 
Summary: 1
Dominating countably many forecasts.*
T. Seidenfeld, M.J.Schervish, and J.B.Kadane.
Carnegie Mellon University
May 5, 2011
Abstract
We contrast de Finetti's two criteria for coherence in settings where more than finitely
many options are combined into a single option. Coherence1 requires that finitely many
previsions cannot be uniformly strictly dominated by abstaining. Coherence2 requires
that finitely many probabilistic forecasts cannot be uniformly strictly dominated under
Brier score by a rival set of forecasts. Though de Finetti established that these two
criteria are equivalent, we show that when previsions/forecasts are based on a merely
finitely and not countably additive probability, the second criterion may be extended to
permit combining countably infinite sets of options, but not the first criterion. Also, we
investigate calledoff previsions and calledoff forecasts given elements of a partition ,
where the calledoff previsions/forecasts are based on the conditional probabilities given
elements of that partition. We show that each coherence criterion is violated by
combining infinitely many called off previsions/forecasts when those conditional
probabilities are not conglomerable in the partition . We show that neither criterion is
violated by combining infinitely many calledoff previsions/forecasts when conditional
