Actually I would say if we developed a system where a tag's relevance could be computed or defined, the ability to sort by relevance is too useful not to implement. I wouldn't let drama stand in the way of that. An item's prominence typically isn't that subjective anyway and could usually be worked out in the comments or on the forum anyway.
I think I actually like your system best of the ones brought forward because it will work with a single tagger and doesn't require mass user participation (like Evazion's), and it isn't tedious or cumbersome or bound by heuristic (like my system would be).
Also a very similar system seems to be working for The Doujinshi DB Project where they use a 5-bar cell-phone signal metric to indicate the prominence of copyrights, characters, and themes in various doujin.
I'm not sure form experience how well it's working for them though since I don't frequent that site. I'm also not sure how well it would translate there since they are a lot more rigid with their editing style than we are. But it seems to be working fairly well.
Overall I think each of the proposed systems have strengths and weaknesses, but yours seems the most balanced.
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My system would be a pretty natural addition and would add utility to a spatial tagging system, if that was something we were thinking about adding anyway. It would also be completely objective, whereas the other systems aren't.
On the downside, it would probably be very cumbersome to require every user to use it for every tag. That would limit people using it, and hence it's effectiveness. Also, as Evazion points out, it is useless for intangible tags and the heuristic breaks down sometimes where small things can be quite relevant and vice-versa.
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Evazion's system would work very well for subjective tags, and is a very natural way of guaging what is prominent in the users' view as a whole. If handled correctly, it's also the one least sensitive to abuse.
Like I state above though, I question whether it would be used by enough users to make it useful for non-subjective tags. It also would prevent new or less popular posts from having relevance set properly.
Regardless of whether we use this system for general use, I would support it as some sort of replacement for subjective pools/tags; and think that private tags / multiple favorite lists are a great idea on their own.
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On the downside, Suiseiseki's system is actually the most subjective since it requires and allows a single person to set the prominence (where the other systems calculate it automatically). The same degree of subjectivity is already present with the current tagging system though, so it's probably not a big deal except with naturally subjective tags.
It also has the least degree of granularity of the three regardless of if we go with 2, 3, or 5 levels (both Evazion and my systems allow for basically continuous gradiation). That could be a good or bad thing.
On the upside, it works with less users participating (only one is required), and is probably the least resource intensive of the three. It's also the one that demands the least effort in general, and as such is probably the most likely to be used widely.