Authors: Andrew Trees
Decoding Love (19 page)
Unfortunately, dating is not like that. The partners in any game are constantly shifting. But you could still achieve similar results if you had good enough communication. When people can communicate the past behavior of others, they can form networks of trust and shut out players who rely on deception. Imagine if each of us was given a rating based on our dating histories, similar to the buyer and seller ratings on eBay. If someone behaved badly, he or she would find it increasingly difficult to find anyone to date. When people lived in one place for most of their lives, gossip essentially served this function and helped impose a standard of behavior, and some Internet sites are now starting to adopt this concept, although it is far from foolproof since users can simply move to a new site. If one dating Web site ever dominates the way that eBay does with online auctions, it will have the power to improve the behavior (or at least the honesty) of men and women when they date—more so than anything since Moses came down with the Ten Commandments.
While all this game theory may be interesting, some of you are probably wondering right about now, so what? Is there some more practical advice that game theory can offer? Well, yes, actually there is. For example, it can finally provide an answer to that age-old question: how many people do you have to date before you meet your true love? The answer: twelve. That’s right. A nice, round dozen. Not too difficult, right? Okay, yes, I realize you are going to need more convincing than that. Many of you have dated far more than twelve people and are still no closer to finding a partner than you were when you were the age of twelve. Others are probably outraged that I would even put a definitive number on such an amorphous task. Besides, what’s so special about the number twelve? It’s not as if Cinderella crossed that threshold, which, by the way, is one of my pet peeves with the romantic story line. The storybook lovers always seem to meet the right person very early on, leaving the rest of us poor schlubs feeling that taking a long time to find love is itself another sign of failure.
But back to the lucky number twelve. How in the world can we possibly arrive at such a precise number? To understand that, I’m going to ask you to play a game. Mathematicians have called this game by a variety of names. We are going to play the version known as the dowry problem. Let me set the scene. You are the king’s most trusted adviser. He wants to find you a lovely bride (or groom), but he also wants to make sure that you truly are as wise as he thinks you are. So, he arranges a challenge for you. He sends out his minions and finds one hundred of the most beautiful women in the land. He then provides each of them with a dowry, only he doesn’t provide them with the same dowry. Each woman has a dowry different in value from all the other women. Your challenge is to pick the woman with the highest dowry. If you succeed, the beautiful bride and the sumptuous dowry are yours to enjoy, and your place at the king’s side is secure. If you fail, he’s going to chop your head off. Oh, and one more thing, you meet the women one at a time, and once you have dismissed a woman, you can never call her back. Ready? Let’s play.
Being the brilliant adviser that you are, you probably have already figured out the math for all of this. I, of course, am terrible at math and am relying entirely on the excellent article by Peter F. Todd and Geoffrey F. Miller called “From Pride and Prejudice to Persuasion: Satisficing in Mate Search,” which can be found in
Simple Heuristics That Make Us Smart.
Once you crunch the numbers, you realize that your best chance is to pass on the first thirty-seven women and then pick the next woman who has a higher dowry than any of the women who came before her. Mathematicians have dubbed this rather obviously the “37 percent rule.” By seeing the first thirty-seven women, you will give yourself a 37 percent chance of choosing the highest dowry. Not the greatest of odds when you are under the threat of having your head chopped off but a better percentage than you will get with any other number. If the king lets you play the field a little bit, you can improve your chances dramatically. If you can keep one woman while you continue your search, you can increase your odds of finding the best dowry to 60 percent. Not too shabby.
Simple Heuristics That Make Us Smart.
Once you crunch the numbers, you realize that your best chance is to pass on the first thirty-seven women and then pick the next woman who has a higher dowry than any of the women who came before her. Mathematicians have dubbed this rather obviously the “37 percent rule.” By seeing the first thirty-seven women, you will give yourself a 37 percent chance of choosing the highest dowry. Not the greatest of odds when you are under the threat of having your head chopped off but a better percentage than you will get with any other number. If the king lets you play the field a little bit, you can improve your chances dramatically. If you can keep one woman while you continue your search, you can increase your odds of finding the best dowry to 60 percent. Not too shabby.
Those of you who feel a little letdown about the 37 percent rule, raise your hands. Thirty-seven is nowhere near the twelve I promised. Dating thirty-seven people sounds exhausting. Well, apparently Todd and Miller agreed with you, and they set about tweaking the game in various ways to see if they could find a better way.
