Interesting idea! Devil's advocate: in the present environment of extreme partisanship, wouldn't people just rank their first choice a "10" and every other candidate "0" in order to inflate their average score?
A more interesting way if one wanted to do this is to allocate each person say 100 points.
Giving a candidate they like a 1 costs 1 vote while 2 points would be 4. 3 Points would be 9 and so forth. Would make deals interesting such as 2 similar candidates working on giving each others voters a 7 each or something. I am guessing a scale of 0 to 5 and 25 points would work better . This would actually encourage "splitting" the vote .
https://en.wikipedia.org/wiki/Quadratic_voting
