White Privilege, the Law of Large Numbers, and a Little Bit of Bayes

I have been told by someone well-versed in critical race theory that the best racial justice work is rooted in storytelling. This strikes me as a good thing. The sharing of individual experiences is a way of cultivating empathy, appreciating the diversity of the human condition, respecting unique voices and perspectives, and awakening conscience from the myopia of its own interests and concerns.

This is also why I detect a shortcoming in the way we talk about the concept of white privilege, and why I think it would be helpful if we begin to think about the concept of white privilege in terms of mathematical concepts like the law of large numbers and Bayes theorem.

Let me explain.

There is a whole academic discipline and literature that focuses on the concept of ‘whiteness’ and ‘white privilege.’ I do not presume to speak as an expert on the matter, only as a lay person who has some understanding of what is meant by the phrase ‘white privilege’ based on the sum total of my reading thus far. For purposes of this article, let me convey my understanding of white privilege as a set of systemic socioeconomic and cultural advantages one enjoys by sole virtue of being white. Commonly cited examples include being able to move into a neighborhood without worrying about whether you may encounter resistance from locals because of the color of your skin, and not worrying about harassment from police because the hue and complexion of your skin is pale. Other advantages may include being able to walk around in a store without having the sneaking suspicion that a store clerk is eyeing you, or being able to curse in public because you got a parking ticket and not having to worry that people around you suddenly consider you a ‘thug’ or a threat.

Like any complicated concept that is novel, ‘white privilege’ can be hard for a white person to wrap his head around, especially since discourse on the topic is not immune to the turgid prose and abstruse lexicons of academic verbiage. A normal white person can easily become frustrated not simply by the cognitive dissonance that makes him question whether the vignettes cited above are, in fact, examples of advantages he is supposed to enjoy, but perhaps even more by the soporific drudgery of making sense of terms like groupals, social constructivism, emancipated subject, and postmodern deconstruction that rear their daunting head in the academic literature about white privilege. And even when the terminology used does not seem like a foreign language, keeping track of all the various conceptual distinctions drawn by scholars can be an additionally daunting task in itself.

In one paper, Lawrence Blum cites the work by Peggy McIntosh on the distinction between privileges worth having (‘being able to buy a house without having one’s race count against one’) and privileges not worth having (‘being able to ignore the perspectives of less powerful groups’). Focusing only on privileges worth having, however, Blum cites a well-known essay by Lewis Gordon in which Gordon argues that what is meant by a privilege, at least one that is ‘worth having,’ is actually a right. In other words, being able to buy a house without having to worry about being a victim of discrimination is a right that we should all expect to have, not a privilege which, by its very definition, tolerates a certain degree of inequality of conditions. A right is something that should be guaranteed to all. No one should be begrudged for having it. A privilege, on the other hand, is something we do not necessarily expect everyone will enjoy (for example, a student may earn the privilege of a meeting with the president because he wins a national essay contest). Blum sticks with the word ‘privilege’ because of its prevalence in the academic literature, and proceeds to focus on privileges worth having. But the distinctions keep on coming. Within ‘privileges worth having’ Blum draws a further distinction between the privilege of being ‘spared’ injustice (being spared of the injustice of being stopped by the police and subject to harassment) and the morally-questionable privilege of unjust enrichment (being ‘unjustly enriched’ because you escape police detection after committing a crime because police focus undue attention on black lawbreakers).

All of this is enough to get your head spinning. And this is only the beginning.

There is a whole academic discipline focused on the study of ‘whiteness’ and, in particular, white privilege. One is left to wonder, then, if maybe storytelling is a way to broaden the discussion, not only in terms of trying to include all possible perspectives on a topic, but in terms of the relative ease with which stories are comprehended by readers vis-à-vis academic verbiage. Maybe. Nonetheless, the concept of white privilege can be a difficult concept to teach and articulate if there is no conceptual rigor to give focus and direction to stories.

For example, if we limit ourselves to our stories, I could tell about the time when I first moved to Washington, D.C. and, within two weeks of moving into a studio apartment in an upscale neighborhood, I was stopped by a cop on an early Sunday evening in the fall. I was walking home from the gym. It was dark. The homes in the neighborhood were quiet. 

I was in jeans and wearing a hoodie sweatshirt. I had a backpack on.

Suddenly I heard police sirens behind me. Patrol cars whipped by to my right. Blue lights were flashing. One car stopped. A cop jumped out of the car and walked briskly across the street toward me.

‘Hey buddy, where ya headed?’ he asked.

‘Headed home,’ I answered.

‘Where’s home?’

I pointed east.

‘Where ya coming from?’

‘The gym.’

‘Where’s the gym?’

I pointed behind me.

‘We’ve had a robbery reported in the area,’ he said, eyeing me closely.

‘Do you wanna check my bag?’ I asked.

‘Yeah.’

