We consider the problem of designing legislative mechanisms that guarantee equilibrium existence, Pareto-efficiency, and inclusiveness. To address this question, we propose a finite-horizon voting procedure that embeds clauses of reciprocity. These clauses grant voters the right to oppose actions that are not in their interest, retract actions that face opposition, and punish harmful actions. We study voters' strategic behavior under this voting procedure using two classical approaches. Following the blocking approach, we introduce two related solution concepts---the reciprocity set and the sophisticated reciprocity set---to predict equilibrium policies. We then show that these solution concepts (1) are always non-empty; (2) only select Pareto-efficient policies; (3) strategically protect minority interests; and (4) are compatible with classical notions of fairness and Rawlsian justice in distributive problems. Following the non-cooperative approach, we provide an implementation of each of these solution concepts in subgame perfect equilibrium, which makes them applicable in a wide range of legislative settings. We also extend them to effectivity functions, a large class of games that includes strategic form games. A comparative analysis shows that the reciprocity mechanism has other desirable features and properties that distinguish it from other well-known voting mechanisms and solution concepts.
Pongou, Roland and Tondji, Jean-Baptiste, A Political Reciprocity Mechanism (September 20, 2021). Available at SSRN: https://ssrn.com/abstract=3343700 or http://dx.doi.org/10.2139/ssrn.3343700