I just came across a situation where a word meaning "having the quality of being compelling" would have been useful. The sentence was along the lines of:
He argued his case passionately. I think this demonstrates the [compellingness] of Yale's philosophy degrees!
I could've paraphrased to something like:
He argued his case passionately. I think this demonstrates how compelling Yale's philosophy degrees are!
.. but in this case I think it would've made the whole sentence more clunky. What I came up with in the end was 'vigor', but I don't like it; is there a word which more closely resembles 'compellingness' (which itself doesn't sound like a word to me, and the dictionary seems to back that up)?