Analyzing Ordinal Data for Group Representation

With n individuals ranking m objects, the exhaustive comparison approach, proposed in this paper, produces a list of order vectors sorted by the relative number of concordant pairs. The exhaustive comparison approach compares all possible order vectors instead of "an" optimal order vector to help the data analyst to consider "practical" solutions rather than a "desired" solution. An overall concordant order ratio is proposed to measure "how well" each order vector may represent the ranking structure of an ordinal data set. And the marginal concordant ratio evaluating the goodness of fit of each object in each order vector is also proposed in this paper. Comparisons among some popular ranking methods are discussed in this article. An empirical survey data regarding how travelers considered various factors for choosing travelling locations are used to illustrate the proposed method and calculations.