…or why you should always ask people out.

One of my favorite math problems is the stable marriage problem. Let’s say that you have n heterosexual men and n heterosexual women where each man has ranked each woman in order of mating preference, and each woman has ranked each man the same way. Can we find a matching such that all marriages are stable (i.e. two people won’t leave their current partners because they’d be happier with each other)?

The answer, perhaps surprisingly, is yes, we can always find such a matching. And one straightforward way to do this is to use the Gale-Shipley algorithm. Essentially, each man goes down his list of women in order of preference, starting with his most desired mate, and proposes to her. Each woman looks amongst her suitors, chooses the one that she prefers most, and rejects the rest, and then the rejected men propose to their next most desired mates on their lists. This process repeats until each man is paired with a woman (for a more thorough explanation, see the Wikipedia article). There are two interesting results: 1) this algorithm provides the most optimal solution to the proposers (i.e. each man ends up with the best possible mate that he could end up with in any stable matching) and 2) this algorithm provides the least optimal solution to the proposees (i.e. each woman ends up with the worst possible mate that she could end up with in any stable matching).

The reason why I love this problem is because it has a real life lesson embedded within: if you ask people out, you’re going to end up with a more optimal mate than if you wait to be asked out. Think about it: if you take the initiative, you can start by asking out your dream date. If he/she says no, who cares? Just move on to the next best person on your list. Eventually, you’ll end up with the best person you could have because you’ve already asked out (and been rejected by) anyone who could be better. By taking control, you give yourself the opportunity to maximize your mate preference.

On the other hand, if you never ask anyone out, you only get to select from the people who ask you out, which is a subset of all people you could date, so your choices are inherently more limited than they could be (or at least no better than they could be). Thus, your choices are non-optimal and you could likely do better.

Taken another way, let’s say that you’re in the market for a new blender. You have two strategies: go online and search for the best blender that you can find, or just buy a blender from the traveling salespeople who knock on your door. Do you think you’ll get a better blender if you take the initiative and search for it yourself, or do you think you’ll fare better if you wait for someone to try to sell you one?

Granted, there are complications to this theorem when trying to apply it to real life. We can’t rank people strictly, we don’t always know our preferences until after we actually start dating people, marriages aren’t just one-sided affairs where only the happiness of one person matters, not everyone gets married at the same time, there are societal norms that say that women shouldn’t ask men out, etc. But I think the message remains the same: take the initiative.

I know, it’s harder than I’m making it out to be, particularly for women, but a common theme in being efficient is taking initiative and being okay with rejection. I’ll write more regarding these themes later. Until then, I’d love to hear: how has taking the initiative and asking people out worked for you?