“Suppose you have two friends who detest each other. The resulting awkwardness often resolves itself in one of two ways: either you drop one of your friends, or they find a way to reconcile,” say Steve Strogatz and buddies from Cornell University. They go on to add that the overall social stress in these situations corresponds to a kind of energy that relaxes over time as relationships switch from hostility to friendship (or vice versa).

That suggests an interesting way of modeling relationships as a network in which the connections between nodes (people) can take either a positive or a negative value, depending on whether they like or hate each other.

The question then is, if left to its own devices, how does this landscape settle?

Past analyses of this idea, which dates back to the 1950s, suggest that the landscape settles into a global minimum-energy state. Now Strogatz and pals say that the picture is significantly more complicated.

Rather than settling into a state of minimum energy, these “social balance networks” can become jammed in conformations that have numerous local minima. And those that become jammed in higher-energy states are significantly more complicated than those in lower-energy states.

A closer study of these jammed states reveals “cliques”: groups that are internally friendly but have antagonistic edges. Obviously, a network with a single clique is a trivial low-energy solution in which all people are friends.

Strogatz and co say that balanced states consisting of two warring factions correspond to two mutually antagonistic cliques that often represent socially undesirable outcomes such as intractable conflict.

They then go on to suggest that more complex states of many antagonistic cliques may be more desirable because “they show less large-scale antagonism.” Because of that, these states of many cliques may represent situations in which reconciliation can occur more easily. The researchers even suggest that the work could be the start of a new theoretical approach to conflict resolution.

That’s an interesting approach, but one in which the analogy with real-world relationships has clearly been taken too far. The idea that complex disputes involving many warring factions are easier to reconcile than those in which there are only two parties is novel, to say the least. In fact, this conclusion looks more like a reductio ad absurdum that makes the idea of a theory of conflict resolution seem somewhat premature.

Ref: arxiv.org/abs/0906.2893: The Energy Landscape of Social Balance