Cheating prevention

A validator could try to cheat by giving high scores to miners it runs itself.

The median makes that hard. Because scores above what the majority of stake supports are cut back, a group of validators with less than half the stake cannot push its own miners up. Their extra score is simply removed.

They also pay for trying. Validators are rewarded for scoring miners the way the majority of stake ends up scoring them, so a validator whose scores keep getting cut back earns less.

This protection rests on one assumption: that most of the stake on a subnet belongs to honest validators. If a single group controlled most of the stake, the median would follow them.