Efficient L1-Based Probability Assessments Correction: Algorithms and Applications to Belief Merging and Revision

In this article we define a procedure which corrects an incoherent probability assessment on a finite domain by exploiting a geometric property of L1-distance (known also as Manhattan distance) and mixed integer programming. L1-distance minimization does not produce, in general, a unique solution but rather a corrected assessment that could result an imprecise probability model. We propose a correction method for the merging of two separate assessments whose direct juxtaposition could be incoherent, and for the revision of beliefs where the core of the assessment must remain unchanged. A prototypical example on antidoping analysis guides the reader through this article to explain the various procedures.