The Balanced Worth: A Procedure to Evaluate Performance in Terms of Ordered Attributes

Abstract

There are many problems in the social sciences that refer to the evaluation of the relative performance of some populations when their members’ achievements are described by a distribution of outcomes over a set of ordered categories. A new method for the evaluation of this type of problems is presented here. That method, called balanced worth, offers a cardinal, complete and transitive evaluation that is based on the likelihood of getting better results. The evaluation of each society is based on the probability of obtaining better results with respect to the others. The balanced worth is a refinement of “the worth” (Herrero and Villar in PLoS ONE 8(12):e84784, 2013. https://doi.org/10.1371/journal.pone.0084784) that overcomes its excessive sensitivity to the differences, due to the presence of ties. We also discuss how this method can be applied for the case of heterogeneous populations and show how it can be applied in different contexts. An empirical example, regarding life satisfaction in Spain is used to illustrate the working of this method.