Who in their right mind would use mathematics to choose a life partner? When you are choosing a life partner, mathematics is probably the last thing that comes to your mind. However, I argue that this knowledge could be very helpful for any such occasion. Mathematics is the world of logic after all. Human beings invented mathematics to formalise logic and communicate logic clearly and efficiently. So, it is no wonder that mathematics is helpful in a lot of real-life situations, including the choice of a life partner. The branch of mathematics that deals with real-life problems is called applied mathematics. And that’s where I’ll be taking you in this article. Without further ado, let’s get right into it.

This essay is supported by Generatebg

The Problem

Almost every human being is faced with the problem of choosing a life partner at some stage in their lives. Let’s say that you have a fairly good idea of what qualities your life partner should possess. Then you set off on a journey to look for one. You come across one person after another. Some of these candidates turn out to be a bad fit to your expectations, while some turn out to be better. But no matter how good the fit is, you know that there are likely more potential partners that you will come across in the future. And any one of these could be a better fitting partner to you than those that you have come across in the past. You can’t just keep going on forever looking for the perfect fit. At the same time, you don’t want to compromise and miss out on the best possible fit either. That is precisely the problem that we are trying to tackle today.

How do you know when to stop looking for a life partner?

How do you maximise the likelihood of finding the best fitting candidate as your life partner?

Using applied mathematics, we will be trying to answer these two questions.

The Starting Point

Mathematics tends to idealise situations. It starts from assumptions. Otherwise, logical formalism struggles to proceed. So, we will start with certain assumptions, and then connect the assumptions with real-world variations once we have a working algorithm for choosing a life partner. For now, our approach makes the following assumptions:

  1. You have clearly defined and objectively measurable quality criteria that your ideal life partner should possess.
  2. You have the precise number for the total number of potential candidates you wish to date or spend time with before you make the choice.

Of course, these assumptions deviate from reality. But once we have a working algorithm, I’ll try to fit the algorithm to the real-life use case. Let’s just not worry about the menacing reality at this stage.

Using Mathematics to Choose a Life Partner Out of 3 Candidates

I’ll start the analysis with 3 potential candidates, and then scale to a higher number of candidates. To simplify things, let us further say that we are trying to solve the problem for a female looking for a male partner. It could be done any other way, and the algorithm would work the same. But for ease of derivation, it helps to lock onto one perspective. Let us consider a situation where one person out of the three is a bad fit, one is an ‘okay’ fit, and one is the best fit. Considering this, you may come across any of them in any order. So, the question here would be how do we maximise our chance of choosing the best partner?

Using mathematics to choose a life partner out of 3 stick figures presented in a picture. From left to right: B for bad, O for okay, and G for Good.
Image created by the author

To do this we are going to use probability theory. Given our current situation, we say that there are 6 permutations or 3! (three factorial) ways in which the combinations could play out. For now, let’s start with an algorithm that follows the following 2 rules:

  1. Always reject the first person you come across.
  2. Choose the next best person you come across.

I have worked out how this algorithm would play out.

Using mathematics to choose a life partner - all combinations of order in which you meet the partners is listed. The algorithm is applied. We see that in 3 out of 6 cases, we end up choosing the best fitting partner. The success ratio is then 50%
Image created by the author

We see that this algorithm leads to a 50% chance of the best possible outcome. With this in mind, we can move to scale the algorithm to more potential partners

Using Mathematics to Choose a Life Partner Out of Many Candidates

When we add just one more partner to the above analysis, the probability of the best possible outcome would drop to 46%. If we keep on increasing the total number of potential partners, how should we scale the algorithm?

Let us use ‘N’ to represent the total number of potential candidates. Furthermore, let us use ‘c’ to represent the critical number after which we stop looking, and choose the next best candidate. Based on these parameters, the modified rules of the algorithm can be written as:

  1. Keep dating potential partners and rejecting them until you arrived at the cth candidate.
  2. After the cth candidate (reject ‘c’ as well!), choose the best fit compared to the ones you have rejected so far.

Let’s see how this algorithm plays out mathematically. To do this, we define success (best possible outcome) as a probability function. This probability function is in turn the summation of the product of two probabilities: 1. Probability of you dating your ideal partner as the nth person you date (out of a total of N possible candidates), and 2. Probability of you actually choosing the ideal person when you are dating them.

Using Mathematics to choose a life parter: The probability of success is defined in written form. P(A) denotes the probability of arriving at the ideal partner and P(D) is defined as the probability of actually choosing the ideal person.
Image created by the author
Using mathematics to choose a life partner - Until the Cth person, we keep rejecting, so the probability of success is zero. From the (C+1)th person onward, the probability terms are being added.
Math illustration by the author

Based on our algorithm, it is clear that the probability of success until (and including) the cth candidate is zero because we reject them all. From the C+1th candidate onwards, we get the following interesting summation:

The summation is as follows: P(C) = (C/N)*(1/C + 1/(C+1) + 1/(C+2) + .... +1/(N-1))
Math illustration by the author

The sum within the brackets can be approximated (mathematically) to the area under the curve of the function f(x)=1/x

The summation within the brackets approximates to the integral of the function (1/x )dx with the lower limit of C and upper limit of N
Math illustration by the author

Solving this further, we get the following solution:

the result of solving the integration is ln(N/C)
Math illustration by the author

When we replace the original summation in the probability of success equation with this solution, we get the following:

First, we define (C/N)=X. Then, we solve for a new probabiltiy function P(x) with C/N replaced by x in the former equation. This leads to P-hat(x) = -x*ln(x). When you plot this function, we get a clear high point, which defines the ideal partner.
Math illustration by the author

From the graph, it is evident to us that we are interested in the ideal partner at the peak of the function curve. To obtain this point, we shall use differential calculus as follows:

We set the first differential of P(x) with respect to x equal to zero. As a result we arrive at a critical point of C/N approximately equal to 0.37. Or in other words 37%
Math illustration by the author

And the Lucky Winner is…

Using mathematical wizardry, we have arrived at the following results:

  1. To maximise your chances of choosing the best partner, you have to reject the first 37% of the dates.
  2. After the first 37%, you further have a 37% chance of landing on your perfect fit for a life partner.

The catch here is that although you reject the first 37% of your dates, you still remain perceptive, and collect data. This data is what you use to compare against the potential dates past the critical number ‘c’.

This is a pretty established mathematical problem in the industry and is known as the optimal stopping problem or the secretary problem. It is applicable to any situation in life where there is an interview-like selection process involved. It makes a few key assumptions that deviate from reality and doesn’t consider the irrational side of human beings when it comes to love. Let’s try and bridge that gap next.

Welcome to Reality

As promised, I’ll try to account for the algorithm’s deviation from reality. However, consider the following proposition: You can be sure that you are not going to kiss a million frogs before you decide on the perfect partner. So, if you can to narrow down on the rough number of partners you wish to date (N), this algorithm gives you the best chance of finding the best fit.

Let’s say you are an adventurous type and wish to date a hundred people. This algorithm says that it is probably not in your best interest if you settle for someone before having rejected the first 37 people. I know. That is indeed a tough pill to swallow. As for irrational feelings, where there is a will, there is a way. Irrational feelings can still be quantified and accounted for if one takes the time to record how one is feeling in the moment. This can then be used for comparison later.

Even if you do not intend to follow this algorithm strictly when it comes to the choice of a life partner, this knowledge could prove useful in giving a bigger perspective. With this said, there is always luck involved in every important decision. So, I wish you the best of luck!

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Further reading that might interest you: The Fascinating Reason Why Temperature Has No Upper Limit? and How To Use Science To Win At Rock-Paper-Scissors?

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