Single-Peaked Opinion Updates

TL;DR

This paper studies opinion diffusion in networks with agents holding single-peaked preferences, identifying voting rules that preserve this structure and analyzing convergence and spread maximization of opinions.

Contribution

It introduces voting rules that maintain single-peakedness during opinion updates and provides algorithms for convergence and maximizing opinion spread.

Findings

Certain voting rules preserve single-peakedness during opinion diffusion.

The process converges to a stable state under these voting rules.

An efficient algorithm maximizes the spread of extreme opinions.

Abstract

We consider opinion diffusion for undirected networks with sequential updates when the opinions of the agents are single-peaked preference rankings. Our starting point is the study of preserving single-peakedness. We identify voting rules that, when given a single-peaked profile, output at least one ranking that is single peaked w.r.t. a single-peaked axis of the input. For such voting rules we show convergence to a stable state of the diffusion process that uses the voting rule as the agents' update rule. Further, we establish an efficient algorithm that maximises the spread of extreme opinions.