I reached this age when my grandma keeps giving me the valuable piece of advice: I should finally settle down, get married and have kids. This idea is quite tempting, especially in the middle of the week, when I’m stuck on the theorem that, according to the author of the paper, is “trivial” and “easy to prove”. Then I definitely would prefer to be a wife of a millionaire and forget about my PhD. But how do I know which guy should be the only one?

As a proper mathematician, instead of dealing with all this love hassle, I decided to look at the problem in a structured way. My task is to choose the best husband. If I settle down too early, I can miss my second half, waiting for me somewhere. On the other hand, if I keep waiting for a prince on a white horse, I might die as a spinster. So how many people should I date to make the optimal decision?

We can assume the following:

- I can date one person at a time (obviously, what were you thinking?!);
- If I decide to change the partner, I won’t be able to come back (begging or threats won’t help);
- When I find the “optimal” person, I get married and stop dating forever and ever.

There exists a mathematical theory that gives a surprisingly exact answer to this quite general problem. Namely, I should say “bye” to n/e first candidates, where n is the number of possible husbands and e is a constant (about 2.718). After that, I have to marry the very first candidate that’s better than all previously dated.

For example, because I live in a big city and meet a lot of people, I can assume that there are 100 potential partners. The algorithm says that I should be careful to not fall in love with any of the first 37 dates, because I’ll have to leave them anyway. The real job begins afterwards: from the 38^{th} partner onwards, I’ll need to compare every guy to all the previous ones. If someone is better than the rest, then we need to tie the knot and live happily ever after. Really?

Only if I’m lucky. Many things can go wrong!

Let’s say that I meet the best guy in the beginning of my dating adventure. Then after magical 37 I won’t find anyone better, which means I’ll have to stay alone till the end of my life, regretting having listened to mathematicians. On the other hand, if I start small and in the beginning date only not very handsome, chivalrous or intelligent people, I’ll probably meet someone better shortly after first 37 trials. But this candidate might be still rather weak – and I can’t be picky, according to the algorithm must marry him (and stay miserable for the rest of my life).

You’re probably thinking: rubbish, relationships don’t work that way! And you’re obviously right. I’ve made way too many unrealistic assumptions for this model to work.

First of all, why would the number of candidates be fixed? In other words, how do I know when to really start looking for a husband? If I lived in a tiny village in the middle of nowhere, this would be clear; it’s a bit more complicated in a huge city, especially that I travel quite a lot. My options seem to be endless.

Well, they seem to be, because don’t forget that it takes two to tango. What if for the guy that should be my optimal husband, I’m the 5^{th} date and he needs to find another partner, regardless of my charm and intelligence? The probability that the algorithm will match us is very low.

However, game theory has more to offer than this toy (and in this case quite useless) model, known also as the secretary problem. But when it comes to relationships, I would follow my heart – at least until mathematicians come up with a better algorithm. Good luck!

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W dniu piątek, 25 listopada 2016 Paula Rowińska napisał(a):

> Paula Rowińska posted: “I reached this age when my grandma keeps giving me > the valuable piece of advice: I should finally settle down, get married and > have kids. This idea is quite tempting, especially in the middle of the > week, when I’m stuck on the theorem that, according to t” >

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