The use of admissible procedures in each of several problems may be inadmissible when the problems are combined, in the sense of summed loss. Thus apparently irrelevant information can sometimes be used to reduce risk over the entire parameter space. This is known as Stein's Paradox. We prove here that this cannot occur when the sample spaces for the problems are finite.
"Stein's Paradox is Impossible in Problems with Finite Sample Space." Ann. Statist. 10 (3) 1017 - 1020, September, 1982. https://doi.org/10.1214/aos/1176345893