Manipulable outcomes within the class of scoring voting rules

TL;DR

This paper characterizes all manipulable outcomes in scoring voting rules and calculates the probability of such outcomes under certain conditions, enhancing understanding of voting manipulation risks.

Contribution

It introduces a new approach to identify all manipulable outcomes in scoring rules for any number of alternatives and electorate sizes.

Findings

Identifies all outcomes that can be manipulated in scoring voting rules.

Provides probability estimates of manipulable outcomes for small numbers of alternatives.

Applies the approach to well-studied scoring rules under common preference assumptions.

Abstract

Coalitional manipulation in voting is considered to be any scenario in which a group of voters decide to misrepresent their vote in order to secure an outcome they all prefer to the first outcome of the election when they vote honestly. The present paper is devoted to study coalitional manipulability within the class of scoring voting rules. For any such rule and any number of alternatives, we introduce a new approach allowing to characterize all the outcomes that can be manipulable by a coalition of voters. This gives us the possibility to find the probability of manipulable outcomes for some well-studied scoring voting rules in case of small number of alternatives and large electorates under a well-known assumption on individual preference profiles.