A Threshold Model for Campus Rape

Imagine a middle-school gymnasium dressed and decorated for a dance, with a battery of 7th and 8th graders lining the walls. The lights are dimmed, an ancient disco ball is spinning, and the chem-teacher-qua-DJ has hit shuffle on a playlist of stale tunes from his own youth, and a song like “Mambo Number 5” is blaring through an ad hoc PA system. Inevitably, some intrepid student will make his or her way onto the dance floor and bust a move. Whether this child does so in a quest for attention or a moment of bravery is unclear—and unimportant, because a second joins shortly after, and then a third, and a fourth. Before long, the dance floor is crowded and only the shyest kids remain along the wall.

This is one of many phenomena that can be described in terms of what sociologists call thresholds. For any particular person, their threshold is the number of other people they would have to see participating in an activity before he or she becomes willing to join in. That first kid on the dance floor has a threshold of zero—he or she does not require implicit social permission to start dancing publicly. The next one out has a threshold of one, and so on, and so on. Threshold models have been used to explain how rumors spread, why riots break out, the progression of Kickstarter campaigns, and even how the Arab spring gained traction.

In the middle school dance scenario, there is more or less a uniform distribution of thresholds: there is one student with threshold 0 (the instigator), and then someone who will start dancing but only if someone else goes first—this person has threshold 1. Up next is the person with threshold 2, someone who needs to be convinced the party is starting before he’ll leave the sidelines, and so on up to the last person who joins in. In scenarios like these, the outcome is more or less inevitable once the instigator acts: there is a domino or “bandwaggoning” effect and participates. It should be noted, however, that the more extreme the scenario, the fewer zero-threshold actors exist. Plenty of people might be the person willing to be the second one to jump out of an airplane with a parachute strapped to their backs. Vanishingly few people would do so without seeing someone else do it first.

Now consider a situation where we’ve replaced the person with threshold one with an otherwise-identical person who has a threshold of two. Even if the instigator acts, no one else will follow suit. Mark Granovetter, the pioneer of this concept, described this scenario with respect to riots: “By all of our usual ways of describing groups of people, the two crowds are essentially identical. But the outcome in the second case is quite different—the instigator riots, but there is now no one with threshold 1, and so the riot ends at that point, with one rioter.” In such perturbations, the result is a single person standing next to a shattered pane of glass as a crowd looks on, or a lone middle schooler krumping on the dance floor. Or you get this incredibly awkward scene from Jerry Maguire:

In March of 1918, an army cook named Albert Gitchell reported sick at Fort Riley in Kansas. Within a week, over a hundred soldiers in his cohort had been hospitalized with a particularly virulent strain of influenza. By the middle of the month, the disease had spread from Kansas to New York; by April, it had spread to most cities in America and had even reached Europe, as Malcolm Gladwell says, “following the trail of the hundreds of thousands of American soldiers who crossed the Atlantic that spring for the closing offensives of the First World War.”

That initial wave of the Spanish Flu was bad enough to be noteworthy – 237 men at Fort Riley contracted pneumonia from the influenza, and of those 237, 38 died—but it was not considerably out of the ordinary. According to Jeffery Taubenberger of the Armed Forces Institute of Pathology, “Illness rates were high, but death rates in most locales were not appreciably above normal.” This changed over the summer, when a second wave of influenza began in Brest, in northwestern France, and quickly found itself carried to Boston by returning American soldiers and to Sierre Leone in steerage on the British navy ship the H.M.S. Mantua. The second wave spread globally between September to November of 1918. It was highly fatal. By the time the Spanish Flu subsided, it had killed more than fifty million people.

It’s hard to conceptualize numbers of that magnitude. Likewise, it’s had to really come to terms with the level of panic and terror the Spanish Flu brought with it. Consider historian Alfred Crosby’s account of the pandemic reaching Alaska:

On or about November 1 the virus reached the finest medium for its propagation in Nome and vicinity, the city’s Eskimo village. Few Eskimos escaped infection. In a single eight-day period 162 of them died. Some Eskimos, hounded by superstitious horror, fled from cabin to cabin, infecting increasing numbers with disease and panic. The temperature fell below freezing, and when rescuers broke into cabins from whose chimney came no sign of smoke, they found many, sometimes whole families, who had been too sick to renew their fires and who had frozen to death. When a number of Eskimos were rounded up from their separate cabins and placed in a single large building so they could be cared for efficiently, several of them responded to what they apparently perceived as incarceration in a death house by hanging themselves.

