Repulsion in controversial debate drives public opinion into fifty-fifty stalemate

TL;DR

This paper shows that repulsion in controversial debates causes public opinion to often become evenly split, leading to stalemates that hinder political decision-making.

Contribution

It introduces a voter model incorporating repulsion and undecided states, revealing how these factors lead to fifty-fifty opinion stalemates in controversial debates.

Findings

Repulsion from opinions promotes fifty-fifty stalemates.

Undecided states increase when agents frequently switch from decided to undecided.

The model explains the persistence of stalemates in controversial debates.

Abstract

Opinion formation is a process with strong implications for public policy. In controversial debates with large consequences, the public opinion is often trapped in a fifty-fifty stalemate, jeopardizing broadly accepted political decisions. Emergent effects from millions of private discussions make it hard to understand or influence this kind of opinion dynamics. Here we demonstrate that repulsion from opinions favors fifty-fifty stalemates. We study a voter model where agents can have two opinions or an undecided state in-between. In pairwise discussions, undecided agents can be convinced or repelled from the opinion expressed by another agent. If repulsion happens in at least one of four cases, as in controversial debates, the frequencies of both opinions equalize. Further we include transitions of decided agents to the undecided state. If that happens often, the share of undecided agents becomes large, as can be measured with the share of undecided answers in polls.