Computing inter-rater reliability is a well-known, albeit maybe not very frequent task in data analysis. If there’s only one criteria and two raters, the proceeding is straigt forward; Cohen’s Kappa is the most widely used coefficient for that purpose. It is more challenging to compare multiple raters on one criterion; Fleiss’ Kappa is one way to get a coefficient. If there are multiple criteria, one way is to compute the mean of multiple Fleiss’ coefficients.
However, a different way, and the way presented in this post, consists of checking of all raters agree on one given item (and repeating that for all items). If rater A assigns two tags/criteria (tag1, tag2) to item A, then the other raters may not assign different tags (eg tag3, tag4) to that item, if a match should be scored. Note that this proceeding allows for different numbers of tags/criteria for the items (eg., item 1 with only 1 tag, but item 2 with 3 tags etc.). However, our grading should give some points, if, say, rater1 assigns tag1 and tag2, but raters 2 and 3 only assign tag1.
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