I removed my backpack from my shoulders, opened it, and stepped away. Best thing to do, it seemed, was to cooperate.

He rummaged through my bag. Then he stood up. 

‘Okay,’ he said, and turned back to his car.

I believe I was stopped because I was a lone male in a hoodie walking in an upscale neighborhood on a dark night after a robbery was reported in the area. The cop was on the alert for suspects. Then he saw me.

But I didn’t panic. I cooperated, let the cop search my bag, and he let me go.

Still, it was jarring. It came out of nowhere. I was sauntering home after a workout thinking about whatever. Then blue lights came flashing and a cop was interrogating me about where I was going and where I was coming from. My white skin did not shield me from a cop’s suspicion. I did not, in that moment, enjoy the ‘privilege’ of sauntering back to my apartment in a tranquil state of mind.

Apparently, my ‘white privilege’ failed me.

Or did it?

Some may be inclined to ask: how would it have been different if I were black? Would the cop have persisted? Would he have cuffed me even after he found nothing incriminating in my bag? Would he have provoked me?

It is hard to say definitively. As economists like to say, it depends. In this case, it would depend on the particular attitude and presumptions of the cop and whether he had a predilection for giving a black man a harder time than a white man. It depends on the man stopped and whether he is more or less prone to cooperation or resistance. And so on.

But even if I was sufficiently privileged to avoid unwittingly antagonizing the cop after he discovered nothing incriminating in my bag, I had not been sufficiently privileged to avoid the cop’s suspicion in the first place. In short, the story I have told implies there are multiple privileges in play, and I am in doubt about whether at least one of those supposed privileges had, in fact, been demonstrated.

What is white privilege if I was stopped by a cop though I had done nothing wrong? What is white privilege given the brusque tone the cop took with me? Maybe it is in the feeling I had throughout that all I had to do was cooperate and all would turn out fine. It did. Except for a few seconds when I saw the cop charging me, I never really worried that I would be unjustly accused and end up roughed up, handcuffed, and arrested. Is this feeling of personal security the essence of white privilege?

Perhaps. It does presume that the black person, as a rule, does not feel that same sense of security, but instead feels a rise in the heartbeat, release of the fight-or-flight hormone, and a feeling of being guilty before proven innocent. All of these might arise instinctively in a black person, and if that is the case, and if I do not have the same reactions, then it would seem I have just experienced an instance of white privilege, i.e. the privilege of presumption of innocence. But there are a lot of hypotheticals in what I have just said. In reality, my feelings at the time were likely rawer and more unfiltered than I remember them. The immediacy of the actual experience, the being there, was probably different in telling ways. But more important, I cannot presume to know how a black person would have reacted.

This is where we reach the limits of storytelling and where it is helpful to turn to a statistical mindset. There is what happened to me, and all the hypotheticals and conjectures one can invoke to explain and interpret what happened.

But then there is what happens on average.

As I reported in a previous article, one study (as distilled in a New York Times article) found that, for every 10,000 stops of civilians by policemen in New York City during the stop-and-frisk era of 2003-2013 (according to police reports, and controlling for gender, age, police precinct, the reason for the stop, whether the stop was indoors or outdoors, the time of day, whether the stop took place in a high-crime area or during a high-crime time, whether the officer was in uniform, the type of identification provided, and whether others were stopped), police are 17 percent more likely to use their hands with blacks than whites, 18 percent more likely to push blacks into a wall than whites, 16 percent more likely to use handcuffs on blacks than whites, 19 percent more likely to draw their weapons on blacks than whites, 18 percent more likely to push blacks to the ground than whites, 24 percent more likely to point their weapon at blacks than whites, and 25 percent more likely to use pepper spray or a baton on blacks than whites? Similar results are found in the study for ‘compliant’ citizens stopped by police in New York City. Examining civilian accounts from a national survey conducted by the federal government, the study also found that blacks were 170 percent more likely than whites to be grabbed by police, 217 percent more likely than whites to be handcuffed by police, 305 percent more likely than whites to have a gun pointed at them by police, and 87 percent more likely than whites to be kicked or subject to a stun gun or pepper spray by police (after adjusting for type of encounter, self-reported behavior, gender, age, employment status, income, population size of civilian’s home, time of day and officer race).

If the black person does indeed feel, when approached by a cop, a rise in pulse, a release of the fight-or-flight hormone, and a feeling of being guilty until proven innocent, the data seem to justify him.

That is, statistically speaking, on average, a black person most definitely can expect to have had a different experience than I had. That does not mean he necessarily will. A story last year reported the case of a black man in Tucson who publicized his experience being pulled over by police while he was carrying a gun with a concealed carry permit and how the experience ended without incident after his full cooperation. But the odds were against him, at least in comparison to a white man like me.

Which brings us back to the law of large numbers referenced above.

