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CONCEPTS: completeness, accuracy, consistency, stability, relevancy

SEMI-RELATE-SUBJECTS: taxonomy, data quality, indexes, keywords, SEO, SEM

FORMULAS: ? ? ?

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From Wikipedia, since I hadn't heard that term before:

A folksonomy is a system of classification derived from the practice and method of collaboratively creating and managing tags to annotate and categorize content; this practice is also known as collaborative tagging, social classification, social indexing, and social tagging.

"Success" is a very vague term here. Any measure of success depends on what your goals are for your site/application, and what the dataset contains. No-one here can really tell you how to measure success.

Furthermore, all the concepts you provide are incredibly difficult to measure in the first place. Take "completeness", for example: do you know the size of a complete set, or is there even a concept of a complete set?

Perhaps providing more information about your site or its data would help us answer, but to be honest I think only you can decide what is successful and how to measure it.

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@DisgruntledGoat: The tagging system and rules on stackexchange would be an folksonomy, and in fact is the website in question, especially in the context of how stackexchange has forced a structure on the community via the sub-sites taxonomy. So, I asked the question in the broad way, but in this case it has completely to do with how stackexchange manages domain and tags... an it's effect on users, clusters of users, and the whole stackexchange community. Basically attempting to make a case that the domains are not in the best interest of anyone. – blunders Oct 11 '10 at 23:54
Well in the case of Stack Exchange, their success is measured by how many experts they can attract. The point of separate domains is to attract experts to one specific site that they feel is "theirs". To quantify that you could look at visitor counts, questions, answers etc. These are all nicely listed on the front page of each SE site. Personally I'd say Stack Exchange is very successful, moreso than one monolithic site would have been. – DisgruntledGoat Oct 12 '10 at 10:54

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