Fair division rules for funds distribution: The case of the Italian Research Assessment Program (VQR 2004-2010)

In a great number of applications, it is necessary to distribute resources or tasks to agents collaborating with each other in order to maximize the social welfare of the structure they belong to. The question in these cases is how to divide in a fair way the outcome that the structure eventually earns, say money, to the participating agents. The paper faces this issue by focusing on a real-world application: the distribution of funds to Italian research structures and substructures, after a research assessment program (known as VQR) that is currently evaluating the Italian research production over years 2004–2010. A number of desirable properties for any reasonable fair division rule are identified and exemplified for the case-study application. For instance, it is argued that the money distribution should be independent of possible alternative allocations of research products, and it should consider the actual contribution of every researcher to the outcome of the structure (s)he belongs to. Moreover, the whole process starting from the preliminary phase of products selection is dealt with, in order to prevent possible strategic behaviors from researchers that may lead their structure to miss its best possible score in the evaluation process. A fair solution based on the notion of Shapley value is described and analyzed. It turns out that the proposed solution enjoys all the desirable properties of fair division rules, and it could effectively be implemented in the VQR, as well as in related division-rules applications.