A simple test of Richter-rationality.

We propose in this note a simple non-parametric test of Richter-rationality which is the basic definition of rationality used in choice functions theory. Loosely speaking, the data set is rationalizable in the Richter' sense if there exists a complete-acyclic binary relation that rationalizes the data set. Hence a data set is rationalizable in the Richter' sense if there exists a variable intervals function which rationalizes this data set. Since an acyclic binary relation is not necessarily transitive then the proposed Richter-rationality test is weaker than GARP. Finally the test is performed over Mattei's data sets.