Say we want to compute the largest common subset among a very large number of sets $Q_i$. One option would be to simply run the command:
Intersection[Q1, Q2, Q3, Q4, Q5, Q6, Q7, ...];
However, this seems to choke for very large numbers of input sets ($10^4$ or so with on-order $10^2$ elements each). Another option would be compute
Q12 = Intersection[Q1,Q2], then
Q123 = Intersection[Q12,Q3], then
Q1234 = Intersection[Q123,Q4], and so forth.
Are these two procedures equivalent? Is there a better way?