Comparative Statics, Informativeness, and the Interval Dominance Order

We identify a natural way of ordering functions, which we call the interval dominance order and develop a theory of monotone comparative statistics based on this order.  This way of ordering functions is weaker than the standard one based on the single crossing property (Milgrom and Shannon, 1994) and so our results apply in some settings where the single crossing property does not hold.  For example, they are useful when examining the comparative statistics of optimal stopping time problems.  We also show that certain basic results in statistical decision theory which are important in economics - specifically, the complete class theorem of Karlin and Rubin (1956) and the results connected with Lehmann's (1988) concept of informativeness - generalize to payoff functions obeying the interval dominance order.