A classifier has scores in [0, 1] and preserves its ranking after every score is squared. What can change in expected-cost decisions and how would you evaluate it?

The monotonic transformation preserves score ordering on zero to one but changes probability meaning and threshold placement. Recheck calibration and proper scoring rules on held-out data. A fixed numerical threshold may select a different set, and expected-cost calculations require justified probabilities. Ranking metrics alone cannot validate that use.