Let us close this year with a model proposed by us and which is based on the Kirman model. The main difference from the original model is that here we have multiple state dynamics. Yet unlike in our three state approach to the financial markets (see the initial post here or the article [1]) this time we allow any number of states to be defined in the model [2, 3].

Significant portion of our works in the last decade are based on the Kirman model, which itself is inspired by the behavior of social insects. Experiments which inspired Kirman to formulate his agent-based model actually used ant colonies as their observation object (recall our first post on the Kirman model). Now it appears that scientists at MIT are doing the opposite - using ants as a living agent-based model.

Let us briefly come back to the Deffuant's model and look at one of its common generalizations. Namely let us allow tolerance to vary. Varying tolerance to different opinions would be a rather natural assumption as it is usually hard to persuade a radical, while it is somewhat easier to persuade a moderate.

It appears that people are even more terrible at randomness than computers. Usually human ``randomness'' is too uniform. In the following video by Numberphile Simon Pampena has put forward an interesting task for Brady - to write down a series of 20 coin flips. The series wasn't as random as one would reasonably expect. Watch the following video to gain some insights into randomness.

Recall our discussion on the "hot hand phenomenon" earlier? We believe that this might be at least tangently related. Both of these observation could be explained a simple fact that we as humans want to see patterns everywhere. We think that the world has to make sense, it simply can't be random. If we see longer streak of successes we believe that it is not random, though as we have now seen streaks of success indeed can be random.

All of the opinion dynamics models we have considered so far had discrete opinions. However it would be rather natural to think about opinions as being continuous. Opinions become discrete only due to the way we observe them, namely ballots in the elections and questionnaires in the polls can have only discrete options (even in case you can write in your own preference). Also discrete opinions are easier to analyze, only then one can talk about the majority or compare their popularity.

Nevertheless there are few interesting models with continuous opinions. Usually these models are based on the concept of bounded confidence. Meaning that people tend to listen to other people who have a relatively similar opinion to theirs. Here in this post we will discuss one of these bounded confidence models proposed by Hegselmann and Krause in [1].