to a comprehensive understanding of the complications introduced by conditional ballots and indicating that conditional approval voting can be applied in practice, albeit under specific conditions.