Math Gets Around: Dating

Unfortunately, the primary disadvantage to the method described below is that if you don’t know about it before you jump into the dating scene, it may be too late for you to utilize. But with an open mind, and a willingness to let mathematics do its work, you can maximize the likelihood that you will find that special someone.

How can mathematics help you find a mate? Let’s formalize the search for love as follows: you want to know when you should commit. Usually the way it works is that you date a few people until you find one with whom you are compatible enough, and one who does not drive you too crazy, and hopefully one for whom these feelings are mutual. So, you date until you find someone with whom you are reasonably confident you could settle down.

But how do you know that someone better won’t come along? Indeed, this is a question that may plague those afraid of commitment. Or, for those of you who have been in the game for some time, you may be asking: when should I throw in the towel and settle down with Mr. or Ms. “I guess they’ll fit the bill”?

If you listen to the advice of mathematics, you will do the following:

Date roughly 37% of the total number of people available to you in your dating pool, but do not stay with any of them. After dating this first 37%, stick with the first person that comes along who is better than any of the previous candidates.¹

If you follow this process, you will pick your ideal mate from out of your dating pool 37% of the time – this is the highest probability you can get, given these circumstances. This is also assuming that there is no going back in your relationships: once things are done, they are done for good.

Let’s take an example. Say that you plan on dating 100 people during your life. In order to find the best match for you, you should date the first 37 people, but not settle down with any of them. Then, the first person who comes along after those initial 37 who you like better than anyone you have dated before is the one you should stick with.

Of course, there are some natural questions that this process raises. Most importantly, what exactly qualifies as “dating”? The nice thing is that however you choose to define dating, this process still applies. So in fact, the choice of definition is not so important. All that matters is that you follow this process according to your definition.

Other common questions fall along the lines of: What if I pass up my true love in that initial 37%? Or what if my true love is at the very end, and so I pick someone else before meeting him or her? Indeed, these are valid concerns. However, as with many things in life, the quest for love is not easy, and there is no guaranteed way to find the one you are looking for. As stated above, this method will provide you with the highest probability of success, but even so, roughly 2/3 of the time you will wind up with a sub-optimal match. Isn’t it romantic?

There are some valid criticisms to this method. One is that few people set out on their dating path with a set number of people they would like to date in their lifetime. Without this number firmly in your mind, how will you know when you have passed the 37% threshold? Because of this, for many people it may be too late to maximize their chances of finding true love.

Another criticism is that in these modern times, the dating game is less information-blind. The above description of dating assumes that you know nothing about your potential dating partners until you actually date them – in particular, you have no idea how compatible you may be with a member of your dating pool until you have begun dating. With the rise of internet dating, however, this is no longer the case: for example, match.com uses sophisticated algorithms to process user data in an attempt to predict compatibility between two people. Therefore, when you go to such a site to try and find a date, you have a sense beforehand of how you will fit with your potential partners: in effect, this allows you to see the ranking beforehand, so that picking should become easier.

The truth, as we all know, is that no method is foolproof. Even if you decry the 37% rule for dating, however, you may find it come in handy in other aspects of your life. What about when you are looking for a new apartment? Or trying to find that new job? In both these cases, there is usually no going back once you have looked at a potential candidate, and so it is natural to ask how long you should look before committing. The rule still holds: you maximize the chance that you are picking the best outcome by going through the first 37% of all available options, and then picking the option that is better than anything you have previously seen.

Note that as a corollary to this rule, as long as you are planning to consider at least two options, you should never pick the first thing you see. This goes for jobs, apartments, pets, cars, and so on. Sorry, high school sweethearts.

Given that this method is the best way for you to find the best match, is it how people act in everyday life? Sadly, the answer is no. The Wikipedia entry on this problem discusses some experimental studies on how compatible this algorithm is with real world behavior. In general, research has concluded the following:

In large part, this work has shown that people tend to stop searching too soon. This may be explained, at least in part, by the cost of evaluating candidates. Extrapolating to real world settings, this might suggest that people do not search enough whenever they are faced with problems where the decision alternatives are encountered sequentially. For example, when trying to decide at which gas station to stop for gas, people might not search enough before stopping. If true, then they would tend to pay more for gas than they might had they searched longer. The same may be true when people search online for airline tickets, say.

1. 37% may seem like an arbitrary number, but the percent is actually 1/e, which is approximately 0.367879… . Wondering how e appears in this problem? Try to derive the solution for yourself! Or, if you have little background in probability, you can find the solution online, with enough sleuthing.