This paper explores the possibility of obtaining and defending a particular conception of social rights based on Robert Nozick´s Entitlement theory. I will sustain that this theory provides several paths towards a more than a minimal State. Here, I will focus on one which was developed by applying the concept of "voluntary exchange" as a starting point. For this purpose, after questioning the narrow concept of “voluntary action” normally adopted by libertarians, we will then introduce Aristotle´s notion of "mixed actions" which reflects the conditions under which agents in fact undertake contracts. We will argue that forging agreements based on mixed actions poses a series of problems for the entitlement theory, dilemmas that can only be remedied by introducing distributive patterns. These patterns should lead to a subsidiary State and the combination of Nozick´s theory with sufficientarist criteria regarding distribution in favor of the most needy members of society