Preferences over Time and under Uncertainty: Theoretical Foundations

We formulate a general theory of preferences over outcome-time-probability triplets and decompose uncertainty into risk and hazard. We define the delay, defer, shift and certainty functions that can be uniquely elicited from behaviour. These individually determine stationarity, the common difference effect and its converse; constant, decreasing and increasing impatience; additivity, subadditivity and super additivity; probability independence, the certainty effect and its converse. We propose a general discounted utility model which encompasses the main empirically supported discounted utility models. We show that our axioms on preferences are satisfied in our general discounted utility model. Finally, we discuss the various explanations of the common difference effect.