Lest you think there aspects of life mathematics doesn’t address, a recent New Scientist article touches on the math of the so-called marriage problem. Assume you had to get married, and had to choose from 100 spousal candidates. You get to interview each candidate once, but once you pass them by, they are lost forever. That is, you must decide at the conclusion of each interview whether or not you will marry that one. In other words, if you pass on the first 99, then you are stuck with number 100. So clearly this isn’t a Bachelor type set-up, and is likely the basis for a pretty bad reality TV show of its own. It seems a rather hopeless quest, full of regrets and wish-I-could’ve-yes-I-should’ve moments. Wait, I guess that would be about par for reality TV.
Anyway, John Gilbert and Frederick Mosteller of Harvard University figured out that you can actually manage a 37% chance of marrying your ideal match in the batch. Of course there’s still a small chance you’ll wind up with troll #100, and it’s that suspense that will keep the ratings up week to week. It turns out that the key is to interview the first 37 people, passing on each one but keeping track of the best match. Then interview the remainder and choose the first person better than the best of the first batch. You derive the size of the first batch by taking the size of the whole batch and dividing it by e (2.72 or the base of natural logarithms).
Perhaps the most amusing perspective on this probability based selection theory is that a couple of mathematicians had the audacity to assume that they had 100 possible mates to choose from. In a more realistic sample size of maybe 5, you interview the first one and take anybody afterward who’s better than her. That sounds more realistic for this demographic.