  Selecting the top-$k$ highest scoring items under differential privacy (DP)
is a fundamental task with many applications. This work presents three new
results. First, the exponential mechanism, permute-and-flip and
report-noisy-max, as well as their oneshot variants, are unified into the
Lipschitz mechanism, an additive noise mechanism with a single DP-proof via a
mandated Lipschitz property for the noise distribution. Second, this new
generalized mechanism is paired with a canonical loss function to obtain the
canonical Lipschitz mechanism, which can directly select k-subsets out of $d$
items in $O(dk+d \log d)$ time. The canonical loss function assesses subsets by
how many users must change for the subset to become top-$k$. Third, this
composition-free approach to subset selection improves utility guarantees by an
$\Omega(\log k)$ factor compared to one-by-one selection via sequential
composition, and our experiments on synthetic and real-world data indicate
substantial utility improvements.
