The Realizing Potential Rule and Other Axiomatic Rankings of Ordinal Performance Improvements

Evaluating performance is essential for designing effective incentive structures that enhance productivity across various domains. This paper introduces and axiomatically characterizes the realizing potential rule, which assesses an agent's potential for improvement (or deterioration) based on past performance. Current performance is then evaluated based on the ratio of improvements (or deterioration) relative to this potential. Our main axiom introduces a novel consistency condition, ensuring that evaluations remain stable when the performance scale is reversed. Alternative rules are also discussed and characterized, and the seemingly natural relative improvements rule is shown to violate our consistency condition. Additionally, we show that building a reward system based on the realizing potential rule is more effective in increasing total productivity compared to reward systems based on more common rules. Finally, extending the framework to a social‐rule setting, our main result provides an extension of realizing potential to cases where the level of maximal performance is not well‐defined. Our results lay a foundation for designing incentive systems that equitably reward improvement while enhancing productivity, with applications in labor markets, education, and healthcare programs.