  In previous work (arXiv:0910.5714), we introduced the Privacy Approximation
Ratio (PAR) and used it to study the privacy of protocols for second-price
Vickrey auctions and Yao's millionaires problem. Here, we study the PARs of
multiple protocols for both the disjointness problem (in which two
participants, each with a private subset of {1,...,k}, determine whether their
sets are disjoint) and the intersection problem (in which the two participants,
each with a private subset of {1,...,k}, determine the intersection of their
private sets).
  We show that the privacy, as measured by the PAR, provided by any protocol
for each of these problems is necessarily exponential (in k). We also consider
the ratio between the subjective PARs with respect to each player in order to
show that one protocol for each of these problems is significantly fairer than
the others (in the sense that it has a similarly bad effect on the privacy of
both players).
