You are after a noble goal. IMO, the work you are doing is great but your intended use is not correct. I think using it to educate people so that we get better reviews more consistently is the answer. Designing a system that decides how ratings count is control.

My research question is, “Given all of the information we have on raters and ratings, is the simple mean rating of a show the best way to measure fans’ collective opinion?”

I think that is great question. I also believe what you learn could be put to wonderful use. Educating the community may encourage more and better ratings.

But I firmly believe that any one person's show ratings, and average show ratings, should be correlated with what happens onstage at a Phish show.

Implementing a system that does this is control.

I know you do not intend it. That is a buy product of the quest for perfection. Variables need to be controlled to get a better signal in the data.

If you want to change the ratings we should completely change the ratings and leave the existing rating alone. I would introduce a new rating that is well defined and understood in terms of its calculation.

Thank you for the discourse. Please keep up the good work, I do really appreciate the thought that has gone into this.