Instead of the 37 percent rule, you could try the “Take the next best” strategy. Of course, you are going to have to give up on the idea of “the one.” If your sole criteria is trying to find the single-best mate, you’ve got to stick with the 37 percent rule. But if you are willing to accept anyone in the top 10 percent, you can follow the 14 percent rule. This rule works as you might expect. You pass on the first fourteen women (or men) and then choose the next woman who is better than those first fourteen. If you do this, you have an 83 percent chance of ending up with someone in the top 10 percent. If you are willing to accept anyone in the top 25 percent, you only need to look at the first seven women and then choose to have a 92 percent chance of success. Let’s say you are unlucky in love and just want to avoid marrying someone in the bottom 25 percent. Then you only need to check out three women, and you will have less than a 1 percent chance of ending up with a loser. That may not sound all that great, but the 3 percent strategy still does a better job of avoiding losers than the 37 percent rule, which has a 9 percent chance of landing you with someone in the bottom 25 percent. While the 37 percent rule provides the best chance of picking the best person, it does worse at almost everything else, including picking someone in the top 10 percent or even the top 25 percent. It also results in a lower overall average mate value.
Running all the numbers, it turns out that the best strategy is the 10 percent rule, which results in the highest average mate value, a high chance of landing someone in the top 10 percent and a very high chance of landing someone in the top 25 percent. To give you some sense of how much more effective the 10 percent rule is than the 37 percent rule, compare the average mate values. The 10 percent rule gives you an average mate value of 92 out of 100 versus an average mate value of 81 out of 100 if you use the 37 percent rule (and you have to date a lot fewer people!). The 10 percent rule isn’t particularly onerous. You only need to date ten people from a field of one hundred. That is lower than the twelve I originally promised. Of course, you are likely going to have to date more than just those ten. Remember the way the game works. The 10 percent rule means that you have to pass on the first ten people and then choose the next person who comes along and is better than the first ten. On average, you will end up working your way through roughly thirty-four potential candidates.
Of course, there are probably some indefatigable daters out there who think that one hundred people is a rather paltry total: the dating decathletes among us who are perfectly happy to date one thousand people if it improves their chances of finding true love. If you are choosing among one thousand women (or men), the 37 percent rule means that you will no longer be doing anything but dating for the foreseeable future. If you are willing to accept someone in the top 10 percent, though, you only need to apply the 3 percent rule for a 97 percent chance of success. And the numbers are even better if you are willing to accept someone in the top 25 percent. After running the game for numbers ranging from one hundred to several thousand, it all boiled down to one simple rule: try a dozen (Cresswell dubbed this the twelve-bonk rule, bonk being a British word for . . . well, I’m sure we all know what bonk means). Todd and Miller found that this number provided excellent results no matter how large the sample size. As they aptly put it, “A little search goes a long way.” We may still choose the wrong person, but the “try a dozen” rule shows that our mistakes are probably not from lack of trying.
Although I have yet to meet anyone who has explicitly used the twelve-bonk rule to choose a partner, the anecdotal evidence suggests that some of us subconsciously follow a method roughly analogous to it. For example, a number of people said that they viewed finding the right person as a simple numbers game. They just had to ensure that they met enough people in order to find the right fit. I realize this contradicts to some extent what I said earlier about too much choice, but it is very different to date several dozen people over the course of several years than it is to scan hundreds or even thousands of online profiles in the course of a few hours. The surprising thing was how often the numbers roughly correlated with what the twelve-bonk rule predicts. One woman decided to get serious about meeting someone and went on thirty-eight dates over a two-year period before finding Mr. Right, which is very close to the average predicted by the “try a dozen” rule. Another woman inadvertently ran her own modified version of the dowry game, albeit without the fatal consequences. She went on a hundred first dates, ruthlessly culled from that list ten men for a second date, ruthlessly culled again and went on a third date with three men. She ended up having a long-term relationship with two of the men, and she married one of them. I also found a variety of other people who had used methods roughly analogous to game theory. One systems engineer even described his marriage as a “system deployment,” a statement that positively drips with romance.
