In many countries, schools have responded to the COVID-19 pandemic by splitting up classes. While the purpose of dividing classes is clearly health-related, the process of doing so poses an interesting question: what is the best way to divide a class so as to maximize the incentive for students to perform better? Using a constructive example, we demonstrate how social-psychological unhappiness can be the basis for an incentive structure that optimally nudges students to improve their performance. The example is based on evidence that students aspire to improve their performance when it lags behind that of other students with whom they naturally compare themselves. For a given set of m students, we quantify unhappiness by the index of relative deprivation, which measures the extent to which a student lags behind other students in the set who are doing better than him. We examine how to divide the set into an exogenously predetermined number of subsets in order to maximize aggregate relative deprivation, so that the incentive for the students to study harder because of unfavorable comparison with other students is at its strongest. We show that the solution to this problem depends only on the students’ ordinally-measured levels of performance, independent of the performance of comparators. In addition, we find that when m is an even number, there are multiple optimal divisions, whereas when m is an odd number, there is only one optimal division.

在许多国家/地区，学校通过拆分班级来应对COVID-19大流行。尽管划分班级的目的显然与健康有关，但这样做的过程提出了一个有趣的问题：划分班级以最大程度地激发学生表现更好的动力的最佳方法是什么？通过一个建设性的例子，我们证明了社会心理上的不快乐如何成为激励机制的基础，该激励机制可以最佳地推动学生改善他们的表现。该示例基于证据，即当学生落后于自然比较自己的其他学生的表现时，他们渴望提高自己的表现。对于给定的m我们用相对贫困指数来量化学生的不幸福感，该指数衡量一个学生在学习表现上落后于其他学生的程度。我们研究了如何将集合划分为外生预定数量的子集，以最大程度地提高总体相对剥夺程度，从而使学生因与其他学生的不利比较而更加努力地学习的动机最大。我们表明，解决该问题的方法仅取决于学生通常测得的表现水平，而与比较者的表现无关。另外，我们发现当m为偶数时，存在多个最佳除法，而当m为奇数时，仅存在一个最佳除法。