Sznajd model, also known as united we stand, divided we fall model, is another classical model in opinion dynamics. It was proposed in 2000 by two Polish scientists in [1] and since then it was heavily studied both by various groups of sociophysicists. It was used not only in the usual generic scenarios (e.g., exploring how fast the opinions converge), but also helped to predict Polish elections of 2015 [2].

It is often said that turning up to vote is not quite rational behavior, because the probability that your vote would decided the outcome is minuscule. Opponents of such outlook say that it is rational to vote, because you might want to show support for the political system (democracy) or to avoid the regret.

I guess at least one person in Byron-Bethany irrigation district in California feels such regret, because the last election outcome in this district was decided by three random rolls of the twenty sided dice. More details in the CBS video below.

We had quite a lot of fun while exploring price formation topic as well as order book models back in 2018. The last year was our best year since 2013 as we have published 39 posts and 15 interactive models, while in 2013 we had 42 posts and 16 interactive models.

Fig. 1:The number of posts written in English and still available on this iteration of Physics of Risk. The wide bars represent total number of posts for each year since 2010, while the narrower bars represent a number of posts with 'Interactive models' tag.

Note that our history stretches back into 2006 and some of the data is not reflected in the graph above. Here we do not account for the posts, which where written in Lithuanian only. While most of these are not lost and are safely stored, their recovery and proper translation is a bit more complicated matter.

So far the plan for this year (2019) is to continue our recently started series of posts on opinion dynamics. What will come next only the time will show.

Few years ago we have already introduced a more sophisticated version of the model we are going to talk about this week. We have already covered so called "Referendum model" by S. Galam [1], while talking about many particle interactions in kinetic exchange models. This time we will cover a precursor to this model, which was also reviewed in [1].

Couple of years ago we have discussed one of the most prominent models in opinion dynamics - voter model. This time we consider a generalization of the voter model, which draws inspiration from the Ising model. This generalization, known as majority-vote model [1, 2], adds thermal noise and hence the average opinion, \( M \), no longer converges to a fixed point if the amount of noise is just right.