202005131422

New Balance Theory

tags: [ networks ]

Balance Theory as it stands is a fairly straightforward and well-established idea from sociology about how signed graphs should form. Most people assume that it is basically an asymptotic realization (with enough time, all graphs will end up being exactly balanced). But actually wouldn’t it be great if we could show that the negative ties actually have some value.

Let’s start with what we know about balance. A graph is weakly balanced if and only if it can be decomposed into disjoint communities. Another way to characterize this is that it becomes perfectly polarized. So one way to think about moving away from balance is actually protecting our society from extreme polarization.

It’s sort of similar to the notion of weak links being these important connections that facilitate communication between disparate groups. This basically takes the more extreme form, no longer just about communication and understanding between groups, but more importantly, controlling animosity.

So in some sense, animosity is always going to be inevitable. However, if you have animosity, and you have strong inclinations for balance, you’re going to end up in a polarized world. So what you want actually are the mediators that are able to prevent the network degenerating into factions.

Though, and I think this is something crucial about all these models that is underappreciated: we have various scales to consider (hierarchical modelling), as we as various dimensions through which we can differentiate ourselves. It seems that the multi-faceted nature of our lives should give rise to interesting complex phenomenon.

Concrete Plan

One idea is to see if we can model how things play out on social media like Twitter. Can we actually identify these mediators and show that given enough of them, and if they have enough clout, then they can stop the collapse of social networks?

Another idea takes a more generative model approach. Balance, for one thing, is a global property, so the question is what kinds of local behaviour can produce the kinds of structure that we see in the real world.