Stable Marriage
Abstract models of human relationships are inherently simplistic and a little bit silly, but thinking about them can give some insights into why people deal with interactions the way they do and how they can be guided.
In the stable marriage problem, there are an equal number of straight men and women and each one of them is going to get married to one of the others, The goal is match them so that there are no two people who would rather be with each other than with the person they’re paired with.
The most intuitive algorithm for finding a solution is as follows: Each of the women proposes to the man she’s most interested in. All the men who have multiple proposals then pick out the woman they most prefer of the ones who have proposed to them and reject all the others. All the women who have been rejected then propose to the man they most prefer of the ones who haven’t rejected them. The men with multiple proposals then reject all but one of them, etc. This continues until all men have exactly one proposal, and then they all settle for whatever proposal they have.
People in dating do behave somewhat like this, trying to keep one or a few people in reserve and rejecting the others. But in the real world the person who has shown the most interest in you might also have expressed interest in others, or someone new they like better might come along later, so having a strict rule of permanently rejecting everyone other than the current top pick is a bad idea. When it comes to designing a dating app you want to make people be more honest in their interests and rejection. For example it would make sense to put a strict limit on the number of new matches people can get per day, so popular people don’t hog all the attention. Likewise it would be good to have a ‘favorite matches’ label with a strict limit on the number and let matches know if they get added or bumped, like a low grade version of Facebook relationship status.
You might wonder if there’s any difference if the men do the proposing. The answer is yes, but very little. For example when you have a cycle of Alice prefers Bob but Bob prefers Claire and Claire prefers Dave and Dave prefers Alice, then you can have either women’s choice of Alice marries Bob and Claire marries Dave, or men’s choice of Bob marries Claire and Dave marries Alice. Stable marriage is actually used to determine what medical schools students get accepted to, and when the system was originally set up it was designed as school’s choice instead of student’s choice, because they designed the system so they got to decide. This caused a lot of controversy for years, until they crunched the numbers and found out that switching to student’s choice would make a difference for an average of less than one student per year, so the schools switched to student’s choice and the issue disappeared. Moral: Always do your research. Other moral: Don’t worry about whether one side or the other being proactive will change what matches happen, it doesn’t matter.