Abstract
In statistical decision theory, Karlin and Rubin derived a sufficient condition for an optimum policy to be given by a "monotone procedure" for a loss function that has one sign change at most. This paper derives a necessary and sufficient condition for an optimum policy to be given by a monotone procedure where there are a general number of actions. This condition is given by the conditional probability of a monitor given the state of the system has a property of TP_2 (total positivity of order 2). That is, the TP_2 property is the only condition with which one can identify the optimal action based on a monotone procedure. If the optimum policy can be limited to monotone procedures, the tremendous amount of calculation time required to find the optimum procedure can be reduced. This enables the best decision to be selected in a much shorter period of time.
