Ranking university libraries with a posteriori weights

In aggregating the wide range of resources and services provided by the university libraries to produce a single composite index for comparison, two types of weights representing the relative importance of the criteria have been discussed in the literature. One is a priori weights assigned by the experts in a subjective manner before the scores for the criteria are measured. The other is a posteriori weights determined objectively from the scores measured for the criteria. Taking into account the opinion of experts, this paper proposes an a posteriori approach based on the concept of least squares to compare university libraries. Since the characteristics of the libraries as revealed by their performance scores on each criterion have been considered in calculating the composite indices for comparison, the results are more representative and are thus more acceptable to the libraries being compared. To illustrate this approach, university libraries in Taiwan are ranked using the proposed approach. The composite indices calculated from this approach are greater and more concentrated than those calculated from the a priori approach. Psychologically, this is very attractive to the libraries being ranked, although most libraries have similar ranks determined from these two approaches.