Determining Winners in Elections with Absent Votes

TL;DR

This paper investigates the computational complexity of determining election winners with absent votes in top-truncated rankings, revealing NP-completeness for several voting rules and polynomial-time solutions for specific cases.

Contribution

It establishes the NP-completeness of the winner determination problem with absent votes for multiple voting rules and identifies a special case solvable in polynomial time.

Findings

NP-complete for single transferable vote, Maximin, and Copeland

Polynomial-time solution for a special positional scoring rule case

Hardness persists even with bounded candidates or missing votes

Abstract

An important question in elections is the determine whether a candidate can be a winner when some votes are absent. We study this determining winner with the absent votes (WAV) problem when the votes are top-truncated. We show that the WAV problem is NP-complete for the single transferable vote, Maximin, and Copeland, and propose a special case of positional scoring rule such that the problem can be computed in polynomial time. Our results in top-truncated rankings differ from the results in full rankings as their hardness results still hold when the number of candidates or the number of missing votes are bounded, while we show that the problem can be solved in polynomial time in either case.