You are walking on a 100-metre long trail, and there is a pebble every metre. When you encounter a pebble, you can choose to pick it up or leave it. If you pick it up, the game is over, and you get to keep the pebble. If you leave it, you cannot go back to it later.

Your goal is to get the largest pebble. What’s your optimal strategy?

This is the famous secretary problem in decision theory.

Monogamy feels a lot like the secretary problem to me – you encounter a more or less fixed number of potential partners over your relationship forming year, and you have to pick one without being able to peek ahead, and you can’t go back to potential partners you have passed over.

Does that make much sense to you? It doesn’t really to me.

Does loving a person really turn off our capability to love another person? It doesn’t for me, and judging by the number of “monogamous” people who cheat, I don’t think it’s just me.

Love is just a more intense form of friendship. We can have multiple best friends and no one has trouble understanding that. Why do we have to be so selfish with love? Why can’t we just love everyone we want to love?

Why do romantic relationships have to be formed and broken with so much deliberate effort? Why can’t they evolve organically just like friendships?

Those are questions I’ve had for many many years (in fact, I believe I wrote a blog post about this back in 2010 or something). Questions that I never found satisfactory answers to, and as a result, I mostly just refrained from dating.

Until recently, that is. I came across the concept of polyamory a few months ago, and have been reading up on it since. Everything just makes sense!

If you are not familiar with polyamory – it’s a relationship model where each person can have multiple partners, but with the knowledge and blessing of all partners involved (this is a huge over-simplification – there at least as many different kinds of poly relationships as there are mono relationships).

Is it for me? I don’t know. It makes perfect sense on paper, but I don’t know how my brain will actually react.

There’s the practical aspect as well – my friend who did give it a try didn’t find it worthwhile, due to the effort required to maintain multiple relationships. As a famous poly saying goes: “Love is infinite, but time and energy aren’t.”

In any case, if I do actually go into poly, it will probably end up being a mono-poly sort of arrangement with me on the mono side… I barely have enough time for one person!

So, what’s the solution to the secretary problem?

As it turned out, there is an elegant mathematical solution – the optimal strategy is to skip over the first n/e pebbles, and then take the first one that is bigger than all you have seen.

n is the number of candidates, and e is the base of natural logarithm (e ~= 2.72).

For example, in the case of 100 pebbles, that means you should skip over the first 100/2.72 = 37 pebbles, and then take the first one that’s bigger than all of the first 37 pebbles.

See the Wikipedia page for proof.