The European Regional Development Fund (ERDF), a significant component of the EU cohesion policy, aims to reduce regional development disparities. Currently, the ERDF allocation is handled through the Berlin method, classifying regions into less developed, transitioned, and more developed categories. However, this allocation can be framed as a claims problem, where regional needs exceed available funds. Previous research, notably Solís-Baltodano et al. (2021), explored various claims problem solutions, finding the Constrained Equal Losses (CEL) rule most effective in promoting convergence. A major drawback of CEL is its potential to assign zero funds to certain regions, making it impractical for real-world application. This paper introduces a novel approach, the CELmin rule, to address this issue by integrating a minimum guaranteed allocation while retaining the convergence-promoting properties of CEL.

The paper reviews existing literature on claims problems and their solutions. It highlights the work of O'Neill (1982) on claims problems, Fragnelli and Kiryluk-Dryjska (2019) on fast computation methods, and Solís-Baltodano et al. (2021) on applying various rules (Proportional, Constrained Equal Awards, Constrained Equal Losses, and αmin-Egalitarian) to the ERDF allocation problem. The authors also discuss related applications of claims problems in diverse sectors, including education (Pulido et al., 2002), fishing (Iñarra and Prellezo, 2008; Iñarra and Skonhoft, 2008; Kampas, 2015), and CO2 emission negotiations (Giménez-Gómez et al., 2016; Duro et al., 2020). The paper further explores concepts like sustainability and preeminence in the context of claims problems, drawing upon the work of Giménez-Gómez and Peris (2014) and Dominguez and Thomson (2006). Finally, it notes the related work by Hougaard et al. (2013a) and Alcalde and Peris (2022) on combining equal sharing principles.

The paper formally defines claims problems, representing agents as a set N = {1, 2,..., n} with claims c ∈ R, and endowment E ∈ R. Three well-known solutions—Proportional (P), Constrained Equal Awards (CEA), and Constrained Equal Losses (CEL)—are defined. The authors introduce the CELmin rule, combining the Min lower bound (Dominguez and Thomson, 2006) with the CEL rule. CELmin guarantees a minimum allocation, min{ci, E/n}, to each agent before applying CEL to the remaining endowment. The paper then conducts an axiomatic analysis of CELmin, comparing it with CEL. Several axioms are considered: Equal treatment of equals, Anonymity, Order preservation, Resource monotonicity, Super-modularity, and Order preservation under claims variations. Proposition 1 proves that CELmin satisfies all these axioms, along with the Min lower bound, while CEL does not satisfy the Min lower bound. The paper then examines axioms not satisfied by CELmin, including Limited consistency, Composition down, Composition up, Reasonable lower bounds on awards, Invariance under claims truncation, Self-duality, and Midpoint property. A table summarizes which axioms are satisfied by CELmin and CEL. Finally, the paper investigates the convergence aspect using Lorenz dominance and the Divergence Ratio (Solís-Baltodano et al., 2021) to compare the effectiveness of different allocation rules in reducing regional GDP per capita disparities.

The axiomatic analysis reveals that the proposed CELmin solution satisfies a comprehensive set of desirable properties, including Equal treatment of equals, Anonymity, Order preservation, Resource monotonicity, Super-modularity, and Order preservation under claims variations, in addition to the crucial Min lower bound property, which ensures a minimum allocation for all regions. Unlike the CEL rule, CELmin avoids zero allocations to any region. The comparison with existing rules using Lorenz dominance shows that CEA > αmin > CELmin > CEL, highlighting CELmin's position as a compromise between equity and the promotion of convergence. The Divergence Ratio analysis, employing data from the 2014-2020 ERDF programming period covering 47 NUTS2 regions, demonstrates that CELmin achieves a Divergence Ratio of 0.7957, almost identical to CEL (0.7957) and superior to P (0.7987) and αmin (0.7989) in promoting convergence. Table 2 details the per capita allocations for each rule across different regions, clearly illustrating the different distribution patterns and the minimum guaranteed allocation under CELmin. The analysis reveals that CELmin effectively addresses the issue of zero allocations faced by CEL, while maintaining a strong convergence-promoting capability.

The findings demonstrate that CELmin offers a practical and effective solution for ERDF allocation. By ensuring a minimum allocation to each region, it addresses a critical limitation of the CEL rule while maintaining its efficiency in reducing regional disparities. The convergence-promoting ability of CELmin, as demonstrated by the Divergence Ratio analysis, is comparable to CEL, outperforming other rules. The axiomatic analysis further validates the robustness of CELmin, showcasing its compliance with desirable fairness properties. The results highlight the importance of balancing egalitarian principles with the need for practical implementation in resource allocation problems. The study’s contribution lies in providing a refined allocation mechanism that addresses the practical shortcomings of existing approaches while retaining their beneficial properties.

This paper presents CELmin, a novel rule for distributing the ERDF budget, successfully balancing egalitarian principles with practical considerations. The rule guarantees a minimum allocation to all regions while effectively promoting convergence, surpassing existing methods in this regard. Future research could explore the application of CELmin in other resource allocation scenarios characterized by conflicting claims and the need for both fairness and practical implementation, such as environmental negotiations or public service resource distribution.

The study uses data from the 2014-2020 ERDF programming period. Future research should consider more recent data to assess the continued effectiveness of CELmin. The model assumes that the claims accurately reflect regional needs; any inaccuracies in claim estimation could affect the results. The model does not incorporate political or other non-economic factors that might influence real-world allocation decisions. Furthermore, the study primarily focuses on the quantitative aspects of the allocation problem and does not delve deeply into the qualitative aspects of regional development needs.