Verifying Proportionality in Temporal Voting

TL;DR

This paper investigates the complexity of verifying proportional representation in a temporal voting model, revealing increased difficulty over traditional multiwinner voting but also identifying cases with efficient solutions.

Contribution

It introduces the complexity analysis of outcome verification in temporal voting and highlights special cases where verification can be performed efficiently.

Findings

Verification is strictly harder in temporal voting than in multiwinner voting.

Certain natural cases allow for efficient verification algorithms.

Abstract

We study a model of temporal voting where there is a fixed time horizon, and at each round the voters report their preferences over the available candidates and a single candidate is selected. Prior work has adapted popular notions of justified representation as well as voting rules that provide strong representation guarantees from the multiwinner election setting to this model. In our work, we focus on the complexity of verifying whether a given outcome offers proportional representation. We show that in the temporal setting verification is strictly harder than in multiwinner voting, but identify natural special cases that enable efficient algorithms.