Trusting Swarms

Idea

I got this idea thinking from Iain Couzin's lecture on collective behavior in the animal world. I believe that certain social situations can be modelled using a similar approach. More specifically, I want to examine what happens when there is a chance that every innocently-looking fellow actor is actuall a predator.

To use an animal metaphor, what happens if we have not only sheep, but also "wolves in sheep's clothing?" What if the sheep are intelligent enough to think about this likelihood and adjust their behavior accordingly? Naturally, the metaphor stops here. I am really talking about people, for whom this kind of calculation is part of every-day life.

Mechanism

• We have a community where everyone knows everyone.
  • this can be relaxed later, but thinking of any different case adds too much complexity for now;

• All actors are essentially the same, but each actor sees the world as separated in two kinds of individuals:
  • "undesirables;"
  • "upstanding citizens;"

• For each actor:
  • individuals perceived as undesirables are to be avoided at all costs;
  • individualss perceived as upstanding are desirable as friends.

• For ease of visualization, actors are displayed on a 2-dimensional plane;
  • the distance between actors represents the strength of their friendship.

• All actors (undesirable or upstanding) "look" the same, so:
  • Actor A has no direct signals on which to base a definitive judgment of whether Actor B is undesirable or upstanding;
  • Actor A looks to his/her friends (Actors C, D, E), and will use their behavior as a cue to how to evaluate Actor B; the cues coming from each other actor will be weighted by the strength of the friendship (i.e. the distance between the two actors);
  • Finally, Actor A makes a decision on their opinion of Actor B.
  • If the decision is that B is upstanding: advance one unit towards B;
  • If A decides that B is undesirable: advance one unit away from B;

• The decision that A makes is based on several elements:
  • A prior distribution, which indicates A's overall level of trustingness. Different skews of the distribution would indicate different likelihoods that A would decide that B is trustworthy, even when A has effectively no information about B.
  • A series of updates of A's prior, coming from successive inputs from A's friends, weighted by strength of friendship (i.e.,"distance");
  • Finally, a random number is drawn fro