My understanding of LATE was that it was the effect of a treatment on individuals who were induced to be treated by the experiment. That is, the effect on compliers. My understanding of Treatment-on-the-treated (TOT) is that it is the effect of individuals who are in the treatment group (which can include both individuals who were induced to be treated, and always-takers who would have accepted the treatment regardless)
However, my notes say the opposite -- that TOT is a subset of LATE, and that LATE allows for the existence of treated individuals who would have been treated even in the absence of experiment. But I don't really understand why one of them is capturing always-takers and the other isn't
What is the right way to think about this?