Aggregating disparate judgments using a coherence penalty

In this paper, practical algorithms for solving the probabilistic judgment aggregation problem are given. First, the scalable Coherent Approximation Principle (CAP) algorithm proposed by Predd, et al., and its computational savings gained through Successive Orthogonal Projection are explained. Implications of de Finetti's theorem in this situation are also discussed. Then a coherence penalty is defined and the Coherence Penalty Weighted Principle (CPWP) is proposed to take advantage of the data structure alongside the coherence approximation. Justification is given for the guideline that more coherent judges should be given larger weights. Simulation results with Brier Scores on both a collected database and simulated data are given for comparison. In addition to the CPWP, a recursive online variant with weight updates is presented to accommodate real-time aggregation problems.