  ldp deployments are vulnerable to inference attacks as an adversary can link
the noisy responses to their identity and subsequently, auxiliary information
using the order of the data. An alternative model, shuffle DP, prevents this by
shuffling the noisy responses uniformly at random. However, this limits the
data learnability -- only symmetric functions (input order agnostic) can be
learned. In this paper, we strike a balance and show that systematic shuffling
of the noisy responses can thwart specific inference attacks while retaining
some meaningful data learnability. To this end, we propose a novel privacy
guarantee, d-sigma-privacy, that captures the privacy of the order of a data
sequence. d-sigma-privacy allows tuning the granularity at which the ordinal
information is maintained, which formalizes the degree the resistance to
inference attacks trading it off with data learnability. Additionally, we
propose a novel shuffling mechanism that can achieve \name-privacy and
demonstrate the practicality of our mechanism via evaluation on real-world
datasets.
