Additive Measures of Perceived Accessibility

A set of necessary and sufficient conditions for the existence of additive accessibility measures is presented, which essentially refines the conditions developed by Weibull (1980). In particular, the central axiom in his paper is shown to be equivalent to a pair of independent axioms, designated as the ‘cumulative dominance’ and ‘cumulative separation’ properties of perceived-accessibility behavior. In addition, it is shown that the degree of perceived substitutability among spatial alternatives plays an important role in distinguishing the behavior implicit in each of these properties. Finally, it is shown that this axiom system together with that in Weibull's paper offers certain analytical advantages over more classical characterizations of additive accessibility measures.