General concepts of value restriction and preference majority

摘要

Regenwetter and Grofman [17] offer a probabilistic generalization of Sen's [25, 27] classic value restriction condition when individual preferences are linear orders. They provide necessary and sufficient conditions for transitive majority preferences on linear orders. They call these conditions net value restriction and net preference majority. We study parallel generalizations for general binary relations. In general, neither net value restriction nor net preference majority is necessary for transitive majority preferences. Net value restriction is sufficient for transitive strict majority preferences, but not sufficient for transitive weak majority preferences. Net majority is sufficient for transitive majorities only if the preference relation with a net majority is a weak order. An application of our results to four U.S. National Election Study data sets reveals, in each case, transitive majorities despite a violation of Sen's original value restriction condition. We thank the National Science Foundation for funding this collaborative research through NSF grants SBR 97-30076 to Regenwetter and SBR 97-30578 to Grofman and Marley. We are indebted to the Interuniversity Consortium for Political and Social Research (ICPSR) for access to the 1968, 1980, 1992 and 1996 U.S. National Election Study (NES) data. We thank Mark Berger for helping us with the necessary data extraction. We are grateful to the action editor and the referees for extensive and helpful comments. Most of this work was carried out while the first author was a faculty member at the Fuqua School of Business, Duke University, which has generously supported our collaboration. Marley was a fellow at the Hanse-Wissenschaftskolleg, Germany, during the paper's completion.