Enabling rational democratic decision-making with collective belief models and game theoretic analysis

We introduce a new approach to aggregating the beliefs and preferences of many individuals to form models for democratic decision-making. Traditional social choice functions used to aggregate beliefs and preferences attempt to find a single consensus model, but produce inconsistent results when a stalemate between opposing opinions occurs. Our approach combines the probabilistic beliefs of many individuals using Bayesian decision networks to form collectives such that the aggregate of each collective, or collective belief has rational behavior. We first extract the symbolic preference order used in social choice theory from each individual’s quantitative Bayesian beliefs. We then show that if a group of individuals share a preference order, their aggregate will uphold principles of rationality defined by social choice theorists. These groups will form the collectives, from which we can extract the Pareto optimal solutions. By representing the situation competitively as opposed to forcing cooperation, our approach identifies the situations for which no single consensus model exists, and returns a rational set of models and their corresponding solutions. Using an election simulation, we demonstrate that our approach more accurately predicts of the behavior of a large group of decision-makers than a single consensus approach that exhibits unstable behavior.