There are a ton of different possible strategies for multi-voting and I don’t see how you could satisfy everybody.
But @sam_saffron, FWIW, I think it would not be a bug farm to add score voting (“range voting”) in particular, where everybody rates the options on a scale from 1 to 10 (or leaves an option “unrated”), and then reports the average. It’s a simple voting system that’s surprisingly well liked by voting geeks. http://rangevoting.org/
That’s what I wound up using for our GOTY polls. What's the best Choice of Game in 2014?