I honestly could not think of a better way to write it. I had the same problem when my friend first showed me this notation. I thought about using "E[P(H=htrue)]" but that seemed more confusing and less standard? I believe this is how they write things in information theory, but those equations usually have logs in them.
Just to add an additional voice here, I would view that as incorrect in this context, instead referring to the thing that the CEE is saying. The way I’d try to clarify this would be to put the variables varying in the expectation in subscripts after the E, so the CEE equation would look like ED[P(H=hi|D)]=P(H=hi), and the PPI inequality would be E(H,D)[P(H|D)]≥EH[P(H)].
I honestly could not think of a better way to write it. I had the same problem when my friend first showed me this notation. I thought about using "E[P(H=htrue)]" but that seemed more confusing and less standard? I believe this is how they write things in information theory, but those equations usually have logs in them.
Just to add an additional voice here, I would view that as incorrect in this context, instead referring to the thing that the CEE is saying. The way I’d try to clarify this would be to put the variables varying in the expectation in subscripts after the E, so the CEE equation would look like ED[P(H=hi|D)]=P(H=hi), and the PPI inequality would be E(H,D)[P(H|D)]≥EH[P(H)].
Yeah, this is the one that I would have used.