# The impact of random actions on opinion dynamics

## TL;DR

This paper demonstrates theoretically that in opinion dynamics models where agents internalize actions instead of beliefs, the final collective decision remains inherently random, highlighting the role of information loss in herding behavior.

## Contribution

It introduces modified opinion dynamics models showing that the final outcome is almost surely random due to internalization of actions, revealing the mechanism behind irrational herding.

## Key findings

- Final outcomes are almost surely random despite possible consensus or polarization.
- Loss of nuanced private information leads to irrational herding behavior.
- Theoretical proof confirms the randomness persists across various models.

## Abstract

Opinion dynamics have fascinated researchers for centuries. The ability of societies to learn as well as the emergence of irrational {\it herding} are equally evident. The simplest example is that of agents that have to determine a binary action, under peer pressure coming from the decisions observed. By modifying several popular models for opinion dynamics so that agents internalize actions rather than smooth estimates of what other people think, we are able to prove that almost surely the actions final outcome remains random, even though actions can be consensual or polarized depending on the model. This is a theoretical confirmation that the mechanism that leads to the emergence of irrational herding behavior lies in the loss of nuanced information regarding the privately held beliefs behind the individuals decisions.