Are there simpler heuristics than page rank? Perhaps a reputation score determines how much your vote is worth?

page rank is a reputation score

Yes, but if computational cost is a concern there are other options.

I fear that's too easy to game at our scale, given the horde out there.

page rank in this context is morally relativistic

How would you apply it in our context?

Not OP. In page rank you have a graph of pages as vertices and links as edges. In this case you'd want users as vertices and up votes as edges.

Page rank would give users a high score if they are up voted by other users with high scores.

I'm not sure if page rank can deal with negative weight edges for down votes but probably.