Deferral, incomplete preferences and confidence

A theory of when to defer a decision is proposed, according to which a decision maker defers if and only if his confidence in the relevant beliefs does not match up to the stakes involved in the decision. It uses the model of confidence in beliefs and the notion of stakes introduced in Hill (2010). Firstly, a representation of deferral of binary choices is proposed and axiomatised; it can alternatively be considered as a representation of incomplete preferences, where indeterminacy of preferences is interpreted as taking the deferral option. Then the question of what the decision maker would do if he was not allowed to defer is studied; mild axioms governing the relationship between preferences in the presence and absence of a deferral option characterise a simple model of how forced choice relates to choice where deferral is possible. Finally, the results are extended to deferral of choices from non-binary menus. Compared to existing accounts of deferral, the theory proposed here is unique in analysing deferral entirely in terms of the attitudes of the agent at the moment of choice, rather than his expectation about his or others' future attitudes, for example. Preliminary axiomatic analysis shows that this difference is behaviourally meaningful.