Expected utility theory, Jeffrey’s decision theory, and the paradoxes

In Richard Bradley's book, Decision Theory with a Human Face (2017), we have selected two themes for discussion. The first is the Bolker-Jeffrey (BJ) theory of decision, which the book uses throughout as a tool to reorganize the whole field of decision theory, and in particular to evaluate the extent to which expected utility (EU) theories may be normatively too demanding. The second theme is the redefinition strategy that can be used to defend EU theories against the Allais and Ellsberg paradoxes, a strategy that the book by and large endorses, and even develops in an original way concerning the Ellsberg paradox. We argue that the BJ theory is too specific to fulfil Bradley’s foundational project and that the redefinition strategy fails in both the Allais and Ellsberg cases. Although we share Bradley’s conclusion that EU theories do not state universal rationality requirements, we reach it not by a comparison with BJ theory, but by a comparison with the non-EU theories that the paradoxes have heuristically suggested.