Deviations from the Majority: A Local Flip Model

TL;DR

This paper explores how probabilistic deviations from local majority rules in opinion dynamics and hierarchical voting models lead to complex behaviors, including multiple fixed points and tipping points, especially in groups of sizes 3 and 5.

Contribution

It introduces a novel probabilistic flip mechanism in the Galam model, revealing complex dynamics and fixed point structures not seen in previous versions.

Findings

Identification of multiple fixed points in group size 5.

Discovery of interplay between attractors and tipping points.

Analysis of larger groups extending the model's scope.

Abstract

We study the effect of probabilistic distortions to the local majority rules used in the Galam model of opinion dynamics and bottom-up hierarchical voting. A different probability for a flip against the local majority within the discussion group is associated with each ratio of majority / minority. The cases of groups of sizes 3 and 5 are investigated in detail. For hierarchical voting, the local flip corresponds to a `faithless elector', a representative who decides to vote against the choice of their electing group. Depending on the flip probabilities, the model exhibits a rich variety of patterns for the dynamics, which include novel features in the topology of the landscape. In particular, for size 5, we uncover for the first time an interplay between five fixed points, which split into either three attractors and two tipping points or two attractors and three tipping points, depending on the flip probabilities. Larger groups are also analysed. These features were absent in the former versions of the Galam model, which has at maximum three fixed points for any group size. The results shed a new light on a series of social phenomena triggered by one single individual who acts against the local majority.