Public opinion by a poll process: model study and Bayesian view

TL;DR

This paper models public opinion formation in open polls using a probabilistic voting process, revealing how initial biases can lead to diverse poll outcomes, and interprets the process through Bayesian analysis.

Contribution

It introduces a beta distribution-based model for public opinion polls and connects it with Bayesian inference, highlighting the impact of initial bias on poll results.

Findings

Poll scores follow a beta distribution in large polls

Contradictory poll results can occur with non-zero probability

Initial bias influences the likelihood of various poll outcomes

Abstract

We study the formation of public opinion in a poll process where the current score is open to public. The voters are assumed to vote probabilistically for or against their own preference considering the group opinion collected up to then in the score. The poll-score probability is found to follow the beta distribution in the large polls limit. We demonstrate that various poll results even contradictory to the population preference are possible with non-zero probability density and that such deviations are readily triggered by initial bias. It is mentioned that our poll model can be understood in the Bayesian viewpoint.