xkcd.WTF!?

Explanation ➲

A young couple (Cueball and Megan) are in love. In the first panel, Cueball says he's lucky to have Megan, a perfectly fine thing to say to someone when you're in love.^{[citation needed]} In the second panel, Cueball tells Megan he loves her most out of all the girls in the world, which is again a perfectly fine thing to say when you're in love. Trouble sets in, however, in the third panel, where Cueball offers his qualifying statement, that he loves Megan the most of the subset of girls who also love Cueball back.

In the title text, written in Cueball's voice, we have another compliment/qualifier pair. Cueball assures Megan that he'll never leave her—so long as some other girl is with someone. Cueball clearly has an unrequited love for another, and so really is being as unreliable and selfish as he initially appeared.

This comic is related with stable marriage problem, which is usually stated as: Given n men and n women, can they all be married off in such a way that there is no possible "adulterous" pairing that both the man and woman would prefer over their current partner? It turns out the answer is yes, and there are even algorithms that can be used to find such a set of marriages. However, such algorithms don't usually give people their first choice, just their first choice among potential partners who prefer them to all the alternatives. The algorithms also favor either the men or the women, so one side will typically get closer to their ideal preferences than the other. Such algorithms do get used in situations like assigning medical students to residencies (technically it's a polygamous generalization, but it's basically the same idea), in which case it's biased in favor of the medical students.

In the comic Cueball and Megan could be a couple arranged through a stable marriage algorithm. In most cases that would mean that they both have potential partners that they would prefer over the one they're with, and the only reason that they aren't with that person is that their love was unrequited. That leaves both of them with a certain amount of emotional baggage that most people would consider detrimental to stable marriage. In short, while a stable marriage algorithm may provide good solutions to certain matching problems, it may not be the best way to produce actual stable marriages.