@wolftune Oh I see, the link is just from someone's website not something you wrote up. Got it, sorry.
I guess where I had seen the description of a "simplified variant" was on the ElectoWiki site, at the bottom of the page. https://electowiki.org/wiki/Bottom-Two-Runoff_IRV
Simplified Variant
If you remove the redistribution step, leaving the candidates in the initial 1st choice sort order for the entire process, BTR-IRV becomes precinct summable. Vote counting only requires the 1st choice vote counts and the pairwise preference matrix from each precinct, not the complete ranking counts.
I think it's an interesting difference. Using your paper ballot example, this would mean putting the ballots into piles based on first choices only, and never redistributing them for the purposes of selecting the bottom two candidates in any round. This is what I understood from that write-up that is linked, as it does not mention any redistribution. It's "simpler" in the sense that you can skip the redistribution process at each step. It is also "simpler" in the compilation complexity sense, that it is precinct summable.
It raises an interesting question- if someone were to go to an IRV advocate and pitch them on a tweak, which variant to propose? BTR-IRV with distribution is closer to traditional IRV, so perhaps that is a reason to propose it, as it is more similar to traditional IRV. But on the other hand, BTR-IRV without distribution is simpler in some ways, which can be viewed as a virtue as well.
It's also worth thinking about how much the distinction matters in practice. Curious if anyone has thoughts on that.
