Abstract
Abstract : This paper investigates the problem of selecting, from k(> or =2) m- sided dice, the fairest die. The fairest die is the one corresponding to the smallest (unknown) value of Theta sub i = sum from j = 1 to m of P sub ij - 1/m where p sub ij denotes the jth cell (face) probability for the ith die. The proposed selection procedures are based on Schur convex functions. The problem is studied in the context of the subset selection approach. For small samples case, a method for finding conservative solutions for the selection constants is given. Large sample approximations have also been provided. A related problem of selecting all good populations is also investigated. A procedure for selecting the die with the greatest bias is also proposed and studied. Tables of constants necessary to carry out the procedure for selecting the fairest die are given. Keywords: Subset selection procedures; Multinomial distribution; Best population; Majorization; Schur convex; Schur concave; Good populations.
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