Of course, life is never so simple. There are numerous ways that the dowry game does not reflect real life, although it would be nice to lie on plush cushions, eat grapes, and wait for beautiful women to be brought to you. We are going to focus on the most important one: mutual choice. The dowry game assumes that you simply get to choose whichever woman (or man) you want. What it fails to recognize is that in our society, the women (and men) also exercise their own choice. They are perfectly free to look at your lazy, grape-eating ass and decide to marry that ruggedly handsome camel trader back in their hometown.
Miller and Todd ran the game again with one hundred men and one hundred women, and they found that the more possible partners both sexes checked out, the lower the rate of people who ended up in a relationship. The reason was that people began setting their aspiration level too high. You may set your sights on a woman in the top 10 percent, but if you are in the bottom 25 percent, you are going to end up single. For people to find their way into a relationship, a new element needed to be added: people had to adjust their aspiration level based on the feedback they were getting. A great deal of math is involved, and Miller and Todd experimented with a number of scenarios on how to determine mate value. To put it in simple terms, if you use the twelve-bonk rule, your expectations are likely going to be too high.
It is also important to remember that many aspects of dating are not susceptible to mathematical analysis. For instance, women would find it very useful to know the ratio of men who are likely to be loyal partners versus those who will cheat. Unfortunately, there is no definitive answer to this question, for the simple reason that the ratio will change depending on the social environment. The best strategy for men is mixed. In other words, depending on the context, it may make sense for a man to be faithful, or it may make sense to pursue opportunistic sex. Game theory itself predicts that players will cultivate unpredictability as a way to avoid being easily manipulated in the game.
Worse, it is quite possible that the players might not even be aware of their own gamesmanship. Our old friend Trivers of the parental investment theory has called this “adaptive self-deception.” If you buy this theory—and anyone who has listened to a friend justify some completely preposterous course of action will—we are so good at deception that we often manage to deceive ourselves as well. This self-deception is incredibly useful to us from an evolutionary standpoint because successfully masking our intentions from ourselves makes it much more likely that we will also deceive those around us. You can see the benefit of this in a host of situations. Just think of a single man on the prowl for a one-night stand. He might meet a woman in a bar and immediately become convinced that she is the love of his life. He woos her intensely and is able to look her in the eye and tell her with great sincerity that he thinks she is far more than some easy sexual conquest for him. Because of this, he convinces her to spend the night with him. When he wakes up in the morning, he realizes that he was deceiving himself the entire time. In the cold light of day, he knows that he has no interest in a long-term relationship with the woman, but his self-deception has already served the purpose that evolution designed it to serve—to spread his genetic material.
Although amusing to examine dating using economics and game theory, these approaches are limited by their failure to account for the irrationality that guides so much of our behavior, particularly when it comes to love. To see this, let’s play a game called How Much Would You Pay For a Dollar? I don’t think it takes a mathematical genius to determine that you should pay no more than ninety-nine cents. What if a wrinkle is added, though, and the second-highest bidder also has to pay his bid, even though he has lost the auction? Now, how much should you pay?
That’s exactly the game that Martin Shubik, an economist, played a number of times with different groups of friends. As he wrote in his article, the game is ideally played under what might be called boisterous conditions: “A large crowd is desirable. Furthermore, experience has indicated that the best time is during a party when spirits are high and the propensity to calculate does not settle in until at least two bids have been made.” Shubik identified three crucial points in the game. The first was whether two people were willing to make a bid. The second crucial moment came at fifty cents when the people bidding realized that any higher bids meant that the auctioneer would make a profit. And the third crucial point was at one hundred cents when someone had, in effect, offered to give a dollar to get a dollar. At this point, his opponent would already be committed to pay his own bid and usually decided to bid $1.01. Even though he would be giving more than the dollar was worth, he would at least get the dollar and only lose one cent, rather than the value of his entire bid if he lost the auction. Once a player bid more than one dollar in order to receive one dollar, the bidding tended to escalate rapidly. Shubik kept track of the results and found that, on average, the dollar bill sold for $3.40. Since Shubik also kept the losing bid, he took in over six dollars and had to pay out only one dollar. Some of the games were even more extreme. One “winner” ended up paying twenty dollars for the dollar and only succeeded with that bid because his opponent ran out of money. On another occasion, a husband and wife bid against each other and were so upset by the experience that they went home in separate cabs.
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