WS MoreOrLess: The maths of dating
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This is the short edition of More or Less, first broadcast on the BBC World Service.
Hello and welcome to More or Less on the BBC World Service. I'm Tim Harford. This week, pregnancy due dates. But before that, we'll hear from Matt Parker, an unusual combination of mathematician and stand-up comedian. Matt recently wrote a book called Things to Make and Do in the Fourth Dimension. It's a collection of tricks, games and puzzles that reveal bigger lessons about the world around us – Maths, says Matt, can even help you find the right life partner. So I laid myself down on his couch and I opened my heart. I'm pleased to say I'm happily married, but occasionally I have doubts as to whether maybe I settled down too soon. Could I have done better if I waited? Seems unlikely, but it's quite possible my wife could have done better if she had waited.
So can maths help me?
I mean, these are very valid concerns and ones you should probably not broadcast on radio. But there is a mathematical approach you could have taken. And the problem you were faced, in fact, we're all faced with, is when you're looking for a life partner, as you're interviewing people, or I believe dating is what it's commonly called. If you meet a candidate and you assess their qualities and then you reject them, later on it's very hard to go back and say, look, I've changed my mind. It turns out you were the best I'm ever going to do. But on the flip side, if you settle down with someone straight away, you have no idea what the general quality of possible candidates was. So you're faced with a problem.
You've got to interview or survey a certain number of possible candidates and reject them to get a sense of the quality. But you don't want to do that for too many or you may pass by the best option. And so the question is, how many people do you reject to get a sense of the standard? And at what point do you stop rejecting and you start trying? choosing. And that is called the optimal stopping problem. And mathematically, we know if you want to get the best person on average, you need to look at the total number of people you will date across your life. You then calculate the square root of that number of people. And so let's say you were going to date 100 people in your life. Your square root is 10.
You then go through that first 10 people and you automatically reject them. But you keep track. I mean, maybe log them in a spreadsheet as to who was the best. And then once you've gone through that, you then keep dating people until you meet someone who is as good as or better than anyone you saw in your original sample as such. And that mathematically will give you the best result on average.
There are all sorts of assumptions that we're making with the optimal stopping problem. Not only the distribution of partners, but what counts as an interview or a date? How long do you need to date somebody before you can assess their quality? We're sort of assuming quality doesn't change. you don't change your partner doesn't change you know so there's no role for divorce in this scenario and we're assuming that you know with certainty how many people you could possibly date over the course of your lifetime so that all sorts of tweaks we could make and they might totally change the answer and so at the risk of being a killjoy i have to say well what's the point of this if it's not going to give us an answer that really works in the real world why are we doing it at all
You're absolutely correct. I mean, as always, a mathematical model is only as good as the starting assumptions, how many things you factor in and how accurate you are at factoring those in. And so I wouldn't recommend living life following this down to the algorithm to clinically locate the person you have then calculated to be your best partner. But it is a reasonably good guide. Research seems to show that people on average settle down too soon. Matt Parker.
Now, when you've found the one, it can lead to thoughts of... ..babies. It's certainly turned out that way for loyal listener Penelope Chaney, who's been in touch with a question.
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