A representation result for choice under conscious unawareness

Abstract

There are many examples in policy-making, investment and day-to-day life where the set of contingencies the decision-maker can conceive of does not resolve all uncertainty about the consequences of actions. In such circumstances, the decision-maker may nevertheless reason that there exist certain aspects of the ‘full’ state space of which she is unaware. That is, she may think it is possible she is unaware of something.

We call this type of belief conscious unawareness and claim that its presence may lead to a violation of Savage’s Sure Thing Principle. We then specify a choice setting in which the decision-maker has preferences over a set of actions stated naturally in English, but where the decision-maker also has preferences on the set of derivative actions, where a derivative action maps from the set of permutations – the product space of the set of contingencies she can conceive of (her subjective state space) and the set of payoff assignments to the actions – to a space of consequences.

We obtain a representation result that makes choice in cases where conscious unawareness is a major concern tractable by means of some of the standard analytical tools of risk and ambiguity analysis. The representation also allows us to characterise the decision-maker’s attitude towards perceived payoff uncertainty arising from factors she is unaware of, in particular we characterise ignorance aversion. Using the same framework, we are able to state a more general representation that allows us to capture source preference in examples where the decision-maker is consciously unaware.

This is an update of a working paper originally published in 2011.