On the multiplicity of the maximum in a discrete random sample

Let Mn be the maximum of a sample X1,.,Xn from a discretedistribution and let Wn bethe number of i's, 1.i.n, such that Xi=Mn. We discuss theasymptotic behavior of thedistribution of Wn as n... The probability that the maximum is unique is of interest indiverse problems, for example,in connection with an algorithm for selecting a winner, and has been studied by several authors using mainly analytic tools. We present here an approach based on the Sukhatme--Rényi representation of exponential order statistics, which gives, as we think, a newinsight into the problem.