by Luke Dormehl
Alice and Tim
Ruth and James
Charlotte and Rob
Bridgette and Rajiv
For all its good qualities, however, there are a few conceptual problems with this problem, which follow as such. For one thing, The Match imagines that all of the men and women on the island are heterosexual, and therefore wish to be paired with members of the opposite sex. This statistically unlikely event is done only for the sake of mathematical simplicity. A scenario where men want to marry men, women want to marry women, or everyone wants to marry everyone, does not necessarily yield the same stable outcome as the relatively straightforward matching I described.
Another issue is that the Stable Marriage Problem presumes that all people of marriageable age do, in fact, wish to get married, and that the location in which they live is so remote that there is no chance whatsoever that any residents could marry someone from outside its boundaries. Yet another problem is that the algorithm assumes marriages only fail in the event of a disruptive third party, who is a better match for one part of a particular couple. While it is undeniably true that a certain percentage of marriages do end for this exact reason, it is by no means a universal, statistically robust rule. Some couples simply find themselves incompatible and conclude that they would be happier living on their own than they would with one another. To return to our original example, perhaps Alice falls head over heels in love with James only to realize after living with him for several months that her idea of a perfect evening is to go out dancing, while James would rather stay in and play computer games. Or maybe James chews with his mouth open, and bad manners are a deal-breaker for Alice.
The part of The Match that causes me the most problems, however, is the piece of information we are asked to take as writ before the algorithm even gets going: namely the idea that each of the men and women addressed by the puzzle is able to compile a list in which they rank, without error, everyone of the opposite gender in the order that they would most happily be married to them. Of all the assumptions made by David Gale and Lloyd Shapley, this seems the most grievous.
I do, of course, write these words with tongue firmly planted in cheek. As noted, the Stable Marriage Problem invokes romantic marriage as metaphor only, being designed for the purpose of matching medical students with hospitals. For this task it is largely suitable—since issues of one party chewing with their mouth open, or ogling a third party, are unlikely to result in separation. But by pointing out these conceptual difficulties, I do make a serious point: that outside of mathematical puzzles human beings have a nasty habit of behaving unpredictably.
And particularly when love is involved.
Madness in Love, Reason in Madness
In 2006, the pop statistician Garth Sundem was asked by the New York Times to create a formula to predict the breakup rate of celebrity marriages.2 Sundem was well known for what he calls his “math in everyday life” equations. He’d appeared previously on the BBC and Good Morning America, and his formulas had proven so popular that he had published a book of them, Geek Logik, which contained mathematical answers to determine everything from whether a person should get a tattoo to how many beers they might want to take on their next work picnic. When the New York Times contacted him, Sundem says that he did what he always does when starting work on a new equation: he sat down at his desk and began thinking of criteria to test against the data on celebrity divorce rate. Did, for instance, the hair color of the couple in question make them more or less likely to divorce? How about the proximity of their home in relation to the Hollywood sign? In most cases, the answer was a resounding no. But data-mining did eventually produce results—as it always does. For example, Sundem discovered that the number of Google hits for a starlet that showed her in skimpy clothing positively correlates with the duration of her marriage. So too did the combined numbers of the couple’s previous marriages.
Here is the formula he eventually came up with:
P=The couple’s combined number of previous marriages
Ab=His age in years
Ag=Her age in years (biological, not cosmetic)
Gb=In millions, the number of hits when Googling his name
Gg=In millions, the numbers of hits when Googling her name
S=Of her first five Google hits, the number showing her in clothing (or lack thereof) designed to elicit libidinous thoughts
D=Number of months they knew each other before getting married (enter a fraction if necessary)
T=Years of marriage. To find the likelihood of their marriage surviving 1 year, enter 1; for the likelihood of it lasting 5 years, enter 5, etc.
Blisis the percentage chance that this couple’s marriage will last for the number of years you chose.
While Sundem’s celebrity marriage formula was less than serious, it nonetheless proved immensely popular, as well as remarkably prescient. Using it to chart a string of recent nuptials involving the rich and famous, some conclusions were to be expected. For example, Prince William and Kate, the Duke and Duchess of Cambridge, turned out to have a far better chance of being a long-term item than, say, Khloe Kardashian and Lamar Odom—the latter of whom announced their divorce in December 2013. But the formula also correctly surmised that, while Katie Holmes and Tom Cruise’s marriage would last five years, there was little to no possibility it would reach fifteen. (Holmes and Cruise announced their divorce in 2012, following five and a half years as husband and wife.) The same fate was predicted for Will Smith and Jada Pinkett, who have passed their five-year anniversary, but who are regular tabloid fodder predicting impending doom. Meanwhile, the formula suggested that if “Brangelina”—Angelina Jolie and Brad Pitt—had married immediately after Pitt divorced previous wife Jennifer Aniston, there would have been a 1 percent chance of their marriage lasting 15 years. Today, their chances of doing so stand at more than 50 percent.
