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.

Additional Metadata
Keywords Coherence, Avoiding sure loss, Polytope theory, Multi-objective linear programming, Incoherence, Dominance
THEME Information (theme 2)
Publisher Elsevier
Persistent URL dx.doi.org/10.1016/j.ijar.2014.03.005
Journal International Journal of Approximate Reasoning
Citation
Quaeghebeur, E. (2015). Characterizing coherence, correcting incoherence. International Journal of Approximate Reasoning, 56, 208–223. doi:10.1016/j.ijar.2014.03.005