Derivation of the Maximin Efficiency Ratio model from the maximum decisional efficiency principle

The Maximin Efficiency Ratio (MER) model was originally proposed as a common weights model for further prioritization of the DEA efficient subset of decision making units (DMUs). Theoretical support for it in that context was based on principles of group decision making proposed earlier by P.L. Yu. Subsequently, the model has been found useful for one-step ranking of the full set of DMUs, albeit without theoretical support in that context. This paper provides a derivation of the MER model in a way which is potentially suitable for either context by use of the Maximum Decisional Efficiency (MDE) principle for aggregating expert estimates. This approach provides theoretical support for the MER model by demonstrating that it is a Maximum Likelihood procedure under certain plausible assumptions. It is necessary to assume that all the DMUs desire to maximize their own efficiency ratio computed on a common weights basis. However, this context is not vacuous since top management will typically wish to evaluate all divisions, projects, individuals, etc., respectively, on a common standard. This paper seeks to extend the frontiers of DEA by supposing the existence of a common performance measure for the DMUs.