Interesting stats, Erik. Thanks for sharing these.
More clarity in the documentation is always good.
For some of the negative alpha agreement values, a couple of possible sources come to mind. There could be bad faith actors, who either didn't really try very hard, or purposely put in incorrect or random values. There could also be genuine disagreement between the scorers about the relevance of the results—David and I discussed one that we both scored, and we disagreed like that. I can see where he was coming from, but it wasn't how I thought of it. In both of these cases, additional scores would help.
One thing I noticed that has been inconsistent in my own scoring is that early on when I got a mediocre query (i.e., I wouldn't expect any really good results), I tended to grade on a curve. I'd give "Relevant" to the best result even if it wasn't actually a great result. After grading a couple of queries for which there were clearly no good results (i.e., everything was irrelevant), I think I stopped grading on a curve.
My point there is that's one place we could improve the documentation: explicitly state that not every query has good results. It's okay to not have any result rated as "relevant"—or this could already be in the docs, and the problem is that no one reads them. :(
Another thing that Erik has suggested was trying to filter out wildly non-encyclopedic queries (like "SANTA CLAUS PRINT OUT 3D PAPERTOYS"), and maybe really vague queries (like "antonio parent"), but that's potentially more work than filtering PII, and much more subjective.
It might also be informative to review some of the scores for the negative alphas and see if something obvious is going on, in which case we'd know the alpha calculation is doing its job.