Counterfactuals, Centering, and the Gibbard-Harper Collapse Lemma

Dr Melissa Fusco (Columbia University)

Melissa Fusco (Columbia) will present "Counterfactuals, Centering, and the Gibbard-Harper Collapse Lemma" at 11 in Old Quad G10.

Abstract: Egan (2007) argued that while Causal Decision Theorists adhere to the motto "do whatever has the best expected outcome, holding fixed [one's] initial views about the likely causal structure of the world", there are cases where we should not hold such views fixed as we act.  In these cases, Egan claimed, agents should use their anticipated credences Cr(a -> s | a) in states s to estimate the expected utility of their acts a, (where `->' is the counterfactual conditional and `|' is the slash of conditionalization).  

However, it has been known since Gibbard & Harper (1978) that if an agent is probabilistically coherent, and the semantics for counterfactuals obeys Centering---roughly, the view that each world is counterfactually closest to itself---Cr(a -> s | a) reduces to Cr(s|a).  It follows that Egan's view of such cases collapses into classical EDT.  This complicates the traditional way of putting the difference between EDT and CDT, according to which the latter, but not the former, requires causal information.  By Gibbard & Harper's result, the work of putting causal information into a simple EDT system is exactly undone by adding conditionalization.    

In this talk, I focus on the dialectic from the CDTer's point of view. The Gibbard-Harper result forces the causalist to choose between (i) the learning norm of conditionalization, (ii) centering for counterfactuals, and (iii) CDT itself, as a theory distinct from EDT.  I explore these options, presenting, along the way, some new cases in which agents' acts seem to give them knowledge of causal relations.