A naive suggestion could be to take log(x) - log(p), where p is the probability given by MAXENT. That is, honor is how much better you do than the "completely uninformed" maximal entropy predictor. This would enable better-than-average predictors to make their honor go up.

This of course has the shortcoming that maximal entropy may not be practical to actually calculate in many situations. It also may or may not produce incentives to strategically make certain predictions and not others. I haven't analysed that very much.