Conditional hypothesis testing systems

We introduce the notion of a Conditional Hypothesis Testing System (CHTS) that specifies the concrete mode of non-Bayesian reactions to unexpected news in a conditional world. We show that Ortoleva's (2012) Hypothesis Testing Model (HTM) has an alternative CHTS representation, and thus Ortoleva's axioms also characterize CHTS. We demonstrate the concept of CHTS can be used to derive the conditional-probability-system expected utility model of Myerson (1986a). In addition, we formulate and show that the CHTS updating rule is order independent—i.e., the order of receiving uncontradictory information never influences the final posterior under the updating rule in all conditioning events. Our study sheds light on the (coherent) dynamic structure of HTM in all conditional worlds.