Perhaps you could give users a limited anti-karma budget they could spend to downmod articles. Something like you may spend 1 point of anti-karma every 24 hours for each 100 karma you have earned.
For ordering purposes, a story's effective karma should be something like (total upmods / (1 + total antikarma)).
For ordering purposes, a story's effective karma should be something like (total upmods / (1 + total antikarma)).