The history preference function H:

(This part I don't understand well. Please help me improve my understanding.)

H is supposed to select a preferred history (or rather like D, a sequence of histories of decreasing preference) to build on from a set S of known possible histories, so write H(S) to represent this.

I think you want H to be consistent with D: Suppose you're at a version of history h right now, and D chooses as decider account a_1 as the first candidate, a_2 as the second candidate, and so on. If the updated versions of history proposed by each a_n is h_n respectively, H should prefer h_1 over h_2, h_2 over h_3 and so on. One way to achieve this is for H to prefer the version of history with the smallest sum of all previous HIT/EFFECTIVE_STAKEs of previous deciders in that version of history, since if you have two versions of history differing only in the last block, the HIT/EFFECTIVE_STAKEs are all the same except for the last decider, so the version with the smallest sum is also the one whose last decider has the smallest HIT/EFFECTIVE_STAKE.

But folks in the main thread were talking about largest sum of 1/EFFECTIVE_STAKEs (of just the deciders?), which isn't consistent in the way I described here, so I don't get this part. Am I missing something?

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H should likewise be consistent with any blacklisting used, I'm not sure what a good modification would be.