This all seems needlessly complicated, and worse, it is custom-tweaked to just one specific scenario. I would much rather simply have the details of who voted for whom remain public and then allow each instance to handle that however they wish.
Spotting karma whores who operate like this, with a group of mutually-upvoting and downvoting bots, will be a trivial pattern for automatic detection. Rather than simply trying to give them an ever-more-complicated "game" to play, just identify them and block them and be done with it. Admins won't want their instances to become known as havens for such behaviour so they'll likely wipe users like that.