Opinion Dynamics lacks a theoretical basis. In this article, I propose to use a decision-theoretic framework, based on the updating of subjective probabilities, as that basis. We will see we get a basic tool for a better understanding of the interact
ion between the agents in Opinion Dynamics problems and for creating new models. I will review the few existing applications of Bayesian update rules to both discrete and continuous opinion problems and show that several traditional models can be obtained as special cases or approximations from these Bayesian models. The empirical basis and useful properties of the framework will be discussed and examples of how the framework can be used to describe different problems given.
We study the dynamics of the adoption of new products by agents with continuous opinions and discrete actions (CODA). The model is such that the refusal in adopting a new idea or product is increasingly weighted by neighbor agents as evidence against
the product. Under these rules, we study the distribution of adoption times and the final proportion of adopters in the population. We compare the cases where initial adopters are clustered to the case where they are randomly scattered around the social network and investigate small world effects on the final proportion of adopters. The model predicts a fat tailed distribution for late adopters which is verified by empirical data.
A model where agents show discrete behavior regarding their actions, but have continuous opinions that are updated by interacting with other agents is presented. This new updating rule is applied to both the voter and Sznajd models for interaction be
tween neighbors and its consequences are discussed. The appearance of extremists is naturally observed and it seems to be a characteristic of this model.
In this article, I investigate the use of Bayesian updating rules applied to modeling social agents in the case of continuos opinions models. Given another agent statement about the continuous value of a variable $x$, we will see that interesting dyn
amics emerge when an agent assigns a likelihood to that value that is a mixture of a Gaussian and a Uniform distribution. This represents the idea the other agent might have no idea about what he is talking about. The effect of updating only the first moments of the distribution will be studied. and we will see that this generates results similar to those of the Bounded Confidence models. By also updating the second moment, several different opinions always survive in the long run. However, depending on the probability of error and initial uncertainty, those opinions might be clustered around a central value.
