A model and the behavioral implications of the calculus of consent: The dilemma of public choice before public choice

The choice of a group decision-making rule is one of the most important political issues. Buchanan and Tullock have provided a framework for analyzing the optimal k-majority rule from the perspective of “methodological individualism.” They proposed the concept of “external costs” and “decision costs” and argued that the optimal k-majority rule takes place where the sum of these two costs–“total costs”–is minimized. Despite the fact that the approach is widely accepted as a tool for dealing with public decision-making rules, the study of formalizing these two costs in a quantitative manner has been relatively rare. We propose a systematic way of modeling these costs considering the assumptions mentioned by Buchanan and Tullock. We find that the resulting shape of the graphs is generally similar to that of the Buchanan-Tullock model, except for some minor details. Then, using this analytical model, we investigate several factors that could affect Buchanan-Tullock’s two costs and the optimal k-majority rule. We show that “clustering of disadvantages” (social factor) and “loss aversion” (personal factor) could increase external costs in Buchanan-Tullock’s model. These factors can result in a separation between the theoretical and actual optimal k-majority rules. Meanwhile, some recent developments in information and communication technologies can not only decrease decision costs, but also increase the same costs simultaneously through amplified “group polarization” (technological factor). If the effect of the former is not the same as that of the latter, this leads to a difference in optimal k-majority rules as well. These discrepancies bring us to the dilemma of “public choice before public choice.”