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].

This year I got to teach a numerical methods course to first year students in Faculty of Physics (Vilnius University). As theory is somewhat boring and feels somewhat detached from practice, I have decided to provide students with practical showcase on how to work with empirical data. For this showcase I have selected a small subset of a larger football data set. Namely, I decided to take a look at English Premier League's 2000/2001 season.

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 Deffuant et al. in [1].