I know these are all similar, but what kind of connotations does each have? Which one is the strongest (to say it is actually the most diverse, while trying to remain "politically correct")?
Start by looking at the definitions; a quick Google gives:
Possibly perhaps (used to indicate doubt or hesitancy). "he found himself alone, possibly the only surviving officer"
Probably almost certainly; as far as one knows or can tell. "she would probably never see him again"
Arguably it may be argued (used to qualify the statement of an opinion or belief). "she is arguably the greatest woman tennis player of all time"
Looking at the definitions it can be seen that in your terms
Possibly is the weakest.
Probably is probably the strongest
And Arguably sits somewhere in between.
Clearly you are giving your opinion, and your opinion is based on your knowledge of the subject:
If you have only a little knowledge on the subject and you think/guesstimate that one student-body is more diverse then use Possibly
If you have an in-depth knowledge of the subject and more than say 50% sure, then use Probably
If you consider that 2 or more student-body's are more or less equally diverse, but one has just that little bit extra, then use Arguably.
- I'm not quite sure what you mean by PC, but I'll assume you mean you do not want to upset anyone? As soon as you have an opinion, someone will disagree with it; if you don't want to upset anyone, don't have an opinion.
In my own reading, I would normally view all three sentences as being suspect without being backed up, and seeing one would make me think the writer was boasting (probably without evidence).
It would be better to focus on statements that you provide evidence, or are considered the prime source anyway. For example:
"In 2014 there were students from 20 countries and with diverse backgrounds."
Finally, the original sentence's focus is on 'diversity', but that in itself would not (at least in my view) be a benefit to a newcomer. All it means is that there are a lot of different people there; it says nothing about how well they get on, what the culture is, or whether they do things together. What is the actual benefit of the diversity you wish to proclaim?
Bringing both threads together, would this be better:
"The National College Awards voted our students as the most welcoming in the country".