Summary: The problem considered is that of an unbiased estimation of \(P[X>Y]\) using ranked set sample data for two independent random variables \(X\) and \(Y\) with unknown probability distributions. Postulating a model for imperfect ranking, it is proved that the ranked set samples provide an unbiased estimator with smaller variance as compared with simple random samples of same sizes, even when the rankings are imperfect. It is further shown that the ranked set sampling provides maximum efficiency when the rankings are perfect.