ON SEIDENFELDS CRITICISM OF SOPHISTICATED VIOLATIONS OF THE INDEPENDENCE AXIOM

An agent who violates independence can avoid dynamic inconsistency in sequential choice if he is sophisticated enough to make use of backwar d induction in planning. However, Seidenfeld has demonstrated that suc h a sophisticated agent with ''dependent'' preferences is bound to vio late the principle of dynamic substitution, according to which admissi bility of a plan is preserved under substitution of indifferent option s at various choice nodes in the decision tree. Since Seidenfeld consi ders dynamic substitution to be a coherence condition on dynamic choic e, he concludes that sophistication cannot save a violator of independ ence from incoherence. In response to McClennen's objection that relyi ng on dynamic substitution when independence is at stake must be quest ion-begging, Seidenfeld undertakes to prove that dynamic substitution follows from the principle of backward induction alone, provided we as sume that the agent's admissible choices from different sets of feasib le plans are all based on a fixed underlying preference ordering of pl ans. This paper shows that Seidenfeld's proof fails: depending on the interpretation, it is either invalid or based on an unacceptable assum ption.