Cognitive perspectives on opinion dynamics: the role of knowledge in consensus formation, opinion divergence, and group polarization

Abstract

Two phenomena that are central to simulation research on opinion dynamics are opinion divergence—the result that individuals interacting in a group do not always collapse to a single viewpoint, and group polarization—the result that average group opinions can become more extreme after discussions than they were to begin with. Standard approaches to modeling these dynamics have typically assumed that agents have an influence bound, such that individuals ignore opinions that differ from theirs by more than some threshold, and thus converge to distinct groups that remain uninfluenced by other distinct beliefs. Additionally, models have attempted to account for group polarization either by assuming the existence of recalcitrant extremists, who draw others to their view without being influenced by them, or negative reaction—movement in opinion space away from those they disagree with. Yet these assumptions are not well supported by existing social/cognitive theory and data, and insofar as there are data, it is often mixed. Moreover, an alternative cognitive assumption is able to produce both of these phenomena: the need for consistency within a set of related beliefs. Via simulation, we show that assumptions about knowledge or belief spaces and conceptual coherence naturally produce both convergence to distinct groups and group polarization, providing an alternative cognitively grounded mechanism for these phenomena.

Appendix: example interaction of model

To clarify the workings of this model, let us suppose that a domain contained five binary features. This could support $2^5=32$ distinct knowledge states, but because of logic or tradition, we might suppose that just five exist in the knowledge space lattice: 00000, 10000, 01000, 11110, and 11111. In the simulation, two agents might begin in any of these five states, and any change in belief must occur between one of these five states. The different simulations in this paper described different ways in which this initial distribution can be chosen. The critical assumption is that not all states are coherent—some features may be, by tradition or logic, inconsistent with others, meaning that to transition between states, multiple beliefs must be changed.

In the simulation, each interaction progresses by selecting two agents at random. Thus, interaction is not constrained by homophily, geography, or group status. Although each of these is likely to constrain interactions in real-world situations, we elected to not incorporate them to determine whether knowledge structure alone could produce the results we observed. For each member of the pair, a candidate belief was generated by changing each feature to the other member’s value with probability $\mu$ (which was typically set to 0.3 for these simulations). If the two agents agreed on a feature, no change in belief was possible. The changes happened in parallel, so it would be possible in some circumstances for two agents to completely exchange belief states. For example, suppose an agent at state 10000 met an agent at state 01000. In this case, for each agent, the only possible outcome states would be 10000, 01000, 11000, and 00000. However, in the belief space we are considering, 11000 is not a coherent belief. This is simply an exclusive OR; someone may support one approach or another approach to solving a problem; but not both. This could be something like economic policy, in which one group believes raising taxes will increase tax revenue and reduce debt, whereas another group believes lowering taxes will grow the economy and reduce debt. The comparison is done on the agents original states; transitions to new candidate states happens only after interaction. Once the new candidate state is identified for each agent, the agent will only transition to that new state if it is coherent and thus exists in the belief space lattice. If it does not exist, the agent will remain at its original belief state.

The basic exchange routine is as follows:

As another example, suppose again that Agent 1 is in belief state 10000, and Agent 2 is in state 01000. They disagree on two issues, but each might be convinced to move to the nearby state 00000, which is more extreme than either of them began. This would produce a polarization effect. Although the same interaction could lead either of them to consider moving to 11000, in this belief space that belief state does not exist and so neither could move there. Again, an example of this might be a simple XOR belief; someone may support higher property taxes if it is used for education (10000), or if it is used for library funding (01000), and would be willing to accept taxes at the current rate (00000), but would not support both tax hikes (11000).

Finally, as a third example, again suppose that Agent 1 is in state 10000, but Agent 2 is in state 11111. As a result of this communication, Agent 1 could not move to 01000, but could move to 11110 or 11111. However, the chance of these moves is $\mu ^{j}(1-\mu )^{k}$, where j is the number of features that must change and and k is the number of differences that must not change. For $mu=.3$, the chance of Agent 1 moving to state 11110 on the basis of this interaction is .0189.