Symmetric kappa as a function of unweighted kappas

It is shown that a symmetric kappa corresponding to a c x c table with c 3 categories can be written as a function of the unweighted kappa corresponding to the same table and the c(c - 1)/2 distinct unweighted kappas associated with the (c - 1) x (c - 1) tables that are obtained by combining two categories. The result is a new MGB-type result.