Distance rationalizability of scoring rules

Collective decision making problems can be seen as finding an outcome that is "closest" to a concept of "consensus". Nitzan (1981) introduced "Closeness to Unanimity Procedure" as a first example to this approach and showed that the Borda rule is the closest to unanimity under the Kemeny (1959) distance. Elkind et al. (2009) generalized this concept as distance-rationalizability, and showed that all scoring rules can be distance rationalized via a class of distance functions, which we call scoring distances. In this paper, we propose another class of distances, i.e., weighted distances, introduced in Can (2014). This class is a generalization of the Kemeny distance that rationalizes the generalization of the Borda rule, i.e., scoring rules. Hence the results here extend those in Nitzan (1981) and reveal the broader connection between Kemeny-like distances and Borda-like voting rules.