In “Epidemic and Peace, 1918,” Crosby shares the harrowing account of a Philadelphia nurse who came upon “a husband dead in the same room where his wife lay with newborn twins. It had been twenty-four hours since the death and the births, and the wife had had no food but an apple which happened to lie within reach.”

“If you autopsied some of the worst cases, you’d find the lungs very red and very firm,” says Taubenberger. “The lungs are normally filled with air, so they are compressible. These would be very heavy and very dense. It’s the difference between a dry sponge and a wet sponge. A normal piece of lung would float in water because it was basically filled with air. These would sink. Microscopically, you would see that the alveoli would be filled with fluid, which made it impossible to breathe. These people were drowning. There was so much liquid in the air spaces of their lungs that patients would have bloody fluid coming out of their noses. When they died, it would often drench the bedsheets.”

In a typical outbreak of the flu, the very young and the very old are the most likely to die from the disease or its complications—put another way, influenza has a U-shaped mortality curve. “The curve of influenza deaths by age at death has historically, for at least 150 years, been U-shaped,” says Taubenberger. Mortality “peaks in the very young and the very old, with a comparatively low frequency of deaths at all ages in between.” The Spanish Flu was different. Rather than being U-shaped, the mortality curve of the Spanish Flue was W-shaped: similar to the U-shaped curve but with the addition of a third distinct peak of deaths in young adults between twenty and forty years of age. Says Taubenberger, “Age-specific death rates in the 1918 pandemic exhibited a distinct pattern that has not been documented before or since.”

W-shaped curve

U- and W- shaped combined influenza and pneumonia mortality, by age at death, per 100,000 persons in each age group, United States, 1911-1918. From Taubenberger.

“This wasn’t just a deadly infectious disease,” says Gladwell. “It was a deadly infectious disease with the singular and terrifying quality of being better at killing the young and healthy than the old and the infirm.”

There are numerous factors that contribute to the proclivity of rape. An important one, for example, is the acceptance of what are known as rape myths. Rape myths are defined as prejudicial, stereotyped, or false beliefs about rape, rape victims, and rapists. Examples of rape myths include fallacies like “Only bad women get raped,” or “Husbands cannot rape their wives,” or even, “Rapists are sex-starved, insane, or both.” According to Neil Malamuth, a psychologist at UCLA and one of the foremost experts on sexual aggression, “beliefs in rape myths are more likely to be held by rapists than by males in the general population.”

Is this relationship causal or merely correlative? Martha Burt of the Urban Institute, and the academic who pioneered the rape myth acceptance scale, believes that rape myth acceptance play an important role in causing rape. Such beliefs justify a rapist’s behavior, she says, and they act as “psychological releasers or neutralizers, allowing potential rapists to turn off social prohibitions against injuring or using others when they want to commit an assault.” Similar beliefs held by the social circle of an assailant may likewise contribute indirectly to such assaults, Burt argues, since they effectively create excuses for the assailant’s actions. It is easier for young men to internalize a message like, “Women get drunk when they want to have sex” when it is reinforced by their confidants.

Rape myth acceptance, however, is far from the only risk factor for proclivity to rape. Malamuth realized that a certain subset of high-risk men never see those risks turn into action. A key difference, he found, between men likely to rape who do and men likely to rape who do not is sensitivity, that is, whether the man is “self-centered” or “nurturant.” “When a high-risk individual is self-centered,” says Malamuth, “he is more likely to actually be sexually aggressive. In contrast, the high-risk individual who is sensitive to others’ feelings is not likely to actually aggress sexually.” Empathy, then, has a moderating effect on sexual aggression—like British author Ian McEwan says, imaging what it is like to be someone other than yourself is the essence of compassion and the core of our humanity. It keeps us from doing horrible things.

Alcohol also has a scaling effect on sexual aggression. “Half of all sexual assault perpetrators are under the influence of alcohol at the time of the assault,” says Antonia Abbey, a psychologist at Wayne State University. According to Abbey, the causal relationship here is well-understood: “There are two primary mechanisms through which alcohol can increase the likelihood of sexual violence in a given situation: pharmacological effects of alcohol and psychological beliefs about alcohol.” Under the influence of alcohol, people have a reduced capacity to “integrate multiple sources of information and make complex decisions.” Or, as Malcolm Gladwell put it, “Alcohol makes the thing in the foreground even more salient and the thing in the background disappear. That’s why drinking makes you think you are attractive when the world thinks otherwise: the alcohol removes the little constraining voice from the outside world that normally keeps our self-assessments in check.” That is, inebriation creates a narrowed focus—myopia—and a reduction of impulse control. “Alcohol facilitates aggression not by ‘stepping on the gas’ but by paralyzing the brakes,” says Brad Bushman, a psychologist at Ohio State who has written about the effects of alcohol on aggressive behavior. According to Bushman, alcohol consumption is particularly effective at facilitating aggression, affecting it as much or more than other social and nonsocial behaviors.

