I found this explanation of the bylaws:
Thanks to the OP for posting the by-laws, the information is very helpful. Here's my reading on two key issues:
1. The Big East CAN be dissolved by the basketball-only members between now and July 1st. Temple does NOT have a vote on this. Why? Because under section 12.01, conference dissolution can be approved by 2/3 of the conference "Directors", and because "Directors" are defined in section 3.01 as CEOs of conference "Members", and because under section 14.01(b) Temple is a "Football Affiliate" this year rather than a "Member" (because it only plays football in the conference). Moreover, section 14.01© explicitly states that "The CEO of a Sports Affiliate [e.g. a Football Affiliate] shall not be a Director of the Conference."
2. On the other hand, despite having a 2/3 voting majority of "Directors" between now and July 1st, the basketball-only members CANNOT convert the Big East to a non-football conference. That's because section 3.01 defines any matter relating to participation in football as a "Football Action", and goes on to say that any vote on a matter constituting a "Football Action" requires majority approval from the Directors of the schools that play football and all other sports within the conference (referred to as the "Division I-A School Directors"). So discontinuing football participation would presumably require a majority vote from among the CEOs of UConn, Cincinnati and USF.
http://csnbbs.com/showthread.php?tid=606580&page=2