Cyril Hédoin (REGARDS, Université Reims-Champagne Ardennes, France) has recently published online a working paper entitled “Decision Theory with Incomplete Preferences: The Counterfactual Principle“.
Abstract: Decision theory typically assumes that agents are endowed with a complete ordering of preferences over alternatives. This is particularly the case for expected utility theory which indicates that in case of risk or uncertainty over the realization of states of nature, a rational agent should opt for the alternative with the highest expected value or utility. It is unclear how expected utility theory can be extended to the case where agents have incomplete preferences. It has even been suggested recently that incompleteness makes the other principles of expected utility theory inconsistent. This paper proposes a plausible principle that allows such extension: the counterfactual principle. I claim that this principle is not only compatible with some our strongest intuitions about the choices over prospects when preferences are incomplete. It also makes the claimed inconsistency between the principles of expected utility theory disappear.
Keywords: Expected utility theory – Incomplete preferences – Rationality – Counterfactualism – Prospectism.