The Gibbard-Harper Collapse Lemma for Counterfactual Decision Theory

Abstract

There is a problem for the debate between causal decision theory, formulated in terms of counterfactuals, and its traditional rival, evidential decision theory: an agent’s credences in counterfactuals concerning their own acts collapse into evidential probabilities on those acts once diachronic conditionalization on the act is taken into account. Given assumptions that both classical CDTers [6] and their critics (prominently, [4]) accept, it therefore follows that three things cannot be distinct: (i) the probability of a state, given an act; (ii) the probability that if the act were performed, the state would result; and (iii) the probability one would have in that same counterfactual, if one learned the act was actually performed.