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In a desionmaking situation if prior information is vague, indecision may result. A model for partial prior information is established and from this arises the notion of a set of feasible decisions. The existence of more than one feasible decision represents the existence of indecision. In many practical situations the partial prior information may be given by linear inequalities on the prior probabilities in which case there is a computationally attractive method for determining the set of feasible decisions.