  The ability to preserve user privacy and anonymity is important. One of the
safest ways to maintain privacy is to avoid storing personally identifiable
information (PII), which poses a challenge for maintaining useful user
statistics. Probabilistic counting has been used to find the cardinality of a
multiset when precise counting is too resource intensive. In this paper,
probabilistic counting is used as an anonymization technique that provides a
reliable estimate of the number of unique users. We extend previous work in
probabilistic counting by considering its use for preserving user anonymity,
developing application guidelines and including hash collisions in the
estimate. Our work complements previous method by attempting to explore the
causes of the deviation of uncorrected estimate from the real value. The
experimental results show that if the proper register size is used, collision
compensation provides estimates are as good as, if not better than, the
original probabilistic counting. We develop a new anonymity metric to precisely
quantify the degree of anonymity the algorithm provides.
