Sanakreon

If a girl wants to initiate relationship, should she approach the guy herself, or should she follow the common tradition and wait for the guy to approach her?

Apparently most girls follow the second way.

As for guys, the culture dictates that they follow the first way.

And this gives us advantage.

But lets formalize this.

Say we have ten guys, and ten girls. Each guy ranks all the girls from 1 to 10, rank 1 being the most desirable to him. Each girl does the same.

Now lets leave them on an isolated island, and wait till they all choose a partner for themselves, where each girl is dating one guy and vice versa.

Now, if we wait some more, after some switches of partners they will actually turn out to be in stable relationships. And by stable relationships I mean the following:

No girl or guy can find anyone they would rather be with, who would rather be with them.

So basically in stable relationships, nobody can switch partners, because their current partner is the best they can get given the preferences of all the other people.

In fact this situation has been mathematically analyzed, it is called “Stable Marriage Problem”.

It has been proven, that for any given set of pairs of guys and girls, and their preferences, there always exists at least one way in which everybody can be in stable relationship. But usually there is more than one, and this is where the guys’ advantage kicks in.

The following are the consequences of Gale-Shapley algorithm, which provides some solutions to this problem.

If only guys propose, and girls only choose between the guys who proposed to them, this situation will eventually lead into a stable relationship. But this stable relationship will favor the guys to the maximum. That is, if an average guy will date a girl which is Xth in his ranking, then average girl will date a guy which is worse than Xth in her ranking, in fact as worse as possible for any stable relationship.

So, if only guys propose, the girls will end up in the worst possible for them stable relationships.

But if only the girls propose, then they will end up in the best possible for them stable relationships, because it is a mirror situation.

So basically those who propose end up in the best situation possible after all the partner switching is done and everyone has settled down. Since guys are generally the ones who propose, we have been enjoying this advantage for many centuries.

Now you know the secret )