Strategic Expert Aggregation: A Hierarchical Bayesian Framework for Robust Decisions in Final Offer Arbitration

In final offer arbitration, a single submission is final, irreversible, and binding: the arbitrator selects one party's number without compromise, and millions of dollars can hinge on whether that number was set well. The decision rests entirely on beliefs about a quantity the decision maker cannot observe, namely the arbitrator's preferred settlement, and those beliefs must be assembled from the conflicting judgments of multiple experts. How those judgments are aggregated is therefore not a methodological detail but a determinant of outcomes: a poorly aggregated prior, fed through the equilibrium mapping, can shift the optimal submission by amounts that change which side wins. We show that standard aggregation methods, namely linear pooling, logarithmic pooling, and the classical performance weighted method, were designed for inferential tasks and can produce decision failures when an elicitation panel includes a single anomalous expert: mean and worst case regret rise sharply, with no warning to the decision maker. We develop a hierarchical Bayesian framework that aggregates elicited quantiles while learning expert specific biases and precisions from disagreement alone, and we propagate the resulting posterior through the Nash equilibrium to obtain a full posterior over optimal offers. We establish analytically that posterior uncertainty in the scale parameter is amplified by a factor of $\pi /2$ when carried into the recommended action, a decision theoretic consequence invisible to inferential comparisons. A simulation study shows that the proposed approach reduces both mean and worst case regret by a factor of four to six in the contaminated regime where the comparison methods fail, while delivering calibrated credible intervals that flag when the elicited evidence is insufficient to commit. A stylized salary arbitration example illustrates how a decision maker reads and acts on the resulting posterior.