[eschwartz]

I believe consortiums merely allow individual libraries to buy a book without sharing it to the other member libraries.

They are not fast-tracking their patrons up the holds list, but they may give their patron, say, the secret 2nd copy of the book that is exclusive to that consortium branch. So you'd get moved up the list faster since people on hold for the book are getting copies faster. You have just as much right to the shared copy though.