Complexity of Manipulative Actions When Voting with Ties

TL;DR

This paper investigates how allowing voters to have ties in their preferences affects the computational complexity of manipulation, bribery, and control in election systems, revealing both increases and decreases in complexity.

Contribution

It extends the analysis of election problems to include voters with ties, providing new complexity results and a general understanding of their impact on election manipulation.

Findings

Allowing ties can both increase and decrease manipulation complexity.

Extended the definitions of election systems to handle voters with ties.

Provided a general result on the effect of ties on control complexity.

Abstract

Most of the computational study of election problems has assumed that each voter's preferences are, or should be extended to, a total order. However in practice voters may have preferences with ties. We study the complexity of manipulative actions on elections where voters can have ties, extending the definitions of the election systems (when necessary) to handle voters with ties. We show that for natural election systems allowing ties can both increase and decrease the complexity of manipulation and bribery, and we state a general result on the effect of voters with ties on the complexity of control.