Relationships Between l¹ Metrics on Linear Ranking Spaces

In this paper we examine various l¹ distance measures on linear ranking spaces. Beginning with the absolute position measure of Blin, we construct two offspring measures—one based on relative rank positioning, the other on relative object positioning. The first is shown to be equivalent to the permutation vector method of Cook and Seiford. The other is equivalent to the preference matrix method of Kemeny and Snell. We also prove that the Kemeny and Snell method can be formulated as a quadratic assignment problem.