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In this study, we introduce a different mechanism with a hybrid ownership definition lying in between public and private ownership. Agents have claims over the endowments and the total production of the economy instead of having absolute ownership rights. We define social desirability as the following: an alternative x is socially preferred to an alternative y if the majority of the agents prefer x to y. In this context, we investigate whether the competitive equilibrium outcome is socially the most desirable outcome and whether there are other efficient outcomes socially preferred to the competitive equilibrium outcome. We use a voting scheme where agents vote on the production alternatives of the economy. We investigate if there is a voting rule that leads to the competitive equilibrium outcome and what kind of a rule this latter is. The central finding of the study is that, for a class of production and utility functions, there is a voting rule that leads to the competitive equilibrium outcome. Moreover, this is a weighted voting rule where agents’ votes are their initial claims. A second important contribution is the analysis of the process of candidate nomination, which is most of the time, neglected by social choice problems. Finally, we consider the transfer problem where agents make transfers to other agents to make them vote on specific alternatives.