Characterizing coherence, correcting incoherence

• We present characterization procedures for the polyhedra of coherent lower previsions.
• These procedures are more efficient and straightforward than those previously known.
• We discuss a procedure for correcting incoherent lower previsions.
• Our characterization procedures can make such corrections computationally feasible.

Lower previsions defined on a finite set of gambles can be looked at as points in a finite-dimensional real vector space. Within that vector space, the sets of sure loss avoiding and coherent lower previsions form convex polyhedra. We present procedures for obtaining characterizations of these polyhedra in terms of a minimal, finite number of linear constraints. As compared to the previously known procedure, these procedures are more efficient and much more straightforward. Next, we take a look at a procedure for correcting incoherent lower previsions based on pointwise dominance. This procedure can be formulated as a multi-objective linear program, and the availability of the finite characterizations provide an avenue for making these programs computationally feasible.