Do you need some help with finding the right lover or do you seek confirmation for your current love? Love is one of the most non-abstract phenomena one knows and as econometricians, there is only one thing we understand perfectly; mathematics. To help you understand love a little better, I will show you that equations and graphs can guide your love life. Lucky for you, Valentine’s day is this Friday, which will be the best opportunity to test if you understand the mathematics of love properly. Let me give you a hint: the magic number is 37. 

Penis + impulse = one-night stand. That’s clear, right? The formula for the perfect first date is easy as well; candlelight dinner + kissing = a second date. The perfect relationship? Timing + communication x mutual attraction – emotional baggage = intimacy. You see! You understand the mathematics behind love already quite good. Unfortunately, we all experienced a situation where everything seems to add up and the outcome looked good beforehand, but it didn’t add up to love…

Sooner or later, most students decide to leave their carefree student life behind and settle down. Occasionally, you are laying in bed while thinking about the days where your life motto was  “No one looks back at their life and remembers the nights they had plenty of sleep”. The wild nights are just vague memories and making long-term decisions is now your biggest worry. But how do you know if you have found “The One”? 

Imaginary list of potential life partners

The best solution would be a list with each dating partner listed based on how good they will be as your life partner. Sadly, such a list does not exist, but it would make the choice a lot easier. How can you select the best person on your imaginary list of life partners, without knowing anything about your future? We assume that the rules of dating are simple: you can not look ahead to see all the partners you could have had and you can not go back after rejecting someone. 

In this way, using the optimal stopping theory is one of the best possible strategies to find your true love. In mathematics, this theory looks at the problem of choosing a time to take a particular action in order to maximize an expected reward. This theory shows that the best approach is spending a bit more time at the playing field when you are young and rejecting everyone you meet as a serious life-partner material. Once you have got a feel for the market, you pick the next person who comes along who’s better than everyone you met before. This sounds quite reasonable, right?

The formula of love

To make it even more clear, we can express this theory in a formula. Your probability of settling down with the right life partner (denoted by P) is dependent on how many potential lovers (n) you have rejected (r), given by the following formula:

Now you can easily calculate how many people you have to reject before you find the perfect partner. For example, if you are going to date ten people in your life, the probability is maximized when you reject your first four lovers (which is 39.87 percent of the time). If your destiny is to date 20 people, you should reject the first eight dates (which is 38.42 percent of the time). Lastly, if you would date an infinite number of people in your life, the maximum probability is when you reject the 37 percent. Hence, by rejecting the first 37 percent of your lovers, you can determine your own fortunes and find your true love! 

But there is one problem… Unless your potential dates are all lined up for the future, there is no way you could know how many people you are going to date. And the chance that you will have an infinite number of dates is also unlikely. 

Duration of your dating life

Let’s put it in a different way. The rules are the same, but the math is much trickier. Now we do not look at the number of people you have dated, but at the expected duration of your dating life. For instance, if you start dating when you are 15 years old and you would like to settle down when you are 40 years old. Use the first 37 percent of your dating life (until you become 24 years old) to get a feeling for the market by rejecting all your partners, such that you get a realistic expectation of what you want in your life love. Following the theory, find the next person who comes along and who is better than the other dates.This will definitely give you the maximal probability of finding the right love. 

Unfortunately, even this method has its flaws. Imagine that you meet your perfect life partner during your 37-percent-rejection phase. Since you have not met everyone on your imaginary list, you have to let this person go. Afterwards, it becomes clear that this person was “The One”  and no one better will ever comes along. Following the theory, you should continue rejecting everyone else for the rest of your life and die alone… On the other hand, imagine that you meet only terrible dating partners in your first 37 percent dating life. The next person you meet is just marginally better than those before. According to the rules, you should marry this person and still get a miserable marriage. 

Other approaches

Since the theory only assumes that you are interested in finding the very best possible partner available to you, it is less appropriate for your love life. Mathematics can still offer answers. The Monte Carlo simulation simulates tens of thousands of different lifetimes of someone with randomly chosen partners of random levels of compatibility. In the end, the program looks back at all the partners it could have had and works out if the strategy has been successful. The simulation looks at three different rejection phases; best partner only (red line), someone in the top five percent (yellow line) and someone in the top fifteen percent (blue line). In reality, many people would prefer a good partner to being alone if their true love is unavailable. This gives the following graph:

If you would be happy to settle down with someone in the top 5 percent of your imaginary list of dates, your best chance of success is choosing the person who is the next best person after the first 22 percent of your dating life. Following this theory, you will settle with someone within the top 5 percent 57 percent of the time. When you settle down with anyone in the top 15 percent, you need to pick the next person who is better than everyone else after 19 percent of your dating life has passed. This gives a 78 percent chance of finding the right one. 

Unfortunately, it is not possible to estimate your optimal love life perfectly with mathematics. Nonetheless, this theory offers some insight into the real-world scenario, and that is what econometrics is all about after all. Otherwise, love would depend only on emotions… 

This article was written by Renske Zijm