Models for collective social phenomena

World news is full of dramatic and unexpected events in politics and economics, from stock market crashes to the rapid rise of extreme political parties. Trust in an institution can evaporate overnight.

The world is plagued by "wicked problems" (corruption, belief in conspiracy theories, poverty, ...) that resist a solution even when considerable resources (money, personnel, expertise, government policy, incentives, social activism) are devoted to addressing the problem. 

Here I introduce some ideas and models that are helpful for efforts to understand these emergent phenomena. Besides rapid change and discontinuities, other relevant properties include herding, trending, tipping points, and resilient equilibria. Some cultural traits or habits are incredibly persistent, even when they are damaging to a community. 

I now consider some key elements for minimal models of these phenomena: discrete choices, utility, incentives, noise, social interactions, and heterogeneity.

Discrete choices

The system consists of N agents {i} who make individual choices. Examples of binary choices are whether or not to buy a particular product, vote for a political candidate, believe a conspiracy theory, accept bribes, get vaccinated, or join a riot. For binary choices, the state of each agent is modelled by an "Ising spin", S_i = +1 or -1. 

Utility

This is the function each agent wants to maximise; what they think they will gain or lose by their decision. This could be happiness, health, ease of life, money, or pleasure.  The utility U_i will depend on the incentives provided to make a particular choice, the personal inclination of the agent, and possibly the state of other agents.

Personal inclination

Let f_i be a number representing the tendency for agent i to choose S_1=+1. 

Incentives

All individuals make their decision based on the incentives offered. Knowledge of incentives is informed by public information.  This incentive F(t) may change with time. For example, the price of a product may decrease due to an advance in technology or a government may run an advertising program for a public health initiative.

Noise

No agent has access to perfect information in order to make their decision. This uncertainty can be modelled by a parameter beta, which increases with decreasing noise. According to the log-it rule the probability that of a particular decision is

1/beta is the analogue of temperature in statistical mechanics and this probability function is the Fermi-Dirac probability distribution! 

Social interactions

No human is an island. Social pressure and imitation play a role in making choices. Even the most "independent-minded" individual makes decisions that are influenced somewhat by the decisions of others they interact with. These "neighbours" may be friends, newspaper columnists, relatives, advertisers, or participants in an internet forum. The utility for an individual may depend on the choices of others. The interaction parameter J_ij is the strength of the influence of agent j on agent i.

Heterogeneity

Everyone is different. People have different sensitivities to different incentives. This diversity reflects different personalities, values, and life circumstances. This heterogeneity can be modelled by assigning a probability distribution rho(f_i).

Putting all the ideas above together the utility function for agent i is the following.

This means that the minimal model to investigate is a Random Field Ising model. It exhibits rich phenomena, many of which are similar to the social phenomena that were mentioned at the beginning of the post. Later posts will explore this.

The discussion above is drawn from a nice paper published in the Journal of Statistical Physics in 2013.

Crises and Collective Socio-Economic Phenomena: Simple Models and Challenges by Jean-Philippe Bouchaud.