Online Temporal Voting: Strategyproofness, Proportionality and Asymptotic Analysis

TL;DR

This paper analyzes online temporal voting rules, establishing their strategyproofness and proportionality properties, introducing the concept of the price of manipulability, and demonstrating asymptotic proportional representation guarantees.

Contribution

It introduces online variants of voting properties, links online independence of irrelevant alternatives to strategyproofness, and analyzes the asymptotic behavior of voting rules.

Findings

OIIA implies OSP in online voting.

Perpetual Phragmen satisfies OSP and PJR.

Serial Dictator is fully strategyproof and asymptotically satisfies PJR.

Abstract

We study online temporal voting, where a group of voters submit 0/1 approvals on sets of alternatives that arrive online over multiple rounds and a single alternative is chosen in each round. We introduce online variants of two well-known game theoretic properties, strategyproofness (SP) and independence of irrelevant alternatives. We show that online independence of irrelevant alternatives (OIIA) is a sufficient condition for online strategyproofness (OSP), and that several known online voting rules satisfy OIIA and thus OSP, but that they are not SP. In particular, we show that Perpetual Phragmen, the only known online voting rule to satisfy PJR, satisfies OSP. The Method of Equal Shares (MES), a semi-online voting rule knwon to satisfy wEJR, also satisfies OSP. We then introduce the price of manipulability, which quantifies the effect of strategic behaviour on proportional representation guarantees. Finally, we introduce asymptotic satisfaction of proportional representation and show that an online voting rule, Serial Dictator, is fully strategyproof and satisfies proportional justified representation (PJR) up to an additive constant.