As I understand it (and I'll give you that it's been a while since I've gone through it mathematically), if you don't have a preference, then you can average the unused entries and give them all the same amount. I think that this would not be a true Borda Count, but it gives the correct result. You do have something of a problem when you want to vote for one person, and against one person, but don't much care about the rest, but really only in a UI way. The math still works out. And, honestly, when's the last time you saw a real-world election with more than four candidates?

There are other methods that work, too, especially in the common idiom of wanting to vote against someone (something I wish I could have done in the last presidential election). At least better than the current plurality method.