Characterizing the Set of Coherent Lower Previsions with a Finite Number of Constraints or Vertices
This work addresses a theoretical bottleneck in imprecise probability for researchers, providing a computational method for finite cases, but it is incremental as it builds on existing coherence criteria.
The paper tackles the problem of characterizing coherent lower previsions with an infinite number of constraints by reformulating the criterion to use only a finite number of constraints, enabling computation of extreme coherent lower previsions as vertices of a convex polytope, and demonstrates the procedure with illustrations.
The standard coherence criterion for lower previsions is expressed using an infinite number of linear constraints. For lower previsions that are essentially defined on some finite set of gambles on a finite possibility space, we present a reformulation of this criterion that only uses a finite number of constraints. Any such lower prevision is coherent if it lies within the convex polytope defined by these constraints. The vertices of this polytope are the extreme coherent lower previsions for the given set of gambles. Our reformulation makes it possible to compute them. We show how this is done and illustrate the procedure and its results.