Comparative Statics with the Interval Dominance Order: Some Extensions. - Quah, J; Stulovici, B (Department of Economics (University of Oxford), 2007)
In Quah and Strulovici (2007) (henceforth to be referred to as QS07), we identified a natural way of ordering functions, which we called the interval dominance order, and showed that this concept is useful in the theory of monotone comparative statics and also in statistical decision theory. This ordering on functions is weaker than the standard one based on the single crossing property (Milgrom and Shannon, 1994) and so monotone comparative statics results based on this property apply in some settings where the single crossing property does not hold. We also showed 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 that obey the interval dominance order. These incomplete notes gather together some new results not found in QS07. The reader is advised to read these notes in conjunction with that earlier paper - http://economics.ouls.ox.ac.uk/14831/