Incomplete Preferences and Confidence

54 Pages Posted: 30 Jun 2014 Last revised: 6 Mar 2015

See all articles by Brian Hill

Brian Hill

HEC Paris - Economics & Decision Sciences; CNRS

Date Written: March 5, 2015


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. We use 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, we consider 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.

Keywords: Incomplete preferences, confidence, multiple priors, choice under incomplete preferences, absence of trade

JEL Classification: D81, D01, D53

Suggested Citation

Hill, Brian, Incomplete Preferences and Confidence (March 5, 2015). HEC Paris Research Paper No. ECO/SCD-2014-1051. Available at SSRN: or

Brian Hill (Contact Author)

HEC Paris - Economics & Decision Sciences ( email )


CNRS ( email )

3, rue Michel-Ange
Paris, 75794

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