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

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

2012-03-15

arxiv.org/abs/1203.3509v1

Computer Science

Artificial Intelligence

Appears in Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence (UAI2010)

Scientific paper

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.

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