Hysteresis, hype, niches, nudges and social change

The world is a mess. Most people want a better world. Sometimes nothing changes. Sometimes things change incredibly rapidly. Sometimes changes are positive. Other times the change is negative. Often this change is unanticipated, even by experts who have been studying the relevant topic for decades. Wicked problems are things that seem to be incredibly resilient to change. Examples of rapid changes that were (largely) positive and unanticipated were the peaceful collapse of the former Soviet empire, smoking in public becoming taboo, and increased public concern about climate change. Examples of negative changes include the rise of Trumpism, misinformation on social media, and the global financial crisis of 2008.

Many people in government, public policy, NGOs, and social activists want to implement policies and take actions that will produce outcomes that (they believe) are positive. Here I discuss some basic but very important insights from "social physics", such as discussed in my previous two posts.

Suppose the system of interest can be modelled by some type of Ising model where the pseudospin corresponds to two choices (good and bad) for each agent in the system. The policy maker wants to change something such as increase the incentive for agents to make the "good" choice. There are two qualitatively different possible behaviours and they are shown in the Figure below (taken from Bouchaud). 

The vertical axis is the "magnetisation", i.e, the fraction of agents who make the good choice. The horizontal axis is the "external field", i.e, the level of incentive provided for agents to make the good choice. 

Case I. Smooth curve (blue). This occurs when the interaction between agents is weaker than some threshold strength. Suppose that a small but not insignificant minority of agents are already making the good choice and then incentive is increased slightly. If one is near the steep part of the blue curve then this "nudge" can produce a desired outcome for the society.

Case II. Discontinuous curve (red). This occurs when the interaction between agents is greater than some threshold strength. People's choices are influenced more by their friends than by what the government or an NGO is telling them to do. Then one has to provided very large incentives to get a change in agent choice, far beyond the incentive required for a single isolated agent. The system is stuck in a state that is not good for the society as a whole. It is a metastable state, as shown in the figure below.

On the other hand, if the "polarisation field" is sitting near a critical value (5 in the figure, a tipping point), then a "nudge" can lead to a dramatic change for good. 

I think there are important implications for social activists of all stripes. Realistic expectations are key.

1. Don't expect even the best-designed and well-intentioned policy or action to necessarily have the impact you hope for.

2. Be sceptical about hype and ideology. In the public space there are a lot of claims, whether from political parties, pundits, or NGOs, that if we just do X (change this law, donate money, do what my book says, ...) then the good Y will inevitably follow.

The problem with unrealistic expectations is that they lead to disappointment, disillusionment, and burnout. People give up. Then the next fad or "silver bullet" comes along...

Inspired by a rugged landscape perspective, a better and more sustainable approach is that of learning and adaptation. One identifies what one thinks the best "nudge" is, tries something, evaluates the effect, adapts, and tries out some new ideas. One does not claim or expect the first few iterations to produce a significant desired effect. Here, somewhat "random" sampling of the landscape may help. Here a diversity of perspectives and methods can play a positive role. A more concrete version of this argument is in a paper concerned with public health initiatives. Rugged landscapes: complexity and implementation science, by Joseph T. Ornstein, Ross A. Hammond, Margaret Padek, Stephanie Mazzucca & Ross C. Brownson 

Postscript. After posting this I remember reading a recent article in The Economist pointing out how nudges often do not work.

Evidence for behavioural interventions looks increasingly shaky 

The academic literature is plagued by publication bias 

It references three recent Letters in PNAS, including this one, that come to the opposite conclusion to an earlier PNAS paper.

The effectiveness of nudging: A meta-analysis of choice architecture interventions across behavioral domains 

Stephanie Mertens, Mario Herberz, Ulf J. J. Hahnel, and Tobias Brosch

Sociological insights from statistical physics

Condensed matter physics and sociology are both about emergence. Phenomena in sociology that are intellectually fascinating and important for public policy often involve qualitative change, tipping points, and collective effects. One example is how social networks influence individual choices, such as whether or not to get vaccinated. In my previous post, I briefly introduced some Ising-type models that allow the investigation of fundamental questions in sociology. The main idea is to include heterogeneities and interactions in models of decision. 

