Sen's Theorem: Geometric Proof and New Interpretations

Author(s): Li, Lingfang(Ivy); Saari, Donald | Abstract: Sen’s classic social choice result reportedly demonstrates a conflict between standard welfare concepts from economics and liberalism—even forms of liberalism that are very minimal. By providing what appears to be the first direct general proof of this seminal result, we reinforce a very di�erent interpretation: Sen’s result occurs because one of his assumptions negates the e�ects of another. Our proof leads to other interpretations of Sen’s conclusion, which identify other kinds of societal conflicts and describes the problems Sen identified in terms of probability. By clarifying the central source of Sen’s result, our proof suggests new and practical ways to sidestep these diculties. But a general resolution remains to be found. 1 2

[1]  A. Sen,et al.  Collective Choice and Social Welfare , 2017 .

[2]  Donald G. Saari,et al.  Negative externalities and Sen’s liberalism theorem , 2006 .

[3]  Christian List,et al.  A simple proof of Sen's possibility theorem on majority decisions , 2005 .

[4]  D. Saari.  Decisions and elections : explaining the unexpected , 2001 .

[5]  Donald G. Saari,et al.  The Sum of the Parts Can Violate the Whole , 2001, American Political Science Review.

[6]  A. Sen,et al.  The Possibility of Social Choice , 1999 .

[7]  Donald G. Saari,et al.  Connecting and resolving Sen's and Arrow's theorems , 1998 .

[8]  J. Kelly,et al.  Sen's theorem and externalities , 1997 .

[9]  K. Suzumura.  Rational Choice, Collective Decision And Social Welfare (位相幾何学と経済学) , 1980 .

[10]  Amartya Sen,et al.  Liberty, Unanimity and Rights , 1976 .

[11]  Ben Fine,et al.  Individual Liberalism in a Paretian Society , 1975, Journal of Political Economy.

[12]  A. Sen,et al.  The Impossibility of a Paretian Liberal , 1970, Journal of Political Economy.

[13]  Amartya Sen,et al.  A Possibility Theorem on Majority Decisions , 1966 .

[14]  Anne Brunel-Petron.  Contribution à l'analyse des droits en théorie du choix social , 1998 .

[15]  Peter J. Hammond,et al.  Game Forms versus Social Choice Rules as Models of Rights , 1996 .

[16]  Prasanta K. Pattanaik,et al.  On Modelling Individual Rights: Some Conceptual Issues , 1996 .

[17]  D. Saari.  Basic Geometry of Voting , 1995 .

[18]  Joshua Cohen,et al.  Review of "Inequality Reexamined" by Amartya Sen , 1995 .

[19]  Amartya Sen,et al.  Liberty and Social Choice , 1983 .

[20]  Julian Le Grand,et al.  The Political Economy Of Public Choice , 1981 .

[21]  K. Arrow,et al.  You have printed the following article : A Difficulty in the Concept of Social Welfare , 2022 .

[22]  Karla Cecilia,et al.  Economica , 2006 .