In order to support economic development across all EU regions, € 351.8 billion -almost a third of the total EU budget- has been set aside for the Cohesion Policy during the period 2014-2020. The distribution of this budget is made throughout five main structural and investment funds, after long and though negotiations among the EU member states. The current paper analyzes the problem of allocating the limited resources of the European Regional Development Fund (ERDF) as a conflicting claims problem (O'Neill, 1982). Specifically, we show how this approach fits this actual problem, and we propose an alternative way of distributing the budget via (i) claims solutions or (ii) the imposition of bounds (guarantees) to each of the regions. We apply this approach to European Union and Spanish evidences. In both cases we obtain that the constrained equal losses rule reduces inequality and promotes convergence more properly. Keywords: conflicting claims problems; public budget distribution; European Regional Development Fund; EU convergence