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The standard coherence criterion for lower previsions is expressed using aninfinite number of linear constraints. For lower previsions that areessentially defined on some finite set of gambles on a finite possibilityspace, we present a reformulation of this criterion that only uses a finitenumber of constraints. Any such lower prevision is coherent if it lies withinthe convex polytope defined by these constraints. The vertices of this polytopeare the extreme coherent lower previsions for the given set of gambles. Ourreformulation makes it possible to compute them. We show how this is done andillustrate the procedure and its results.

Characterizing the Set of Coherent Lower Previsions with a Finite Number of Constraints or Vertices