I recently came across the famous Secretary Problem while reading Algorithms to Live By a book by Brian Christian and Thomas L. Griffiths.
This problem aroused my interest as it lies at the confluence of romantic relationships, optimization, self-interest, and maths.
Who am I kidding, who likes maths. But we are all interested in love in some form.
A simple explanation of the problem is as follows:
You want to hire a secretary out of N candidates. For each candidate you interview, you have to make a decision whether to accept or reject him/her. Assume each candidates can be ranked against each other. How do you select a candidate in a way that there is a maximum change of finding the best out of all candidates?
This brings us to Love.
For all of real life’s complexities, we see similar parallels in dating with the secretary problem. For most people, they go on first dates, have an impression of their date, continue or reject (sometimes ghost) them after.
So how do you choose the one that is going to be your life partner?
Finding ‘The One’
Across geography and cultures there are many different ways of solving the problem of ‘the One’. From arranged marriages to hookup culture.
It will take an infinite amount of time to discuss the merits and cons of each. Today we will look into the mathematical way of solving this problem.
The Stone Unturned vs. The One That Got Away
We know that marrying the first partner we meet might not be the best idea. We don’t know what dating other people are like, such as other ethnicities, cultures and ages that could be an even better fit for us. We are motivated to “Leave no stone unturned.”
Yet we can’t casually date everybody. By the time that happens, we will be too old or we will end up singing Katy Perry’s famous song: “The One That Got Away.”
The Annoying Contradiction
How can I balance discovering other dates yet not miss my chance when a good one comes along?
When you stop too early, you leave your dream partner undiscovered. Yet when you stop too late, you might miss on that same dream partner.
Depending your age and attractiveness, the longer you wait, the more urgent for you to make a decision.
The Answer Is…
The answer is 37%.
Out of all the people that we can potentially date in our lifetime, let’s say 100, the math says we casually date 37 of them to get an idea of what the dating pool is like, then commit to the first person that surpasses the benchmark that we have discovered while casually dating.
Why 37%
We can know the number to stop is at exploring is at 37% through this simple scenario.
If you can only date two people in the world, there is a 50/50 chance of success in selecting the best option.
When we add a third person to this dating pool, a random selection will have a success rate of 1/3 or 33%
Yet we don’t necessarily have to randomly select, and it boils down to what we do with the second date.
Consider this:
Date #1 — No experience
Date #3 — No agency, we don’t have any other choice. (Or stay single forever)
Date #2 — A little bit of both.
We know Date #2 is better or worse than the first and we still have the freedom to accept or reject.
What happens when we date her depending on if she’s better than the first applicant?
This turns out to be the best possible strategy when facing three applicants: you will get a 50% success rate. Which is much higher than 33% by random chance.
Here’s the logic.
Out of six possible orderings of the three applicants:
[1–2–3]
[1–3–2]
[2–1–3]
[2–3–1]
[3–1–2]
[3–2–1].
The sequences bolded will have you successfully choosing the highest applicant by deciding to accept or reject the second applicant based on the rating of the first.
“Enumerating these scenarios for four applicants tells us that we should still begin to leap as soon as the second applicant; with five applicants in the pool, we shouldn’t leap before the third. As the applicant pool grows, the exact place to draw the line between looking and leaping settles to 37% of the pool, yielding the 37%”
Excerpt From: Brian Christian. “Algorithms to Live By”.
Love Calculator Idea
Now that we know the selecting the best possible candidate for our love lives can depends on us drawing the line at 37% of our potential dating pool, why not build an algorithm to estimate whether someone is in their benchmarking phase or committal phase.
In the words of Gen-Z, should you still be in your “ho phase” living your best life or should you transition to the “trad life” expeditiously.
This is the big idea for my project. Build a web app with the limited HTML+CSS+JS knowledge I have, that given inputs on their dating experience and personal info, can tell a person to explore or commit.
The Hard Parts
What Is Our Dating Pool?
How do we estimate the total number of people we can potentially date in our life time?
All else being equal, we know physically attractive people will have a larger dating pool than a less attractive person.
We know that a male with a higher net worth will also have a larger dating pool. Same goes for fame.
Geographic spread also influences your dating pool. By having a presence in multiple cities and countries will be exposed to a deeper pool of people.
With online dating, the dating pool becomes exponentially larger compared to small town networks that our ancestors used to rely on.
How do I accurately take all of these into account?
Determining attractiveness without visual inputs through self reported data
The more accurately we can estimate someone’s attractiveness, the better we can estimate their potential dating pool.
When we talk about attractiveness in the context of the Love Calculator, we will take into account multiple metrics beyond purely physical attractiveness and look into a more general concept as I cannot build an AI face analyzer for attractiveness yet.
One idea of attractiveness I have been exploring is assigning a ‘mate value’ to a person.
This has been covered in studies such as ‘Components of self-perceived mate value’ (Fisher, Cox, Bennett, & Gavric, 2008) and Edlund, John & Sagarin, Brad. (2014). The Mate Value Scale. Personality and Individual Differences.
Gender differences — ‘Men marry down, women marry up’
For men, and as male this seems apparent. Men with high net worth, status, fame are likely to have a high ‘mate value’, thus being more attractive, and in turn, have a larger dating pool.
For women, it seems more complicated. If the common adage that men marry down and women marry up are true, then a women’s education, status and net worth seems less important. What then besides visual queues can we use to quantify a women’s attractiveness?
Is there any subtle non-visual hints that clues us on a women’s attractiveness without looking at her?
Self-reporting physical attractiveness
Unattractive people commonly overestimate their own physical attractiveness according to the study: Unattractive people are unaware of their (un)attractiveness by Tobias Greitemeyer published in 2020.
This shows it is an unreliable way to gauge someone’s true attractiveness.
Limitations of math
Real life is much more complicated that what the optimal solution can effectively solve.
In the future, I would have to take into account of scenarios such as:
- Dating multiple people at once
- Going back to previous dates
- Infidelity
This would pose interesting implications to the accuracy of the Love Calculator.