But some of the effects of alcohol are caused by our cultural beliefs about alcohol. Widely held beliefs induce placebo effects. “American culture glamorizes alcohol consumption,” says Abbey, “and links it to sexual desire, sexual performance, aggression, and other types of disinhibited behavior.” To the people who wanted to act aggressively, alcohol gives them implicit permission to do so. At the same time, the intoxicated are more likely to interpret the behavior of others in the light of these cultural expectations. To the drunk, says Abbey, “a smile is more likely to be viewed as a sign of sexual attraction and a mildly negative comment is more likely to be interpreted as grounds for an aggressive response.” Each culture, including our own, has created a particular set of codes for what it means to be drunk, and many of ours facilitate sexually aggressive behaviors. “Persons learn about drunkenness what their societies import to them, and comporting themselves in consonance with these understandings, they become living confirmations of their society’s teachings,” the anthropologists Craig MacAndrew and Robert Edgerton say in their book, Drunken Comportment. “Since societies, like individuals, get the sorts of drunken comportment that they allow, they deserve what they get.”

This is not to say that alcohol creates sexual aggression where it didn’t exist previously, nor does it excuse the violent of their violent acts. Some studies have shown that men at high risk for sexual aggression are those most affected by alcohol consumption. Abbey underscores this point. “Alcohol increases sexual violence only when perpetrators are near their violence threshold. Most men are expected to have a high threshold for using violence to obtain sex, thus even when intoxicated, they are unlikely to cross that line. Other men … have such a low threshold for violence that alcohol is not needed for them to become sexually violent. And for a subgroup of men who are near their violence threshold, intoxication may push them over that line.” Context causes shifts in our threshold for many activities, and alcohol consumption plays into that. “Alcohol is one of many factors that increase the likelihood that a man will feel comfortable forcing sex on an unwilling woman. For some men, on some occasions, it can be the ‘final straw’ that produces sexual violence, but its effects cannot be understood in isolation.”

In the normal course of a flu season, the milder strains of the virus tend to prevail. Those infected with more severe, nasty strains of the diseases tend to get more severe, nasty symptoms, and as a result, they tend to isolate themselves at home as they convalesce. Those who contract milder strains are less likely to disrupt their vocational and social commitments, so they continue to go into work, they continue to shop, and they continue to be out and about in public, increasing the odds that they’ll pass their illness onto someone else.

In the case of the Spanish Flu, the First World War turned this pattern on its head. Soldiers were packed tightly into barracks during basic training and then into ocean liners transporting them across the Atlantic. Some 30,000 American soldiers died en route to France. Once they arrived at the battlefield, the epidemiological profile only made matters worse. “As soldiers in the trenches became sick,” says Carol Byerly, “the military evacuated them from the front lines and replaced them with healthy men. This process continuously brought the virus into contact with new hosts—young, healthy soldiers in which it could adapt, reproduce, and become extremely virulent without danger of burning out.” Meanwhile, the evacuated ill would end up in field hospitals, spreading their illness to the injured, some of whom were returning home. This cycle spread waves of infected and infectious men across the world. Socio-political reality reversed the standard progression of influenza. From the trenches of France, as Byerly put it, the Spanish Flu would “travel the highways of war, circling the globe.”

Obviously, war is not the only thing that creates such unusual social arrangements. Any community built around a particular trait—that is to say, any group of people displaying either an artificial or intentional selection bias—will have unique susceptibilities to various outcomes. If someone throws a rock through a window at a state fair, a riot is unlikely to break out. But a group gathered together in their outrage over a police shooting is composed almost entirely of people who are furious, exasperated, and impatient about persistent injustice. A shattered window, in that context, invites a very different reaction. Likewise, if you try to create a spontaneous dance party in the middle of a school lunch hour, it will be comparatively more difficult to get kids to start dancing than it is when they are intentionally attending a dance. Economists trying to explain why immigrants in certain cohorts earn more than American citizens working similar jobs have leaned on self-selection as the explanation: the sort of person motivated to go through the immigration process are more likely to also have traits that favor excellent job performance.

