Let me start with something most would agree: Dating is hard .
( If you donвЂ™t agree, thatвЂ™s awesome. You probably donвЂ™t spend that much time reading and writing Medium posts like me T вЂ” T)
Nowadays, we spend countless hours every week clicking through profiles and messaging people we find attractive on Tinder or Subtle Asian Dating.
And when you finally вЂget itвЂ™, you know how to take the perfect selfies for your TinderвЂ™s profile and you have no trouble inviting that cute girl in your Korean class to dinner, you would think that it shouldnвЂ™t be hard to find Mr/Mrs. Perfect to settle down. Nope. Many of us just canвЂ™t find the right match.
Dating is far too complex, scary and difficult for mere mortals .
Are our expectations too high? Are we too selfish? Or we simply destined to not meeting The One? DonвЂ™t worry! ItвЂ™s not your fault. You just have not done your math.
How many people should you date before you start settling for something a bit more serious?
ItвЂ™s a tricky question, so we have to turn to the mathematics and statisticians. And they have an answer: 37%.
What does that mean?
It means out of all the people you could possibly date, letвЂ™s say you foresee yourself dating 100 people in the next 10 years (more like 10 for me but thatвЂ™s another discussion), you should see about the first 37% or 37 people, and then settle for the big church search first person after that whoвЂ™s better than the ones you saw before (or wait for the very last one if such a person doesnвЂ™t turn up)
How do they get to this number? LetвЂ™s dig up some Math.
LetвЂ™s say we foresee N potential people who will come to our life sequentially and they are ranked according to some вЂmatching/best-partner statisticsвЂ™. Of course, you want to end up with the person who ranks 1st вЂ” letвЂ™s call this person X.
Before we explore the optimal dating policy, letвЂ™s start with a simple approach. What if you are so desperate to get matched on Tinder or to get dates that you decide to settle/marry the first person that comes along? What is the chance of this person being X?
And as n gets larger the larger timeframe we consider, this probability will tend to zero. Alright, you probably will not date 10,000 people in 20 years but even the small odds of 1/100 is enough to make me feel that this is not a great dating policy.
We do what people actually do in dating. That is, instead of committing to the first option that comes along, we want to meet a couple of potential partners, explore the quality of our dating fields and start to settle down. So thereвЂ™s an exploring part and a settling-down part to this dating game.
But how long should we explore and wait?
To formularize the strategy: you date M out of N people, reject all of them and immediately settle with the next person who is better than all you have seen so far. Our task is to find the optimal value of M. As I said earlier, the optimal rule value of M is M = 0.37N. But how do we get to this number?
I decide to run a small simulation in R to see if thereвЂ™s an indication of an optimal value of M.
The set up is simple and the code is as follows:
We can plot our simulated results for basic visualization:
So it seems that with N = 100, the graph does indicate a value of M that would maximize the probability that we find the best partner using our strategy. The value is M = 35 with a probability of 39.4%, quite close to the magic value I said earlier, which is M = 37.
This simulated experiment also shows that the larger the value of N we consider, the closer we get to the magic number. Below is a graph that shows the optimal ratio M/N as we increase the number of candidates we consider.
There are some interesting observations here: as we increase the number of candidates N that we consider, not only does the optimal probability decreases and see to converge, so does the optimal ratio M/N. Later on, we will prove rigorously that the two optimal entities converge to the same value of roughly 0.37.
You may wonder: вЂњHang on a minute, wonвЂ™t I achieve the highest probability of finding the best person at a very small value of N?вЂќ ThatвЂ™s partially right. Based on the simulation, at N = 3, we can achieve the probability of success of up to 66% by simply choosing the third person every time. So does that mean we should always aim to date at most 3 people and settle on the third?