Abstract
Most studies of cooperative firms have been conducted using neoclassically inspired economic models that consider the characteristics and behavior of capitalist companies and their owners, thus failing to accommodate the wide range of criteria that motivate the creation of cooperative firms. These models have traditionally been at odds with the real objectives of cooperative firms due to their inability to accommodate a series of often conflicting criteria. We put forth a set-theoretic model of governance of cooperative firms that allows us to investigate how different models of cooperative governance can be implemented and how cooperative decision-making can be solved using a multicriteria decision analysis approach.
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In the context of common goods, appropriators are conceptually equivalent to end beneficiaries or users.
The cooperative global values of a process \({\mathfrak{p}}_l\) in \({\mathbb{P}}^1 = {\mathbb{P}}^*\) is given as per Eq. 4 of Definition 32, where \(q_l\) stands for both the number of shareholders of subtypes 1.1 and 1.2 that are allowed to participate in the process \({\mathfrak{p}}_l \in {\mathbb{P}}^{1} = {\mathbb{P}}^*\), with l such that \(1 \le l \le p_2\), and the number of shareholders of subtype 1.1 that are allowed to participate in the process \({\mathfrak{p}}_l \in {\mathbb{P}}^{1} = {\mathbb{P}}^{*}\), with l such that \(1 \le l \le p_1 = p^*\). \(\xi ^l_{j}\) is the global value collaboratively assigned to alternative j by all shareholders of subtypes 1.1 and 1.2.
Without loss of generality, we are assuming that the cooperative decision \({\mathfrak{d}}_l\) in \({\mathbb{D}}\) is characterized as a sorting problem. A sorting problem can be solved by a multicriteria decision analysis (MCDA) method such as the one introduced in Sect. 3.5. If the cooperative decision \({\mathfrak{d}}_l\) were to be characterized as a classification or a filtering problem, we would apply other MCDA methods to come up with the stakeholder global value matrix of a process.
Note that, as per Definition 36, these sets are not required to be distinct.
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Acknowledgments
The authors owe a debt of gratitude to the management team of Copeval for their time and cooperation regarding the case study described in Sect. 4 of this article and to two anonymous reviewers whose comments and suggestions greatly improved earlier versions of this article. The authors were supported by the Faculty of Economics and Business at Diego Portales University in Chile and by the Department of Business Administration at the University of Zaragoza in Spain.
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Paredes-Frigolett, H., Nachar-Calderón, P. & Marcuello, C. Modeling the governance of cooperative firms. Comput Math Organ Theory 23, 122–166 (2017). https://doi.org/10.1007/s10588-016-9219-z
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DOI: https://doi.org/10.1007/s10588-016-9219-z