Decreasing Returns to Sampling Without Replacement

We study sampling from a finite population without replacement when seeking an extreme (lowest or highest) value. An example is a buyer searching for the lowest price. It is well known that there are decreasing returns to sampling from continuous populations: the expected minimum is a decreasing and discretely convex function of the sample size. We show that is true for sampling without replacement from a finite population. We also give a simple sufficient condition on population values for the properties to hold for other order statistics.