In this paper, we introduce a new ranking system where the data are preferences resulting from paired comparisons. When direct preferences are missing or unclear, then preferences are determined through indirect comparisons. Given that a ranking of n subjects implies paired preferences, the...

We provide two methods to compute the largest subset of a set of observations that is consistent with the Generalised Axiom of Revealed Preference. The algorithm provided by Houtman and Maks (1985) is not comput ationally feasible for larger data sets, while our methods are not limited in that...

This paper presents a method of calculating sharp bounds on the average treatment effect using linear programming under identifying assumptions commonly used in the literature. This new method provides a sensitivity analysis of the identifying assumptions and missing data in an application...