To model the assumptions of cultural cognition, we have employ a series of agent-based simulations similar to those used by others modeling norm transmission.  See, e.g.,  Randal C. Picker, Simple Games in a Complex World: A Generative Approach to the Adoption of Norms, 64 U. Chi. L. Rev. 1225 (1997)).

Factual Enlightenment

The first model we develop simulates typical assumptions about rational belief transmission in the absence of cultural cognition. The Factual Enlightenment Model of belief formation and transmission, as we will call it, can be seen to rest on two assumptions, one cognitive, the other social. The cognitive assumption is that individuals have the capacity to recognize truth and a disposition to assent to it. The social assumption is that normal human interactions transmit the truth and make it available for adoption.

For the simulation, we use a 100x100 grid to represent a society, whose members are represented by cells in the grid. At any period of time, each member of society or agent holds one of two beliefs — which we’ll designate as “true” and “false” — about the consequences of gun control. The particular belief that is held evolves dynamically consistent with this “learning rule”: if an agent held the “true” belief in the previous period, then she continues to hold the “true” belief in the next period; if an agent held the “false” belief in the previous period, then the probability that she’ll adopt the “true” belief in the next period equals the number of agents who held the true belief in the previous period divided by the total number of agents in the society.

To see the output of a typical run of the simulation, click on the graphic to the right. Agents who hold “true” belief are colored gray, those who hold “false” belief white. In the first period, only one agent is assigned the true belief, yet by the end, everyone in the society believes the truth.

Cultural Polarization

Dramatic and, unfortunately, unrealistic. Unrealistic because it fails to account for the cognitive and social mechanisms that constrain the transmission and acceptance of information. (We describe these in detail in the paper. To read it, click here.)

The processes by which factual beliefs are formed and transmitted are likewise amenable to a simple computer simulation that we call the “Cultural Polarization Model.” Again, we use an 100x100 grid to represent a society of that many agents. The grid, however, is now subdivided into four equal parts, each of which represents a distinct cultural orientation. Agents again hold one of two beliefs about the consequences of gun control, either “true” or “false.”

Once more, agents’ beliefs evolve. But the learning rule in this simulation is different from the one used in the Factual Enlightenment Model. If in the previous period, an agent held the view that was numerically predominant within her cultural-orientation quadrant, then she continues to hold that belief in the next period. If, however, she held the belief contrary to the numerically predominant one in her quadrant, then the probability that she’ll switch her belief in the next period is equal to the total number of agents who hold the predominant belief in her cultural-orientation quadrant divided by the total number of agents in that quadrant.

To see the output of a typical run of the simulation, click on the graphic to the right. In the first period, beliefs (again color-coded gray for “true” and white for “false”) are randomly assigned, with probability .5 for each belief, across all members of the entire society. Thus, at the outset, beliefs are almost (but not exactly) evenly divided in each quadrant. But eventually each quadrant is either solidly gray or solidly white. Because the initial distribution of views was not precisely evenly divided, the dominant view in each feeds on itself over successive periods, generating the pattern of homogeneity within and heterogeneity across orientations associated with group polarization. So here we see (not surprisingly) a striking confirmation of the claim that culture determines factual belief.

Truth Versus Culture

But what if, as is often the case, people both prefer the truth and are constrained by cultural cognition? We simulate this in what we call the “Truth versus Culture Model.”

To accommodate the interaction of cultural influences and empirical evidence of the truth in determining belief, the simulation uses an iterated coordination game. In the game, each agent interacts with the culturally like-minded “neighbors” who occupy the cells that immediately surround hers on the grid (Picker, 1997). In any period, each agent’s payoff is a function of two variables. The first is with how many of her neighbors she matches or coordinates beliefs. The second is on which belief they coordinate: payoffs for matching true beliefs are twice as large as payoffs for matching false ones. Beliefs evolve in this simulation, too: the belief that a player holds in any period is the one held by the culturally like-minded neighbor (from among the cells adjoining hers) who earned the highest payoff in the previous period.

Because it rewards agents for coordinating with others who share their orientations, yet rewards them more for coordinating on true rather than false beliefs, the payoff function used in the simulation treats agents as if they value both agreeing with their cultural peers and knowing the truth. This is exactly the picture of individual attitude-formation that our empiricist critics emphasize when they say attack us for insisting on the priority of reforming the expressive idiom of gun politics.

In the first period, beliefs (“true” gray, “false” white) are homogeneous within and heterogeneous across cultures. This is the pattern that one should expect to see as a result of group polarization in a world in which the empirical truth about guns has not yet been discovered. By the second period, however, truth has emerged, and 25 agents who hold the true belief — a vanguard of “strong and eager minds” who’ve “embrace[d] [an] original opinion[]”— are injected into each of the benighted cultural-orientation quadrants. But even though individuals who hold false beliefs do indeed have a “preference for good argument over bad” — they get twice as large a payoff in this simulation when they coordinate on true than they do when they coordinate on false belief — the truth doesn’t make enough converts quickly enough to overcome the countervailing disposition of individuals to conform to the belief that’s dominant among those who share their orientation.

Breakthrough Politics

The Truth vs. Culture Model showed empirical evidence and social meaning at war. We now describe a state of affairs in which the two might peacefully coexist. We’ll call it the Breakthrough Politics Model.

Like the one used to illustrate Truth vs. Culture, this simulation reflects a coordination game, with asymmetric coordination payoffs for true and false belief, played by agents (in an 100x100 society, divided into four cultural-orientation quadrants) with their culturally like-minded neighbors. But the learning rule — the algorithm used to generate evolution in beliefs — is different. In the simulation used for Truth vs. Culture, agents adjusted their beliefs by considering only the payoffs earned by culturally like-minded neighbors in previous periods. In this simulation, however, individuals adopt the belief that generated the highest payoff in any neighboring cell in the previous period, even if that neighboring cell is inhabited by an agent of a differing cultural orientation (Picker, 1997).

This simulation accurately reflects how the three-steps associated with Breakthrough Politics, described in the paper, affect the various mechanisms of individual belief formation. What happens? Again assume that beliefs (“true” gray, “false” white) in the first period are distributed consistent with the signature patter of group polarization — homogenous within and heterogeneous across cultural orientations. Again assume that the payoff for coordinating on true belief is 2X the payoff for coordinating on false belief. The output of the model is a happy one.

Related Papers

Modeling Facts, Culture and Cognition