The categorial disorder δ we want to estimate is the average value taken by D for true pairs only, which formally corresponds to the conditional expectation of D given the event truePair, and is given by Equation (2): In other words, what we really get from an alignment is a "fuzzy set" of true pairs rather than a classical set, and the best estimate of δ we can get from this data is the weighted (by p i ) average value of {δ i }.
this is one of the most important features of γ cat , because it corresponds to the most frequent situations (annotators usually combine different kinds of discrepancies), and proves that this measure is fully focused on categorization.