2 min read

The intersection problem

Suppose you're coordinating a group movie night with a few friends. There is no ongoing theme, so you try to pick movies everyone will like. Alice likes horror movies and comedies, Bob likes action and comedy, and Carol will watch anything. You end up watching a lot of comedies.

After a while, this gets boring. Even the staunchest fan doesn't want to watch comedies all the time. People need a little variety. But as long as we're aiming to watch movies that everyone will like, that's what we're stuck with.

I think of this as the intersection problem. We can model every group member as having a set of movies they'd like to watch. Then the set of good group movie options is the intersection of all these sets.

Taking the intersection eliminates a lot of options. For a movie to get crossed off the list of good options, it only takes one person who doesn't want to watch it. That means that unless group members are pre-selected to have similar tastes, a lot of things are going to get crossed off and we should expect to end up with a pretty narrow selection.

Even pre-selection isn't a guarantee, because people don't have stable preferences. Our preferences drift. This is why always watching comedies gets boring. Even if Alice, Bob, and Carol were selected for agreement that horror movies are great, that is no guarantee that they will all still be on the same page after watching a hundred such movies. Maybe Bob becomes bored out of his mind with horror after watching Jason rise from the dead for the third time.

The more people you add, the more annoying this gets. With a big enough group it becomes impossible to find an option that meets everyone's preferences rather than merely annoying—or at least, impossible as long as we think of this as a preference set intersection problem.

The intersection problem suggests we should expect to see smaller, more stable groups and larger, less stable groups. The small stable groups are small enough to watch comedies one week and horror another week, because they are small enough to have largely compatible preferences over time. The large unstable groups have a lot of churn because people move in and out as they fall in and out of love with the group's theme. They work by accepting preference drift. These two options seem broadly consistent with the kinds of groups I know of or expect to exist.

But this feels incomplete. It treats the movies themselves as the only factor. That makes sense to a degree for large interest groups, but clearly doesn't for a small friend group. It's missing the social dynamic of this problem, which is a whole other thing. That dynamic seems worth exploring separately.