I’m pressed for time at the moment so I’m going to cheat and present some notes on interesting papers that I’m working into my thesis. The first two identify sources of failure in social cognition, with the first demonstrating the effect a committed group can have on the population’s views and the second showing the population-level cognitive failures that can result from seeing others’ actions but not their rationale for those actions. The latter has particular relevance for a later post I plan on the mistaken assumption that market prices (which are really just the residue of a series of actions) by definition contain valuable signals and information. The third paper is related in that it demonstrates the danger that can result from a population whose preferences are too homogeneous.
These notes are rough and not meant for publication, so YMMV in interpreting the papers.
Xie, J., Sreenivasan, S., Korniss, G., Zhang, W., Lim, C., Szymanski, B.K. (2011). Social consensus through the influence of committed minorities. Physical Review E 84, 011130
Summary: Committed minorities who can not be swayed can create consensus around their issue once their number reaches 10% of the population.
The authors use what they call a “binary agreement model,” which they contrast with sociological models of innovation diffusion by allowing individuals to change their mind at little cost (as opposed to adoption being a final state). They structure their simulation such that the system randomly chooses first a speaker and then a listener. If the speaker transmits an opinion that appears in the range of possible values of the listener, then both retain only that “opinion.” The catch is that most individuals start with two opinions, but there is a small subset that has only one opinion, and that will never change that opinion even if they hear the opposite. They do this by setting the condition at the outset of the game that all agents have opinion B save a small group that has opinion A, with the smaller set being uniquely unwilling to consider B.
The authors run simulations using large/infinite networks, finite networks and sparse networks, and in all cases they find a “phase transition” when the committed minority reaches 10% of the population, at which point the system converges on consensus around their viewpoint. The key appears to be their unwillingness to cooperate, coupled with the open-mindedness/lack of commitment of the rest of the population.
Lorenz, J., Rauhut, H., Schweitzer, F., Helbing, D. (2011). How social influence can undermine the wisdom of crowd effect. Proceedings of the National Academy of Sciences of the USA, 108(22): 9020–9025
Summary: Social influences destroy the accuracy of prediction and assessment through three primary mechanisms defined in the study, two statistical and one psychological.
The authors (one systems theorist, one quant sociologist and one undetermined) conduct an experiment (N=144) to test the relative accuracy of individuals’ assessments of factual information in the presence/absence of information about others’ assessments. They find that the social impact significantly reduces the accuracy via herding, which they categorize as operating through three mechanisms:
1.) Social influence effect: Social cues (in the form of knowing others’ choices) reduces the range of estimates without any increase in accuracy
2.) Range reduction effect: As the estimates become concentrated, the impact of errors will be larger (the authors give the example of mistaken military intelligence that consolidates around the wrong information due to pressure to conform)
3.) Overconfidence: As individuals perceive their choices to be in the socially established range, or move their choices to be consistent with the crowd, they become more confident in their ability to predict, regardless of the accuracy of their predictions.
The authors note that these effects are all statistically significant, even in the case where the subjects were given minimal information (only what others chose, not whether it was accurate).
Levy, M. (2005). Social phase transitions. Journal of Economic Behavior & Organization, 57(2005), 71-87.
Summary: In modeling complex social systems, Levy finds that vulnerability to discontinuous jumps is a function of homo/heterogeneity.
Levy works from the assertion that change in social systems of all kinds is typically continuous, but that “dramatic, discontinuous transitions due to a small or even unnoticeable change…are observed in a wide variety of social systems ranging from stock markets to political systems, norms of drug abuse, and even traffic flow” (p. 72). He goes on to create a model based on statistical physics and economics that treats discontinuous jumps as akin to “phase transitions” in physical systems (e.g. water’s characteristics change continuously from 33 degrees up to 99 degrees C, but are discontinuous from 99.9 to 100 degrees).
In his model, an individual’s choice of whether or not to act is based on a range of parameters including the average behavior of the rest of the population. The overall system is in equilibrium when the marginal individual’s preference is equal to the average population preference. Under a variety of conditions, Levy models shifts in this equilibrium as discontinuous jumps that result from changes in individual and aggregate preferences. More generally, he finds that these jumps are far more likely to happen – and are more likely to be of greater magnitude – in populations where preferences are homogeneous. Conversely, he finds that social systems with greater heterogeneity are less likely to experience such jumps.
Although he does not develop the idea fully, Levy also points to the instability of equilibria after phase transitions, giving the resurgence of government power after Tian’anmen Square and the rapid reversals in the stock market after major crashes as examples.
Notably, the paper does not consider the local effects of influential people, or of neighborhood effects, though Levy points to this as a possible area of future research that goes beyond aggregates.