Mandatory events within my chapter were chapter meetings, ritual, anything to do with rush (retreat, work week, rush itself), and anything Panhel made mandatory. You would have to be on your deathbed to be excused from initiation.
For social activities, we had to go to a certain percentage. Formals counted as two activities. This was a good compromise between sisters in relationships (who really weren't interested in mixers) and sisters not in relationships (who wanted to skip the date party).
For everything else, we had a points system. You got points for things like attending other GLOs' charity fundraisers, doing community service with the chapter, etc. I think we got points for the social stuff too. The sister with the most points each semester got an award and a small discount on her dues. If you didn't get a certain number of points, you were called to standards.
Would something like this work? The carrot and stick approach, but more carrot than stick.
ETA: Something else we tried was specifying that once you agreed to attend a non-mandatory event (especially mixers) it became mandatory for you and you could face repercussions if you didn't keep your word. This was especially important with mixers because we were one of the smallest GLOs on campus, so if the majority of sisters didn't want to go, there wasn't much point to scheduling a mixer... then if we held the mixer and only 5 women showed up because a bunch of women who said they'd go bailed, it made us look bad and offended the fraternity.