Back in early 2016 when the primaries were in full swing, I was sitting around the lunch table with colleagues, when the conversation turned to politics. At the time, an outsider named Donald J. Trump was having remarkable success and was quickly turning into the favorite for the Republican nomination. One of my colleagues remarked, “I don’t understand how this is happening. I have not met a single person who supports this guy and somehow he seems to be on pace to win the nomination.” That struck me as a remarkable statement. At the time, I was working at Rose-Hulman Institute of Technology which is located in Southwestern Indiana in a county that has been a political bellwether for decades. In other words, we lived in a place that had a mix of Republicans and Democrats and whose makeup mirrored that of the nation as a whole. How could someone live in such a place and not know a single Trump supporter?
When we try to make sense of the world, we often rely on local cues to help us understand what the world is like. We use the characteristics and perspectives of the people that we are connected to (our friends, our coworkers and our acquaintances) as a window into the characteristics and perspectives of society as a whole.
The idea that we can use small samples to learn about the characteristics of a large population is foundational to the study of statistics. Countless theorems have been proven about the power of sampling and the types of conclusions we can draw from them. These results are based on the principle that random samples will typically be representative samples, i.e. they reflect the characteristics of the population of interest. The problem is that, although it may sound straightforward, random sampling is actually quite difficult to achieve. For example, even if you go to the phonebook (yes, I still remember those) and pick random phone numbers, that will not lead to representative samples of the population as a whole because not everyone has a landline and some demographic groups may be more likely to answer the phone than others. You run into similar problems when you try to use the mail (some people don’t have an address) or the web (some people don’t visit your site). As a result, it is much easier to resort to what is called a convenience sample, in which you draw your conclusions from the people that are easy to reach. The problem with this approach is that you lose guarantees that your samples will represent the population as a whole and you make your conclusions susceptible to sampling bias.
Looking to your connections for insight into the broader characteristics of society is a classic example of a convenience sample. As a result, we need to be very careful about drawing sweeping conclusions from the characteristics, attitudes, and experiences of our friends. Study after study has shown that social networks (meaning the patterns of connections between people and not necessarily online platforms like Facebook and Twitter) exhibit a property known as “assortative mixing” or “homophily”. In his seminal paper on this phenomenon, Mark Newman (a physicist from the University of Michigan) defines this property as follows:
“In the study of social networks, the patterns of connections between people in a society, it has long been known that edges [think friendships] do not connect vertices [think people] regardless of their property or type. Patterns of friendship between individuals for example are strongly affected by the language, race, and age of the individuals in question, among other things. If people prefer to associate with others who are like them, we say that the network shows assortative mixing or assortative matching.” MEJ Newman, PRE 2003
This phenomenon is relatively straightforward to quantify using the assortativity coefficient. You simply compute the fraction of connections between individuals of the same type (sex, language, race, age, etc.), subtract the fraction of connections you would expect if connections were made at random and then rescale so that the result stays between -1 (meaning there are only connections between individuals of different types) and 1 (meaning there are only connections between individuals of the same types) with zero corresponding to the case where connections between individuals of the same type occur no more often than in a random network. Depending on the precise definition of a connection between people, this quantity can take on different values, but it tends to be quite positive in social networks. For example, if you look at the network of married couples and look at the age of partners, you see that the assortativity coefficient is around 0.574 meaning that people are much more likely to marry someone close to their age. If you do something similar with race instead of age, the result is even higher. So, using this idea, researchers have assembled a mountain of evidence to suggest that people tend to associate with people that are similar to them.
The consequence of this phenomenon is that we tend to think that the rest of the world is more similar to us than it actually is. In my case, I am Caucasian male; I have a graduate degree; I am very involved in my church; I enjoy playing basketball; and I have a white collar job. As a result, the people that I associate with are likely to be whiter, more educated, more religious, taller/more into sports, and have higher incomes than the typical American.
This also means that we should expect that our perceptions of what is going on in the world will be skewed somewhat by our surroundings and these differing perceptions can have a profound impact on the way we behave. To illustrate this, let’s consider the example of fireflies (not the earworm of a song, the insect). Fireflies flash their lights in a repetitive way. Each firefly has its own rhythm and, in isolation, this varies from one firefly to the next. However, when certain species of fireflies congregate something remarkable happens. They synchronize their flashes. You can see an example of this in this TED talk by Steve Strogatz (the fireflies show up around the 8:50 mark).
How do they do this? By responding to stimuli from their neighbors! Essentially, they speed up or slow down their flashing lights based on what their neighbors are doing. If their neighbors are out of sync, there is no clear signal and so they largely ignore them. But, once their neighbors start to synchronize, a clear signal emerges and then these small changes in behavior can cause an entire swarm to sync up.
When these types of interactions are localized (meaning that fireflies only respond to the behavior of nearby fireflies) interesting patterns called chimera states can form. This results from the fact that some look at their neighbors, see coordination, and decide to get with the program while others see chaos and therefore have no choice but to do their own thing. You can reproduce these sorts of behaviors using mathematical models. For example, this video shows a network of interacting oscillators (like the fireflies) represented by blue dots.
