Tricks with the BoD model and an application to the e-Government Development Index

Abstract

In this paper we examine the implications of the ideal and the anti-ideal decision-making units on the Benefit-of-the-Doubt (BoD) model. In particular, we verify that, in the presence of an ideal (anti-ideal) decision-making unit, the efficiency scores of the BoD (inverted BoD) model can be obtained without solving the relevant linear programming problems. In this case, it suffices to choose the largest (smallest) of the element-wise divided component indicators of the evaluated decision-making unit by those of the ideal (anti-ideal) decision-making unit. We then illustrate one practical use of this simple enumeration algorithm by providing empirical results for a BoD-based e-Government Development Index within a traffic-light reporting system.