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 everyone believes in thechance that every innocently-looking fellow actor is actually 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;
  • individuals 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.
  • Actors start out on a grid, equidistant from one another.

• 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. 1/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;
  • Also, a minimal distance (similar to the zone of avoidance) has to be maintained between two actors: the strength of a friendship cannot become infinite.

• The decision that A makes is based on several elements:
  • An uninformative prior distribution, signifying 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, we have a random number draw, according to the posterior distribution we have just calculated for A.
  • If the number is greater than a threshold (tau), then A decides that B is trustworthy; else, A decides B is untrustworthy.
  • Tau indicates A's overall level of trustingness. High taus mean A is very "suspicious," low taus mean a very "naive" A.

Research Question and Hypotheses

• This is not really a story of "predator" and "prey," but one of conflict.
  • Everyone thinks that there are some sort of "predators" in the community, which should be avoided at all costs;
  • The question is, how do different levels of overall trustingness influence behavior?
    • I would expect that if taus are low, and everyone is trusting, ultimately communal influence would win out, and most (or all) actors would cluster together in a big clump of friendship;
    • If we increase the taus for everyone (make them less trusting), I would expect to see smaller groups ("clans") form, the members of which consider the members of other groups to be untrustworthy and undesirable;
    • Ultimately, with very high taus no one interacts with anyone whatsoever, and the first state of the system (where all actors are equidistant) is stable. This state would be much like the "natural state" so dear to Contractarian political philosophers.
• While these conclusions might be easy enough to draw without an agent-based model, I want to investigate what happens when the taus differ between actors in the model. What if the taus are normally distributed? What if we introduce some completely naive actors? Many more variations could work.

Potential Applications and Extensions

• This model by itself can provide some insight into the dynamics of large groups of people. More concretely, I want to investigate under what condition clans appear. This can be useful for understanding lower- and higher-trust social systems, and for providing a clear theoretical model of how low or high levels of trustingness create very different patterns in society (i.e. differential development between low-trust Southern Italy and high-trust Northern Italy).
• This is a general model of social cohesion, so there are many extensions possible:
  • conflict: what if actors actually try to kill the undesirables? What distribution of trust does it take to have genocide?
  • resources and exchange: what if actors can also exchange resources, but they will only exchange with those they trust? what if exchange strengthens friendships?
  • mobilization: what if there are certain goals for actors to follow (like getting to a different part of the board), but there is a minimum number of actors necessary to make the move?
  • what if there are actual predators, who either kill other actors or steal their resources?

Suggested References

Jon M. Kleinberg, Katrina Ligett: Information-Sharing and Privacy in Social Networks CoRR abs/1003.0469: (2010)

Kleinberg - Networks, Crowds and Markets - Chapter 5

Granovetter - Threshold Models of Collective Behavior;