  We consider the following sample selection problem. We observe in an online
fashion a sequence of samples, each endowed by a quality. Our goal is to either
select or reject each sample, so as to maximize the aggregate quality of the
subsample selected so far. There is a natural trade-off here between the rate
of selection and the aggregate quality of the subsample. We show that for a
number of such problems extremely simple and oblivious "threshold rules" for
selection achieve optimal tradeoffs between rate of selection and aggregate
quality in a probabilistic sense. In some cases we show that the same threshold
rule is optimal for a large class of quality distributions and is thus
oblivious in a strong sense.