The college social environment compounds the self-selection process. Students admitted to various colleges tend to have other traits in common, things like race, relative age and home location. Consider, for instance, the fact that 65% of students enrolled at the University of Minnesota come from Minnesota, and an additional 15% hail from the Upper Midwest. 70% are white. In comparison, 80% of students at the University of St. Thomas, a private Catholic liberal arts college in St. Paul, are white and 95% of them are culled from the Midwest. Nationwide, more than 85% of full-time college students on traditional campuses are under 25. Not all colleges conform to these profiles, but the ones that don’t have peculiarities of their own. Many Ivy League schools favor the children of alumni: Harvard’s legacy admission rate is around 30%, four times the rate for non-legacy students. Intentional or not, Harvard selects for Harvardness, and the University of Minnesota selects for Midwesternness. The self-selection process hardly stops at admissions. Any subgroup—clubs, intramural sports teams, academic concentrations—results in further self-selection.

This is not inherently a bad thing: there is nothing wrong with creating groups that can be categorized with increasing specificity. I know I enjoyed my time with Upper Midwestern, academic, Christian, athletic, relaxed Frisbee players. The net effect, however, is that the more narrowly-tailored the selection process, the more we also select for correlated traits. This is the basic premise behind statistical sampling procedures: when we rely on demonstrably non-random samples to measure something, we may be measuring something correlated with the sample instead. If we want to establish drug use rates among teenagers, taking a sample of high school students may overrepresent the problem by ignoring the home schooled.

Studies have shown that men who join fraternities are more likely to commit rape than men in the general student population, with one showing they are three times more likely to commit rape than other men on campus. John Foubert, one of the authors of the latter study, offered an important insight on this result. “Before they got to college, fraternity men were no different from other male students. They committed the same number of incidents of sexual assaults before college. But here’s the difference. Guys who joined a fraternity then committed three times as many sexual assaults as those who didn’t join. It is reasonable to conclude that fraternities turn men into guys more likely to rape.” There is something about frat life that cultivates sexual violence.

Perhaps there is an element of self-selection bias at play. That is, perhaps when selecting for frat-worthiness, those groups are also accidentally selecting for men with a low rape threshold. Theoretically, this plays out well: fraternities select for 1) men typically between the ages of 18-20, 2) who are willing to engage in high-risk drinking (at a rate of roughly 80% among frat members), and 3) are drawn to a cultural presumption of frat life, i.e., a lifestyle with rampant partying and hook-ups. Is it hard to believe that this population correlates heavily with high self-centeredness/low empathy and an espousal of rape myths? Foubert argues that frat members receive “male peer support” to commit acts of sexual violence. In such an environment, all the risk factors for sexual violence coalesce in terrifying synergy, and a group of high-risk/low-threshold men need only the feather-light provocation of a zero-threshold actor to give them contextual permission for their own acts of sexual aggression. A individual act of sexual aggression in isolation is horrific enough as it is. A torrent of such acts committed with the perceived approval of the people nearby is a breeding ground for tragedy.

There is a caveat to this idea. Fraternity membership is comparatively low. Even though members commit rape at three times the rate of the general student population, in a typical school non-fraternity members outnumber fraternity members by an average rate of eight to one. Due to the size difference in populations, non-fraternity members commit nearly three times as many rapes as frat members. And that’s at a typical college. In schools with lower fraternity enrollment, like the University of Minnesota, the general population aggregates fourteen times the number of rapes.† As much as people may find it convenient to push the blame onto frat culture, it cannot directly explain the majority of campus rapes.

But what if the same self-selection factors are at play in other aspects of campus life? Perhaps other sub-cultures attract high-risk/low-threshold actors. Perhaps the culture of binge-drinking and the archetypal conception of the collegiate experience create a selection bias in general and influences how certain types of men congregate at certain types of parties. We should expect many of those high-risk/low-threshold actors to flock to fraternities, but not all of them (and, conversely, it should be noted that not all frat members are at high-risk for rape). This is the crux of the issue: when angry, frustrated people get together, it is more likely to result in a riot than having isolated malcontents isolated in otherwise happy crowds. But a riot describes group behavior. Those isolated few may still smash some windows.

Imagine a house party at a college campus. “Blurred Lines” is blaring through stereo speakers. There is a keg on the back porch and a kid with a sideways hat and curly blonde hair is operating the tap. People are dancing in the living room, talking animatedly through plumes of cigarette smoke in the kitchen, and discarding red Solo cups on every visible surface. Scattered through the crowd, there are people making out. At some point, with an audible laugh and a shit-eating grin, some kid gropes a girl in spite of her wobbly gait and the disgusted look on her face. His friends laugh. It’s not hard to imagine what happens next.


It should be noted that this is a mathematical calculation based on the population sizes compared to the presumed rate of rape in both populations. Foubert’s 3:1 rate was assumed for these calculations.

Old School

Perceptions of party life are shaped by culture and therefore act as self-fulfilling prophecies.