The reconciliation of multiple conflicting estimates: Entropy-based and axiomatic approaches

Abstract

When working with economic accounts it may occur that multiple estimates of a single datum exist, with different degrees of uncertainty or data quality. This paper addresses the problem of defining a method that can reconcile conflicting estimates, given best guess and uncertainty values. We proceeded from first principles, using two different routes. First, under an entropy-based approach, the data reconciliation problem is addressed as a particular case of a wider data balancing problem, and an alternative setting is found in which the multiple estimates are replaced by a single one. Afterwards, under an axiomatic approach, a set of properties is defined, which characterizes the ideal data reconciliation method. Under both approaches, the conclusion is that the formula for the reconciliation of best guesses is a weighted arithmetic average, with the inverse of uncertainties as weights, and that the formula for the reconciliation of uncertainties is a harmonic average.