Abstract
AbstractInfinite regress lies within every democratic procedural choice. If society members try to select an appropriate rule [social choice correspondence (SCC)] entirely endogenously, they will need an appropriate rule to choose such a rule. However, this should also be selected by an appropriate rule to choose a rule to choose a rule, and so on. This paper explores how to solve this infinite regress. A preference profile over the set of alternatives is said to converge if, at a sufficiently high level, every feasible SCC in the menu ultimately results in the same alternative, and hence, further regress has no effective meaning. A menu is said to be convergent if all preference profiles converge under the menu (i.e., infinite regress can “always” be resolved). First, we characterize the convergent menus under a special case. Then, we prove two general possibility theorems: (1) there exists a menu of SCCs that is strongly convergent (i.e., the outcome is uniquely determined); (2) any set of scoring rules can be extended to a superset that is asymptotically convergent for a large society (i.e., the probability of a convergent profile occurring goes to one as the population goes to infinity). Therefore, such a large society can “almost always” resolve the infinite regress by adding multiple SCCs. These theorems are expected to build new ground for SCCs in a distinct way from the axiomatic characterizations of standard social choice theory.
Funder
Japan Society for the Promotion of Science
The University of Tokyo
Publisher
Springer Science and Business Media LLC
Subject
Management of Technology and Innovation,Strategy and Management,General Social Sciences,Arts and Humanities (miscellaneous),General Decision Sciences
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