On the Complexity of the Two-Stage Majoritarian Rule

TL;DR

This paper analyzes the computational complexity of various decision problems related to the two-stage majoritarian rule in sequential voting, providing a comprehensive complexity landscape for these problems.

Contribution

It offers a detailed complexity analysis of key election and manipulation problems under the two-stage majoritarian rule, expanding understanding of its computational properties.

Findings

Complexity results for agenda control and coalition manipulation.

Complexity classifications for possible and necessary winner problems.

Insights into the computational difficulty of standard election control problems.

Abstract

Sequential voting rules have played a crucial role in shaping decisions within parliamentary and legislative frameworks. After observing that the existing sequential rules fail several fundamental axioms, Horan and Sprumont [2022] proposed a sequential rule named two-stage majoritarian rule (TSMR). This paper examines this rule by investigating the complexity of {\sc{Agenda Control}}, {\sc{Coalition Manipulation}}, {\sc{Possible Winner}}, {\sc{Necessary Winner}}, and eight standard election control problems. Our study offers a comprehensive insight into the complexity landscape of these problems.