Viability based tiering should be a non-starter. Viability Rankings are incredibly raw and unofficial.
They do not fit the mold of our defined metagames (OverUsed, UnderUsed, etc., not OverlyViable, UnderlyViable, etc.), they would require guidelines on what defines viability that are impossible for everyone to agree upon, and would shift the deriving of metagames from the playerbase to a small group of people.
To one of your minor points, if we would switch to viability-based tiering, we can still absolutely keep the OverUsed, UnderUsed, etc. names, even if we're not going off usage anymore. The names are historically entrenched in Smogon's identity and changing them would be purely cosmetic, unlike changing the tiering system, which is looking to actually fix issues with the system.
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To the more major point, while Viability Rankings may seem "raw and unofficial," the beauty of the method that
I mentioned earlier is that you get a pretty objective consensus among the voters, and a good picture of what is viable, even if defining viable is hard. There doesn't need to be definite definitions of viability that everyone agrees on. You just rank the Pokemon approximately in order, and then the script compiles the rankings and spits out groups of Pokemon that are similar to each other. These ranks are then defined as S, A+, B-, whatever, to fit what people are used to. In RBY, we use stuff like "S1," "B2," "C3," etc. instead of +, neutral, - ranks, because of a possibility of there being like, B1, B2, B3, B4 or something based off what the program spits out. But it's still easy to follow in my opinion.
To quote vapicuno:
"Q: This is a pain.
Do I really need to rank every Pokemon precisely?
A: No, the beauty of the method is that
you don't need to precisely rank things you don't know! Just rank approximately. If you can't properly rank C-tier mons, but know where the cutoff is from D-tier mons, and everyone else kind of agrees with you where the cutoff is, the tiers will be formed correctly regardless of how you ranked it."
This means that if you have a selection of voters that are ranking, say, 100 Pokemon each, your voters do not need to stress about whether Great Tusk is specifically one spot "more viable" than Kingambit. As long as they are in the same general area (say, well above Pokemon like Chansey and Quagsire), and there's a general community consensus about that, then Great Tusk and Kingambit will be ranked in the same group. The data is "cleaned" to account for outliers too, so if one or two of your voters think that Kingambit is overrated and actually sucks, it's not going to affect the rankings all that much, especially if you have a decent number of rankers.
About individual ranks within groups: it is ordered within the group at the end, so the results will tell you community consensus about which one specifically is "more viable" I guess, but at the end of the day every Pokemon in the group should be "relatively indistinguishable" from another Pokemon in the group. The individual ranks are just used to calculate rises and drops from the previous VR. I see that the current OU VR is not ordered within ranks, it's ordered alphabetically. If you really want to, I suppose that you could just remove the numbers and still keep it like that, since Great Tusk and Kingambit should be "relatively indistinguishable" from each other within their group, so it doesn't necessarily matter which is ahead of the other. But if you wanted to be more specific like RBY and say that yes, Exeggutor is one spot "more viable" than Starmie despite being in the same group, you're free to do that as well.
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I'm not arguing that viability-based tiering is without its flaws. As you say, it does change who holds "the power" from the whole playerbase to much fewer people, ones that are "qualified" to be a part of the VR process. But then again, the whole purpose of this thread is that one person/bot (or a group of people/bots) is disproportionately influencing tiering anyway at the moment. It seems like a damned if you do, damned if you don't situation in that someone or some people are going to have more influence than others over the tiering process. In my opinion, I would actually rather have it be people that know and are passionate about the tier rather than a literal brainless bot. This is probably going to get called elitist or oligarchical, especially by people on the outside looking in, but that's how I feel.
As I said before though, I don't have all the answers. I don't know how to determine who would get to vote, or how often (because as stated before, monthly seems like a hell of a chore). But I did want to give a defense against the naming conventions argument, as well as the argument that defining viability is impossible. I understand the reticence towards overhauling the current system, but there's clearly stuff about it isn't working as intended and making people unhappy, so I'm just making a potential suggestion based off something that works well for older gens.
Regardless, I feel like if the bot issue really is unresolvable according to PS! tech people, something should change about the system. And if that means a complete overhaul, so be it.