Sunday, June 5, 2011

Aggregation dynamics of conditional psychological dispositions

We can use computational modeling techniques to aggregate individual behavior into collective patterns. A simple version of this is Thomas Schelling's segregation model (Micromotives and Macrobehavior).

Most commonly these tools have been used to model the results of rational choices by the actors involved, often using the tools of game theory. But the approach is more general; any common behavioral feature at the individual level can be aggregated through similar modeling techniques as well if we can specify our assumptions about conditionality plausibly.

Here is a hypothetical example illustrating the feasibility of modeling non-rational social dynamics. Suppose individuals have a social behavior disposition that is variable depending on the behaviors of other individuals in their acquaintance spaces. Examples might include: cooperative behavior, racist behavior and intolerance, abuse against women, or philanthropy. Assume individuals exist in an extended social graph of "acquaintance", so each has a specific list of immediate acquaintances (for example along the lines of the Framingham Heart Study graph below). And assume a contagion rate: the probability of switching when one acquaintance switches is p, the probability of switching when two acquaintances switch is p', and so forth.

Now we are in a position to do some interesting modeling based on recursive calculation of each individual's state based on the states of individuals within his/her acquaintance space. (This is analogous to Schelling's segregation model.) Calculate each individual's state based on the states of his/her acquaintances in the previous iteration. And run this recalculation through the whole population as many iterations as you like. The series of full iterations will represent moments in time as this dynamic system moves to a new equilibrium. Each represents a frame in an animation of the spread of intolerance through the population. (It should be possible to embody this simulation in a spreadsheet. Models like these are sometimes referred to as cellular automata.)

Now we can do a number of interesting things. We can observe the spread of racist attitudes and behavior. We can introduce disturbances in various parts of the graph and observe the transmission process. We may be able to document path dependency: perhaps it matters where the disturbance occurs.

After performing a large number of iterations, four large possibilities exist: everyone intolerant, everyone tolerant, stable neighborhoods within the graph of tolerance and intolerance, and no equilibrium at all.

(Actually, based on the assumptions outlined so far, it is inevitable that the graph will eventually go 100% "infected" with intolerance, since there is no recovery mechanism at the individual level. So we would probably want to incorporate some influence that turns individuals from intolerant to tolerant once in a while. We could also introduce more complexity into the model by postulating multiple states for the actor -- perhaps high, moderate, low intolerance. Individuals moving up or down the scale could infect their neighbors in the same direction. And we might attribute different infection rates to different individuals, to see how this affects the outcome.)

This example also creates the possibility of strategic intervention by outsiders: knowing how these dynamics work affords both the state and activist organizations to undertake actions designed to alter the outcome by strategically "seeding" the graph with intolerant individuals. Racist anti-immigrant organizations in western Europe appear to be doing exactly this at present.

If actors are wired this way (i.e. their social dispositions are a function of those of the individuals in their acquaintance space), then racism, philanthropy, and violence against women will behave like a communicable disease and the tools of social epidemiology will be applicable. And the consequences are great: some societies will have a stable anti-racist population and others the opposite, depending on contingent events, the nature of the network, and deliberate actions and policies.

This example is framed in terms of behavioral dispositions of social psychology. But it is equally pertinent to any individual characteristic that is variable in response to social contacts: slang, manners, social perception, ... Any psychological, cognitive, or emotional state with behavioral consequences that is responsive to context in this way is amenable to the same kind of modeling.

This is an example of social aggregation dynamics that is not grounded in strategic rationality but rather in features of conditionalized social psychology. The example is fully compatible with the requirement that macro-outcomes need to be explained on the basis of mechanisms with microfoundations. And it does not depend on the assumptions of rational actor theory or game theory.


Benjamin S Nelson said...

Interesting. Is there any (free) software available to do this sort of modelling?

Daniel Little said...


You might look at NetLogo; they provide a platform and a number of models. Here's one that is somewhat relevant:

Cosma Shalizi said...

So, about that Framingham study... This doesn't change the conceptual point, of course (see especially section 3 of our paper), but connecting models like this to data raises surprisingly deep methodological issues.

Anonymous said...

It may not depend on on game theory, but just this sort of diffusion process is frequently modeled using the tools of game theory.