What follows is drawn from Sections 2 and 3 of the following paper from the Journal of Statistical Physics. 

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

Bouchaud first considers a homogeneous population which reaches an equilibrium state. This is then described by an Ising model with an interaction (between agents) J, in an external field, F that describes the incentive for the agents to make one of the choices. The state of the model (in the mean-field approximation) is then found by solving the Curie-Weiss equation. In the sociological context, this was first derived by Weidlich and in the economic context re-derived by Brock and Durlauf.  (Aside: The latter paper is in one of the "top-five" economic journals, was published five years after submission, and has been cited more than 2000 times.)

As first noted by Weidlich, a spontaneous “polarization” of the population occurs in the low noise regime β>β c , i.e. [the average equilibrium value of S_z] ϕ ∗≠1/2 even in the absence of any individually preferred choice (i.e. F=0). When F≠0, one of the two equilibria is exponentially more probable than the other, and in principle the population should be locked into the most likely one: ϕ ∗>1/2 whenever F>0 and ϕ ∗<1/2 whenever F<0.

Unfortunately, the equilibrium analysis is not sufficient to draw such an optimistic conclusion. A more detailed analysis of the dynamics is needed, which reveals that the time needed to reach equilibrium is exponentially large in the number of agents, and as noted by Keynes, "in the long run, we are all dead." This situation is well-known to physicists, but is perhaps not so well appreciated in other circles—for example, it is not discussed by Brock and Durlauf.

Bouchaud then discusses the meta-stability associated with the two possible polarisations, as occurs in a first-order phase transition. From a non-equilibrium dynamical analysis, based on a Langevin equation, 

one finds that the time τ needed for the system, starting around ϕ=0, to reach ϕ ∗≈1 is given by: 𝜏 ∝ exp[𝐴𝑁(1−𝐹/𝐽)], where A is a numerical factor. This means that whenever 0<F<J, the system should really be in the socially good minimum ϕ ∗≈1, but the time to reach it is exponentially large in the population size.  The important point about this formula is the presence of the factor N(1−F/J) in the exponential.

In other words, it has no chance of ever getting there on its own for large populations. Only when F reaches J, i.e. when the adoption cost C becomes zero will the population be convinced to shift to the socially optimal equilibrium...

This is very different from the standard model of innovation diffusion, based on a simple differential equation proposed by Bass in 1969 [cited more than 10,000 times].

In physics, the existence of mutually inaccessible minima with different potentials is a pathology of mean-field models that disappears when the interaction is short-ranged. In this case, the transition proceeds through “nucleation”, i.e. droplets of the good minimum appear in space and then grow by flipping spins at the boundaries. 

This suggests an interesting policy solution when social pressure resists the adoption of a beneficial practice or product: subsidize the cost locally, or make the change compulsory there, so that adoption takes place in localized spots from which it will invade the whole population. The very same social pressure that was preventing the change will make it happen as soon as it is initiated somewhere.

This analysis provides concepts to understand wicked problems. Societies get "trapped" in situations that are not for the common good and outside interventions, such as providing incentives for individuals to make better choices, have little impact.

In the next post, I hope to discuss the role of heterogeneity (i.e. the role of a random field in the Ising model). A seminal paper published in the American Journal of Sociology in 1978 is Threshold models of collective behavior  by Mark Granovetter. It has been cited more than 6000 times. The central idea is how changes in heterogeneity can induce a transition between two different collective states.

Aside: The famous Keynes quote was in his 1923 publication, The Tract on Monetary Reform. The fuller quote is “But this long run is a misleading guide to current affairs. In the long run we are all dead. Economists set themselves too easy, too useless a task, if in tempestuous seasons they can only tell us, that when the storm is long past, the ocean is flat again.”

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.