Convergent menus of social choice rules

Abstract

Suzuki and Horita [11] proposed the notion of convergence as a new solution for the procedural choice problem. Given a menu of feasible social choice rules (SCRs) F and a set of options X, a preference profile L0 is said to (weakly) converge to C⊆X if every rule to choose the rule (or every rule to choose the rule to choose the rule, and so on) ultimately designates C under a consequential sequence of meta-preference profiles. Although its frequency is shown, for example, under a large society with F,= {plurality, Borda, anti-plurality}, a certain failure (trivial deadlock) occurs with small probability. The objective of this article is to find a convergent menu (a menu that can “always” derive the convergence). The results show that (1) several menus of well-known SCRs, such as {Borda, Hare, Black}, are convergent and that (2) the menu {plurality, Borda, anti-plurality} and a certain class of scoring menus can be expanded so that they become convergent.