You cannot see the connections between them, but each oscillator is responding to the behavior of its neighbors. The oscillators on the left and right sides look at their neighbors and see coordination (as evidenced by the fact that they are lined up and appear stationary) and therefore they coordinate as well. The oscillators in the middle see disorder, and so they remain disordered. Note: a measure of the local order that each oscillator perceives is displayed in the lower panel.
The remarkable thing about this model is that all of the oscillators are playing by the exact same rules. In this particular example, all of the oscillators would naturally travel at the same speed without interactions. The only reason that they are behaving differently is that they receive different information from their surroundings! Their distinct perceptions of the world around is the only thing that leads to different behaviors.
This has important implications for society:
1. We need to recognize that our perceptions of the world may be biased by the types of people we interact with. This is particularly problematic in the racially charged circumstances in which we currently find ourselves. For example, it is not uncommon to hear people express confusion over the issue of racism saying things like “I haven’t seen anyone treated poorly because their race and none of my friends have either.” As a result, they conclude that this isn’t really a significant and pervasive issue. However, the reality is that America looks very different than your circle of friends. In all likelihood, your friends tend to be very similar to you and so their experiences are only representative of the experiences of a narrow sliver of society rather than society as a whole. If we recognize that, then it makes it much easier to understand how other people could have such a radically different experience of life in America than your own.
2. We also need to recognize that local information can have a profound impact on how we view the world and can influence how we respond to it. Obviously, human beings are far more complex than fireflies, and unlike fireflies, we have an ethical responsibility for our actions. However, when people behave differently than you do, it is worth thinking about what local information and local behaviors (which you might not be privy too) contributed to that response. Case in point: I would like to believe that most people were outraged by what happened to George Floyd. But, you don’t need a degree in statistics to be able to tell that the level of outrage in the African American community is on a whole different level from the level of outrage among white Americans. This is not because one group finds murder more offensive than the other and I suspect that it is not just because George Floyd was black.
I believe that it is due (at least in part) to the fact that the world looks a lot more racist to African Americans than it does to Caucasians. If you are at all like me, then you might be able to look out at your social network and confess, “I don’t have a lot of first or even secondhand experience with racism.” I will freely admit that I cannot fully appreciate what it is like to be treated poorly because of the color of your skin. I have lived in other countries (Costa Rica and Peru) where I was a racial minority. I have been viewed differently (mostly as a curiosity) because I looked different than my friends and neighbors, but that is nothing compared to what we witnessed on May 25, the day George Floyd was killed, or on February 23, when Ahmaud Arbery was shot, or on any other day across the country. I have never had people look at me in fear because of the color of my sin. I have never lived with the fear that I might be harassed or questioned by the police without cause. I won’t pretend that I fully understand the experience of black Americans, but I do know this: If prejudice and oppression had been a part of my entire life and I had seen friends and neighbors victimized by it, then seeing it happen time and again would make me very angry, even angrier than I already am.
Surveys suggest that these experiences are far more prevalent than we would like to admit. A 2019 Pew Research poll found that 65% of black Americans reported being viewed suspiciously due to their race, 60% reported being treated as if they were not smart, and 49% reported experiencing unfair hiring practices at work. Similarly, a 2017 NPR poll that asked African Americans about whether they believed that they or someone in their family had been treated unfairly due to their race found that 60% reported being unfairly stopped or treated by the police, 45% reported unfair treatment by the courts, and 31% reported that fear of discrimination had led them to avoid calling the police. Another poll found that more black Americans (63%) were worried about being a victim of police using deadly force than were worried about being a victim of violent crime (52%). In contrast, white Americans, were equally concerned about violent crime (50%) but significantly less concerned about the police (21%). Regardless of your personal experiences, that type of data is hard to ignore.
If you think these poll results are just the result of “liberal bias” or a “victim mentality”, consider this statement from a recent podcast appearance by former RNC Chairman, Michael Steele, who is both a conservative and an African American:
“Your [white people’s] mildly unpleasant encounter with the police is often a deadly one for me and my sons, and particularly the men in my community. And, that’s the difference. Your encounters with law enforcement, your encounters with the legal system, the criminal justice system is very different. You never had to have a conversation with your sons or your nephews or young men in your community about how they have to handle themselves when they meet the police. In fact, as you were growing up and probably as you raised your kids, you would probably tell them, ‘look, if you get in trouble, call the police.’ That is not the advice we give, because that actually could be begging for trouble. That actually could escalate into a worse situation.”
In light of this, I think it is appropriate to remind ourselves that even if we have limited exposure to racism or police brutality (or Trump supporters for that matter), that does not mean that we should discount their impact. Because of the assortativity of social networks, the world can be quite different than we perceive based on our social circles. Perhaps reminding ourselves of that fact might help us be a little more empathetic, a little slower to judge and a little more willing to listen to the concerns and experiences of others.
PS. Assortative mixing is the natural way our social networks tend to be structured, but it is worth considering: Is that a good thing? Is it worth rethinking the way that we form social ties?
PSS. I am not saying that our different experiences make it OK to respond to evil with evil. We should guard against the tendency to treat evil as acceptable just because it was provoked. However, we must also guard against the opposite tendency: to dismiss legitimate concerns about injustice, just because a select few use that injustice as license for wrongdoing.
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