By Sundem’s own admission, he is not a serious mathematician. The success of his pop formulas speaks less to the rigor of his empirical approach than to the general public’s overwhelming eagerness to find answers to replace those that in a less technological society might have been chalked up to fate. If there is one absolute truth that comes out of his celebrity marriage equation, it is not that millions of Google hits doom a relationship from the very start, but that as people we are spectacularly bad at predicting who they are going to be well matched with when it comes to marriage.
After all, if the wealthiest, most successful and best-looking 1 percent of the population (i.e., celebrities) can’t guarantee that they will be happy with their chosen marriage partners, what hope do the remaining 99 percent of us have? About half of first marriages fail in the United States, as do two-thirds of second marriages and three-quarters of third marriages. That we are extraordinarily bad at choosing our romantic partners in marriage shouldn’t come as a great surprise. If there is one thing that we are told over and over again in movies, songs and novels, it is that love is fundamentally unpredictable by its very nature. Take Wagner’s 1870 opera Die Walküre, for instance, in which the lovers turn out to be long-lost brother and sister, although this fact alone is not enough to stop them falling in love. Or consider the immortal words of pop singer Joe Jackson: “Is She Really Going Out with Him?”
In many cases, the unpredictability of love has rendered even the most scientific of minds incapable of explanation. “The heart has its reasons, which reason knows nothing of,” Blaise Pascal, the French mathematician and inventor of the mechanical calculator, famously proclaimed. At the start of his 1822 book On Love, the French writer Stendhal lays out his desire to describe “simply, rationally, mathematically . . . the different emotions which . . . taken together are called the passion of Love.”3 The results, at least according to fellow wordsmith Henry James, w
ere “unreadable.” The problem, at least for those in the natural sciences, may be that there is not necessarily a natural law as relates to love. It might be eternal, but is it also external? Maybe not. “Love is intrinsically ametric,” observed the British psychotherapist David Brazier, speaking of love’s refusal to succumb to quantification.4 Compounding the problem yet further is the suggestion that the merest attempt to analyze pleasure or beauty all but destroys it—not dissimilar to trying to get a closer look at an exotic bird, only to have it fly away when it senses our designs.5
This may be a defeatist approach, however, which is why two centuries after Stendhal’s failed attempt to describe love, technologists continue to try to discover love’s code—perhaps taking at face value Friedrich Nietzsche’s assertion that “there is always some madness in love, but there is always some reason in madness.”6 And when it comes to this nobly scientific pursuit (worth upward of $4 billion globally in online dating fees alone7) there are few better people to examine than Neil Clark Warren and his eHarmony empire.
Seeking Harmony
Judged on first impressions, Neil Clark Warren is one of the more unlikely entrepreneurs of the Internet age. Born September 18, 1934, Warren was 65 years old when he launched his Internet dating company, eHarmony, in 2000. In the world of high tech, where acne is good, wrinkles are bad, and programmers throw in the towel at 30 because “coding is a young man’s game,” 65 might as well have been 165. Warren wasn’t—and isn’t—a computer whiz. According to him, he didn’t even know how to send and receive e-mail until his company was up and running. “I’m confessing up front that I don’t know much of anything about algorithms,” he says soon after he and I begin our conversation. “I think you’re going to be terribly unimpressed.”
But if Warren is too old to have grown up as part of the computer revolution, he was just the right age to have lived through another major change in American life. On October 28, 1935, when Warren was barely one year old, the New York Times ran a story in which it reported that the country’s divorce rate had increased by more than 2,000 percent. Worse, the statistics didn’t tell the whole story: according to the article, half of all American couples were supposedly unhappy; living, as one expert phrased it, “not really married but simply undivorced . . . in a sort of purgatory.”8
As is often the case with moments of profound social change, the tipping point that had led to this crisis of marriage wasn’t limited to one factor but was rather the result of a number of different factors converging simultaneously. Love was being increasingly emphasized over duty in marriage—with the implication that matrimony should be the fount of all human happiness. For the first time, divorce was also a real option to those outside of elite society. America’s cities were growing bigger by the day, as people moved away from their small, tight-knit communities and experienced a smorgasbord of new, previously unimaginable possibilities. The country was similarly more secular, as religion’s influence receded and The Formula’s advanced.
