Score contribution per author:
α: calibrated so average coauthorship-adjusted count equals average raw count
There are situations where the rewards associated with an outcome differ based on whether a certain threshold is exceeded. This paper examines how the threshold affects individual effort levels and the performance distribution. When performance uncertainty is small, only individuals near the threshold increase their effort. In contrast, large performance uncertainty increases the likelihood of exceeding the threshold, motivating more people to exert costly efforts. Consequently, the distribution can be either unimodal or bimodal. These findings suggest that examiners can effectively enhance the overall performance of an assessed population by appropriately setting the threshold and managing score uncertainty.