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This paper generalizes the Kemeny-Snell distance function for distances between weak orderings to a distance function for the collection of all partial orderings of a set. This generalization explains some of the seemingly strange properties of the Kemeny-Snell distance, and extends it to such important classes of orderings as semiorders and interval orders. In section four I consider possible applications of the distance function and describe a number of problems that arise in attempts to apply the distance function. In section 3 I discuss the concept of a distance function in more general terms and introduce a new distance function defined by a set of axioms different from those given in Section 2. [ABSTRACT FROM AUTHOR]