In a small society of four families, a situation may arise regarding buying a car in each family. The wives may feel the importance of buying a car and the husbands may stand for an opinion opposite to that. If each of them is determined to defend their own interests, then the consensus formed for and against the motion is exactly half. In such a scenario, both the parties try to convince each other showing their reasons and interests. Interestingly, one day, one of the wives made a successful attempt to convince her husband and buys a car. Gradually, the consensus starts building up for the motion through logic and discussions, and the whole society gets biased towards buying a car. The full consensus is established and it goes for the motion. A similar thing happens in fashion trends, marketing strategies and economy.
Opinion and agreement are the crucial factors of social group behavior. Recently physicists have started taking their interest on this fact and many different models have been put forward to study such dynamics. The voter model, majority rule model, social impact theory and Sznajd model are some of the well-known models . Out of these, the Sznajd model has proved its utility more towards predicting the opinion dynamics of social groups. The basic principle that the model considers is the fact that convincing somebody becomes easier for two or more people than a single individual.
Simply put, the conditions are:
Thus, if the neighboring agents ( ) share the same opinion, they convince their respective neighbors. Otherwise, if they disagree, then each agent imposes the opinion on each other’s neighbor.
The most successful application of the model has been done in politics. The modifications to the Sznajd model could successfully reproduce the distribution of number of candidates according to the number of votes they received in Brazilian and Indian elections . The model has also proved to be successful in predicting the market behavior. Consider the situation in a duopoly market. Two products A and B, with A being superior to B. The question is, how strong the advertisement has to be for B, in order to occupy the whole market. Naturally, the advertisement and the neighbor’s choice influences a customer’s response to a product. The advertisement, however, acts as an external field. In this case, the model predicts a critical level of advertising and a critical value of the initial concentration of customers above which the particular product will grab the market. It is found, for an initial customer concentration of 0.1, the critical advertising level happens to be 0.25 .
Besides politics and the market, sometimes there are issues of national importance. The nation’s consensus always doesn’t come with clarity and rather there are shades in it. Let us divert a bit and go back to the situation of post-World War II. The tensed cold war situation between Russia and America was shaking the world. In the middle of this, a study was made by Maurice Faber on the human psychology of show-down. The study was conducted on the American minds through a questionnaire. Faber coins the term “Armageddon Complex” to portray the frame of mind which wanted a showdown on Russia against all the odds. Deep within the core of this complex, lies the drama of a showdown and a war seems to be necessary or inevitable. Interestingly, people having this complex of Armageddon happens to be categorically different. Male participants were more towards favoring an Armageddon than female, those who had slightly or highly unsatisfactory future outlook were favoring the Armageddon more than the people with relatively better future prospects. There was even religious outlook to this complex of Armageddon .
In the modern world, cities having multicultural diversity and cosmopolitan distribution, there could be many issues upon which a consensus need to be formed. The extreme conditions of volatility such as an Armageddon, once parameterized would help in formulating the conditions influencing the situation. Despite being individuals, in many situations, people behave like particles without a feeling and free will . The models help to explore this and predict possible social behavior. The other strong model, called the voter model, considers the notion that adoption of an opinion depends upon the frequency of that opinion in the neighborhood . The Sznajd model is, in fact, a special case of this model.
In conclusion, it is of crucial importance for any society to parameterize the factors influencing the opinion so that better, positive and strong consensus could be formed.
The gif shows a crude evolution of consensus based on the first condition above. Initially, the opinions are randomly distributed and at each time step, a pair is also randomly selected. The red and blue dots corresponds to mutually opposite opinions. If all the dots are of the same color, a full consensus will be said to be established.