  Experiments often include multiple treatments, with the primary goal to
compare the causal effects of those treatments. This study focuses on comparing
the causal anatomies of multiple treatments through the use of causal mediation
analysis. It proposes a novel set of comparative causal mediation (CCM)
estimands that compare the mediation effects of different treatments via a
common mediator. Further, it derives the properties of a set of estimators for
the CCM estimands and shows these estimators to be consistent (or conservative)
under assumptions that do not require the absence of unobserved confounding of
the mediator-outcome relationship, which is a strong and nonrefutable
assumption that must typically be made for consistent estimation of individual
causal mediation effects. To illustrate the method, the study presents an
original application investigating whether and how the international legal
status of a foreign policy commitment can increase the domestic political
"audience costs" that democratic governments suffer for violating such a
commitment. The results provide novel evidence that international legalization
can enhance audience costs via multiple causal channels, including by
amplifying the perceived immorality of violating the commitment.
