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

We study the formation of public opinion in a poll process where the current score is open to the 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 those 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.