Symmetry Arguments in Probability Kinematics

Abstract
Probability kinematics is the theory of how subjective probabilities change with time, in response to certain constraints (accepted by the subject). Rules are classified by the imposed constraints for which the rules prescribe a procedure for updating one's opinion. The first is simple conditionalization (constraint: give probability 1 to proposition A), and the second Jeffrey conditionalization (constraint: give probability x i , 0 i ). It is demonstrated by a symmetry argument that these rules are the unique admissible rules for those constraints, and moreover, that any probability kinematic rule must be equivalent to a (simple or Jeffrey) conditionalization preceded by a determination of the values x i to be given to the members of such a partition. Next two rival rules which can go beyond such conditionalization are described. INFOMIN (minimize relative information) and MTP (maximize transition probability). Their properties are investigated and compared.
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