Metric Methods for Analyzing Partially Ranked Data (1985)

A full ranking of n items is simply an ordering of all these items, of the form: first choice, second choice, -. ., n-th choice. If two judges each rank the same n items, statisticians have used various metrics to measure the closeness of the two rankings, including Ken- dall's tau, Spearman's rho, Spearman's footrule, Ulam's metric, Hal1l11ing distance, and Cayley distance. These metrics have been em- ployed in many contexts, in many applied statistical and scientific problems. Thi s monograph presents genera 1 methods for extendi ng these metri cs to partially ranked data. Here "partially ranked data" refers, for instance, to the situation in which there are n distinct items, but each judge specifies only his first through k-th choices, where k