Have to dispute the Ivy name trivia
There was never a (4) IV team league. In the early 1900's Princeton, Yale and Harvard formed the Big Three. In the 1930's a sportswriter coined the phrase ivy referring to the ivy covered walls of many northeastern schools and other sportwriters picked up on this creating over time a fictional "ivy league" that included today's 8 members, plus army and navy.
In the late 40's or 50's the Presidents of the 8 (to be) Ivies formed a coaltion of sorts with respect to athletics as well as academics and dubbed it the Ivy group. This soon then became the Ivy league.
As such, any formal alliance went from 3 (Harvard, Yale and Princton) to eight. There never was a group of 4 (so no IV). the name is just an evolution from a sports writer's pen.
(The other answer though is far more fun).
Now, how 'bout why does the Pac10 have only 9 baseball participants (although they recently did have 10, but not all were Pac10 schools) or why the big10 isn't 10 at all.