Turning relative deprivation into a performance incentive device

The inclination of individuals to improve their performance when it lags behind that of others with whom they naturally compare themselves can be harnessed to optimize the individuals' effort in work and study. In a given set of individuals, we characterize each individual by his relative deprivation, which measures by how much the individual trails behind other individuals in the set doing better than him. We seek to divide the set into an exogenously predetermined number of groups (subsets) in order to maximize aggregate relative deprivation, so as to ensure that the incentive for the individuals to work or study harder because of unfavorable comparison with others is at its strongest. We find that the solution to this problem depends only on the individuals' ordinally-measured levels of performance independent of the performance of comparators.