Incomplete Preferences and Confidence

A theory of incomplete preferences under uncertainty is proposed, according to which a decision maker’s preferences are indeterminate if and only if her confidence in the relevant beliefs does not match up to the stakes involved in the decision. The author uses the model of confidence in beliefs introduced in Hill (2013), and axiomatise a class of models, differing from each other in the appropriate notion of stakes. Comparative statics analysis can distinguish the decision maker’s confidence from her attitude to choosing in the absence of confidence. The model naturally suggests two possible strategies for completing preferences, and hence for choosing in the presence of incompleteness. One strategy respects confidence – it relies only on beliefs in which the decision maker has sufficient confidence given the stakes – whereas the other goes on hunches – it relies on all beliefs, no matter how little confidence the decision maker has in them. Axiomatic characterizations are given for each of the strategies. Finally, the author considers the consequences of the model in markets, where indeterminacy of preference translates into refusal to trade. The incorporation of confidence adds an extra friction, beyond the standard implications of non-expected utility models for Pareto optima.