Thomas Schelling, Game Theory and anti-racism
What the model of a Nobel Prize-winning economist can tell us about building diverse communities.
Few economists are as versatile or innovative as Thomas Schelling. The sociologist James Coleman once wrote that Schelling used to live “by his wits”, which were not strictly research-based. Prior to winning the Nobel Prize in Economics in 2005, the game theory pioneer had written about nuclear conflict and tacit communication, famously comparable to two people trying to meet in New York City without setting a meeting point — — all a game of guessing each others’ guesses. Beneath a lot of his work lies the general principle of beginning to address any problem by first trying to look at it through other people’s eyes. A simple yet underestimated lesson that many negotiators often fail to remember. Through this precise principle, his inventive model on neighborhood segregation is still useful today. It ended up providing conceptual insights into understanding the difference between non-racist and anti-racist behaviour and how micro decisions might lead to undesired macro outcomes.
His work arguably saved the field of game theory from irrelevance and helped the world avoid a nuclear war. It mixed elements of behavioural economics and mathematics, and applied it to real-world examples. He relied on thoroughly constructed analogies as well as well-chosen words, which made his material accessible to any curious reader.
Like most models, its empirical applications are limited. William Easterly has argued that Schelling’s work doesn’t explain the segregated neighbourhoods in the USA. A wide range of variables affects one’s decision to move, such as transportation, work commute and safety, all of which the paper does not cover — although some adjustments in the original model have been made to explain real-world neighbourhoods in Israel. Nonetheless, it can be quite useful to draw ideas from it on a conceptual level.
The model consisted of 138 agents divided into two types (blacks and whites, let’s say) organised in a 13x16 space, each agent occupying one single space, having only preferences on who are the neighbours, and being able to move. A neighborhood was defined as the 3x3 space that an agent was in. Having a 1/2 preference threshold, thus, would mean for an agent to prefer having 3 alike neighbours and a maximum of 4 different ones. At first, Schelling assigned all the agents by chance and eventually a few got dissatisfied and would wish to move. If randomly positioned agents had that 1/2 tolerance threshold mentioned, however, after multiple iterations the outcome would be stable segregated neighbourhoods. More remarkably, the outcome is still segregation when the preference threshold drops to a 1/3 demand for alike neighbours. In other words, even if people are willing to be in a 1/3 minority, neighbourhoods are likely to be segregated. If agents demand to be at least in a 1/2 situation, segregation over time is even greater. That is to say, if we had individuals which do not necessarily want to live in a neighborhood with no diversity, but do not want to live in a neighborhood in which they are in a less than 1/2 scenario, over time we would reach segregation. More shockingly, the same happens if the individuals are open to go as far as to be in a 1/3, but not further. The figures below are from Schelling’s original paper. It shows that somewhat tolerant individuals can make decisions that lead to undesired aggregate outcomes.
And it gets worse. In his model, we can have unequal demands. A type of agent can be more demanding than the other. If so, both sides are affected equally because separation is reciprocal by definition. We can also have unequal numbers, in which a type of agent can be in a minority. In real life, we often have unequal demands and unequal numbers at the same, and, in addition, most neighbourhoods were not randomly organised from the beginning. Quite the opposite, segregation is commonly the norm, not the exception. Starting from an already segregated scenario and aiming to revert it to a randomly organised one is far harder than simply maintaining the latter scenario, but this is unfortunately the reality we are faced with. The tragedy is that each of these adjustments, in line with some features of reality, invariably results in even more segregated outcomes.
Moreover, preferences are not equally distributed across agents and we don’t have a 50–50 split of them.
In other words, imagine, for instance, that we are talking about a neighbourhood full of white people and there are different degrees of racism across households. The most racist residents will not tolerate any Black family there. When the first family arrives, they leave. Their departure, however, affects the remaining households. Since the percentage of Black people in the neighborhood has increased, the second most racist group might not tolerate that and leave as well. At some point, even those who have a high tolerance threshold might be compelled to leave. That is the tipping point part of the theory. A few individual decisions, thus, generate a self-reinforcing cycle of segregation which leads to undesired aggregate outcomes — neighborhoods with no diversity. Certainly, the majority of people in that neighbourhood do not wish to have near-zero diversity, but since they have mere tolerance towards diversity, that ends up being the aggregate outcome.
A possible analogy to draw would be to see tolerance as a non-racist attitude. Anti-racism, in this analogy, would be to actively seek diverse neighbours. Instead of merely being tolerant or indifferent, an anti-racist person would be one actively seeking to be surrounded by different people. Or the one actively looking to diversify the authors on their shelves with books by Chimamanda Ngozi Adichie, Reni Eddo-Lodge, or Ralph Ellison.
Schelling has translated this idea to his model by including integrationist preferences. Now, instead of having a mere preference for their alike, agents also have a preference for integration. That is, they want to have different neighbours as well as alike neighbours. In the previous cases, agents were not seeking to have near-zero diversity, but would not mind if that were the case. In this new set up, however, they have an upper limit as well as a lower limit of tolerance for alike neighbours. Now, therefore, agents would not get satisfied if all their neighbours were alike. By doing so, Schelling has obtained strikingly different results, as Fig. 17 from his original paper shows. Nicky Case has gamified these ideas into another model. As Figure 1 below shows, when the initial organisation is segregation, and the demand for alike neighbours is 1/5, the agents barely move and the outcome is segregation. However, from the same initial settings, when agents have a demand for 1/5 different neighbours as well as for 1/5 alike ones, an outcome with barely any segregation is reached. In both Schelling’s and Case’s, integration requires more complex patterning and, equilibrium, when possible, is only reached after more iterations.
Thus, if this change in the model can be taken as a proxy of the difference between non-racist and anti-racist attitudes, a possible conclusion is that both attitudes do, in fact, result in different outcomes. One can be tolerant, but if diversity in the neighborhood is not actively sought, the result reached is still suboptimal. To go beyond mere dropping the demand for alike neighbours and increasing the tolerance threshold, therefore, the conversation must go forward and demand people to adopt an active role in pursuing diversity and, as importantly, acknowledge and speak up about near-zero diversity environments. A look at one’s surroundings can often reveal a lot about how easily people naturalise homogeneous settings, not unlike the first agents in Schelling’s model. Just a bit of demand for diversity, fortunately, can change it.
Bibliography:
Case, n., & Hart, v. (n.d.). Parable of the polygons. Retrieved 06 18, 2020, from https://ncase.me/polygons/
Easterly, W. (2009). The Tipping Point: Fascinating but mythological? Retrieved 06 18, 2020, from https://voxeu.org/article/tipping-point-fascinating-mythological
Harford, T. (2005). How an economic theory beat the atomic bomb. Retrieved 06 18, 2020, from https://www.ft.com/content/6d00b8f6-3a81-11da-b0d3-00000e2511c8
Harris, E. A. (2020). People Are Marching Against Racism. They’re Also Reading About It. Retrieved 06 18, 2020, from https://www.nytimes.com/2020/06/05/books/antiracism-books-race-racism.html
Hatna, E., & Benenson, I. (2012). The Schelling Model of Ethnic Residential Dynamics: Beyond the Integrated — Segregated Dichotomy of Patterns. Journal of Artificial Societies and Social Simulation, 1(15).
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The Economist. (2009). Tipping point. Retrieved 06 18, 2020, from https://www.economist.com/news/2009/04/20/tipping-point
Zeckhauser, R. (1989). Distinguished Fellow: Reflections on Thomas Schelling. Journal of Economic Perspectives, 3(2), 153–164.
