Consider a social network in which people (agents) hold a belief or opinion about the state of something in the world, such as the quality of a particular product, the effectiveness of a public policy, or the reliability of a news agency.
[1] Some of the main questions asked in the literature include:[2] Bayesian learning is a model which assumes that agents update their beliefs using Bayes' rule.
This parameter could correspond to an opinion among people about a certain social, economic, or political issue.
According to the DeGroot model, each agent takes a weighted average of their neighbors' opinions at each step to update their own belief.
Since the DeGroot model can be considered a Markov chain, provided that a network is strongly connected (so there is a direct path from any agent to any other) and satisfies a weak aperiodicity condition, beliefs will converge to a consensus.
In the case of a converging opinion dynamic, the social network is called wise if the consensus belief is equal to the true state of the world.
It can be shown that the necessary and sufficient condition for wisdom is that the influence of the most influential agent vanishes as the network grows.
In one such experiment, 665 subjects in 19 villages in Karnataka, India, were studied while communicating information with each other to learn the true state of the world.
The study showed that agents' aggregate behavior is statistically significantly better described by the DeGroot learning model.