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Diana Richards, Principal Investigator

The Probability of Collective Choice with Shared Mental Models for Large Choice Sets

There are abundant theoretical results from the field of social choice showing that, for a large number of individuals with random preferences over a large set of alternatives, there will almost surely be no single stable collective outcome. These results have significant implications for a variety of complex systems that can be seen as engaged in collective decision making. One obvious application is in societal decision making, where an intriguing puzzle is how stable collective decisions are reached empirically when a group of individuals must aggregate their diverse preferences. Another application is in understanding the human brain, which can be viewed as consisting of a large number of semi-autonomous neural modules acting as "agents." However, theoretical results suggest that such aggregation processes will be generically subject to instability. Yet, this is not what is observed. Thus, a fundamental puzzle in both social science and cognitive science is how and when the information and beliefs of a collection of semi-autonomous agents is aggregated to reach stable, non-cyclic collective outcomes.

Re-examining Arrow's General Possibility Theorem, that no democratic aggregation procedure can guarantee a stable collective ranking, these researchers focus on the assumption that agents may rank order choices in any way. More specifically, it is assumed that the information held by the agents is not arbitrary, but is constrained by an agent's mental model, or knowledge structure, of the world. Shared mental models are focused on, and a knowledge structure as the representation of a mental model is produced. When agents have similar mental models of a domain, the choices and the relationships between choices have a common underlying structure. A knowledge-structure constraint on collective choice has been shown to overcome the aggregation paradox for small choice sets. However, it was also shown that as the choice set becomes very large, a shared knowledge constraint does not prohibit cyclic behavior in collective decision making. This negative result was based on the tough criterion that, for any given shared knowledge structure, if there was any single distribution of agent information that failed to produce a stable collective outcome, then the aggregation was classified as "potentially unstable." Here, this criterion is relaxed, and the probability of collective instability is examined given any shared knowledge structure. Now, the results are much more positive. Early results suggest that collections of diverse preference orders constrained by a shared mental model nearly always result in stable collective aggregation.

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