This is a law in mathematics that states that the average result of a large number of trials will approximate what you expect based on the inherent probability. A die has six possibilities when rolled. Each possibility has an equal chance of coming up. Thus, the inherent probability of coming up with a six is one-sixth. Now, it’s quite possible you could roll the die six times and get a six every time rather than once, as the inherent probability suggests. But you have only rolled the die six times. By the law of large numbers, if you roll the die a thousand times, you are more likely to come up with a six one out of every six rolls.

In applying the law of large numbers to encounters with police, we do not possess the true probability that a black or white person will suffer abuse by police in the same way we have the true probability of getting a six when rolling a die. Getting this probability would require gathering data on every single encounter with police that every single person has ever had. That is, of course, not possible. But the law of large numbers allows us to infer the true probabilities if the sample size is large enough. In the study referenced above, one of the data sources used by the author (Roland Fryer) consists of five million individual police stops in New York City as part of its Stop-and-Frisk programs from 2003 to 2013. That is a lot of police stops, probably sufficient to give us some insight into the true probabilities that black and white people are likely to confront abuses in their encounters with police. Maybe not the actual quantifiable probability that a particular black or white man will suffer abuse by police (like, say, 40 percent versus 20 percent for the black and white man, respectively; or whatever the percentages may be), but at least a sense of whether it is more probable for the black man than a white man. In all likelihood, it is (though the Fryer study found that police officers who had not yet been attacked were more likely to shoot a white man than a black man).

The upshot is that statistical analysis can be an effective tool in fleshing out the various micro-concepts and distinctions embedded in the general concept of white privilege. The cognitive dissonance encountered by white people is understandable to the extent that they are unfamiliar with the academic verbiage, or to the extent that their own experiences, like mine, do not, at first glance, appear to support the general claims made by those who devote much time to the study of white privilege. Every individual has a different experience, and every experience is subject to varying interpretations. But that’s not to discount the importance of recognizing systemic discrimination or abuse. By systemic, I mean that, on average, the black person can expect to encounter difficulties that a white person does not based on the color of his or her skin. If we performed a large number of trials, the claim of white privilege analysis is that a black person is proportionately more likely to face discrimination on the basis of skin color. That does not mean it will always turn out that way. But on average, it will. That’s what the law of large numbers tells us.

At the risk of complicating my analysis with a bit of abstract verbiage of my own, I should note that a full treatment of the mathematical framework discussed in this article would be remiss if it failed to note that a Bayesian analysis would add even more rigor to the analysis of systemic discrimination. Bayes’ theorem is a general theorem about the probability of an event given a signal—for example, the probability of being abused by the police given that one is black (being black is the signal). What it is the probability of being abused by the police given that one is black? It is derived by dividing the percentage of the total population that is black and abused by the police by the percentage of black people in the total population. More technically, the probability of being abused by the police given that a person is black is equal to the probability that a person is black given that he is abused by the police times the probability that a person is abused by the police, divided by the probability that a person is black:

Prob(one is abused by police given that one is black) = [Prob(one is black given that one is abused by police) * Prob(one is abused by police)]/Prob(one is black)

Again, this is essentially equal to the percentage of the total population that is black and abused by the police divided by the percentage of black people in the total population.

Although there is the challenge of collecting the data to calculate relevant probabilities, a Bayesian framework successfully applied would thus allow us to compare the probability of being abused by the police given that one is black to the probability of being abused by the police given that one is white. It would also allow us to gauge probabilities associated with any other instance of white privilege: the probability of being followed by a store clerk given that one is black compared to the probability of being followed by a store clerk given that one is white; the probability of seamlessly moving into a new neighborhood given that one is black compared to the probability of seamlessly moving into a new neighborhood given that one is white; and so on. And the same framework makes use of the law of large numbers. To the extent that statistical studies show a differential impact of police abuse on blacks and whites, or show any kind of systemic advantage for whites compared to blacks, the law of large numbers allows us to infer the true probabilities of socioeconomic and cultural ‘events’ that demonstrate advantages one enjoys, on average, simply by being white.

In explaining the concept of white privilege to white people, much effort is expended to explain the systemic nature of the advantage conferred by being white, but what it often fails to overcome is the tendency of the white person to say: but my experience is different. I imagine that this greatly frustrates practitioners who want to convey that a white person’s unique experiences do not negate the systemic nature of advantages conferred by being white. Thus, storytelling only gets us so far. Practitioners, or academics who write papers that employ abstract terminology consisting of phrases like ‘transcendence from social contingency,’ might do well to include a mathematical approach. At least for whites with a reasonable level of mathematical literacy, it could serve to facilitate understanding by white people about the systemic advantage they derive from being white, in many cases at the expense of black people.

It’s all about the probabilities.

The role of men is changing in the 21st century. Want to keep up? Get the best stories from The Good Men Project delivered straight to your inbox, here.

Photo Credit: Getty Images