Weighted Distances Between Preferences

Individual disagreements are assumed to be reflected in the preferences. Distance functions, e.g., the well-known Kemeny (1959) distance, are used to measure these disagreements. However, a disagreement on how to rank the top two alternatives may be perceived more (or less) than a disagreement on how to rank the bottom two alternatives. We propose two conditions on distance functions which characterize a class of weighted distance functions. This class allows to quantify disagreements according to where they occur in preferences. We provide some examples within this class and show one of them to be the generalization of the Kemeny distance on strict preferences.