Right on cue came the new field of sociologists: invoking the metaphor of marriage as a machine, to be kept well oiled and in good working order at all times. As Paul Popenoe, one of the founding practitioners of American marriage counselling, observed:
There is nothing mysterious about [marital relations], any more than there is about the overhauling of an automobile that is not working properly. The mechanic investigates one possibility at [a] time: he checks the ignition, the carburettor, the transmission, the valves, and so on; finds where the trouble lies; and removes the cause if possible. We do the same with a marriage.9
Warren’s own parents fell into the category of troubled marriages. Although they stayed married for 70 years, Warren never felt that they were well matched with one another. “My dad was just so stinking bright, and my mom was so sweet, but she was two standard deviations below him in intelligence,” he would recall. Warren’s father—a business-minded man who owned a Chevrolet dealership, a John Deere outfit and a food shop—was interested in world politics, constantly questioning issues like the ongoing conflict between the Jews and Arabs. His mother, Warren has said, “didn’t know there was a Middle East.” When his father ran for office in Polk County, his mother voted for the other candidate.10
“I originally planned to go into the ministry, but discovered that I’m more of an entrepreneur than I am a minister,” Warren says. After earning a PhD in clinical psychology from the University of Chicago in 1967, he started out working as a marriage counselor. In 1992, he found fame by publishing a book called Find the Love of Your Life. It sold around a million copies, but Warren found himself feeling despondent. Even premarital counseling, he had concluded, was leaving things too late for many couples. “People have a tendency to form bonds very early in their relationship, and no matter what they find out at that point about whether they should get married or not, they will very seldom break up,” he says. “I came to realize that the only way to match people up with one another is to do it before they have met and got involved.”
Unlike a lot of psychologists, Warren discovered early in his career that he was interested in the quantitative parts of the field that scared off most people. He decided to put this to work by investigating the quality of marital relations. After Find the Love of Your Life, Warren started work on a large-scale research project, in which he conducted in-depth interviews with 800 couples. When this was done, he compared the results of the 200 most satisfied and least satisfied couples and used this to derive a robust set of psychometric factors he found remarkably predictive of compatibility in marriage. “The results overlapped so much with what I had found from 40 years of therapy that I became more and more confident that I knew what I was talking about,” he says. To help make sense of the data, he called in the services of a young statistician named Steve Carter—who is today eHarmony’s Vice President of Matching. On one occasion early in the two men’s working relationship, Warren threw out a curveball.
“How about building a website?” he said.
“To test for marital quality, you mean?” Carter answered.
“Not exactly,” Warren countered. “I was thinking more along the lines of a matchmaking site. We could use our compatibility models as a start and go from there.”
Despite some initial misgivings, Carter began working on the site: diligently reinterpreting the data Warren had gathered as a 436-question personality profiling test. Matching was done according to a checklist called the “29 Dimensions of Compatibility.” These dimensions were composed of two main variables described as Core Traits (“defining aspects of who you are that remain largely unchanged”) and Vital Attributes (“based on learning and experience and are more likely to change based on life events and decisions you make as an adult”). Although the algorithms involved remain largely black-boxed to avoid scrutiny, a number of details have come to light. Women, for instance, are never matched with men shorter than themselves, which means that men are similarly never paired with taller women. There are age parameters, too, which vary with gender, so that a 30-year-old woman will be matched with men between the ages of 27 and 40, while a 30-year-old man will be matched with women between 23 and 33.
In all, eHarmony’s arrival represented more than just another addition to an already crowded field of Internet dating websites—but a qualitative change in the way that Internet dating was carried out. “Neil was adamant that this should be based on science,” Carter says. Before eHarmony, the majority of dating websites took the form of searchable personal ads, of the kind that have been appearing in print since the 17th century.11 After eHarmony, the search engine model was replaced with a recommender system praised in press materials for its “scientific precision.” Instead of allowing users to scan through page after page of profiles, eHarmony simply required them to answer a series of questions—and then picked out the right option on their behalf.
The website opened its virtual doors for the first time
on August 22, 2000. There were a few initial teething problems. “Some people were critical of the matches they were getting,” Warren admits. “One woman who worked for a public relations firm was annoyed because we had matched her with two truck drivers, one after the other. My point was, ‘You know, a truck driver can be very smart,’ but in her mind there was such a status difference that she just thought it was absurd. She felt we weren’t doing our job at all.”
The point where, in Steve Carter’s words, “shit took off” was when Jay Leno put on a wig and started spoofing Neil Clark Warren on his television talk show. “He was fascinated that this old guy, with gray hair, was talking about matching up people for marriage,” Warren says. Although he was embarrassed, this was the moment he knew the website had struck a chord. By the end of 2001, eHarmony had more than 100,000 members registered. By August the following year, it had 415,000 members. By November 2003, the number had jumped to 2.25 million; followed by almost 6 million by December 2004; 8 million by October 2006; and 14 million by March 2007. Today, eHarmony credits its algorithms with generating 600,000 marriages in the United States—and a growing number overseas.12 As it turned out, there was a demand for scientific approaches to matchmaking, after all. “From my point of view, I can’t imagine anything I could be doing using statistics that would be more impactful on society than what I’m doing,” Carter says.
Categorize Your Desire
eHarmony doesn’t present itself simply as another coffee shop, nightclub, workplace or anywhere else that we might meet potential spouses. In its own words, it is designed to “deliver more than just dates” by promising connections to “singles who have been prescreened on . . . scientific predictors of relationship success.” To put it another way, the person who uses eHarmony’s algorithm to find dates isn’t just being offered more dates, but better ones.