  It has been previously noted that optimization of the n-call@k relevance
objective (i.e., a set-based objective that is 1 if at least n documents in a
set of k are relevant, otherwise 0) encourages more result set diversification
for smaller n, but this statement has never been formally quantified. In this
work, we explicitly derive the mathematical relationship between expected
n-call@k and the relevance vs. diversity trade-off --- through fortuitous
cancellations in the resulting combinatorial optimization, we show the
trade-off is a simple and intuitive function of n (notably independent of the
result set size k e n), where diversification increases as n approaches 1.
