Islam, Jamal and Mohajan, Haradhan and Moolio, Pahlaj
(2008):
*Preference of Social Choice in Mathematical Economics.*
Published in: Indus Journal of Management & Social Sciences
, Vol. 3, No. 1
(20 April 2009): pp. 18-38.

Preview |
PDF
MPRA_paper_50665.pdf Download (343kB) | Preview |

## Abstract

Mathematical Economics is closely related with Social Choice Theory. In this paper, an attempt has been made to show this relation by introducing utility functions, preference relations and Arrow’s impossibility theorem with easier mathematical calculations. The paper begins with some definitions which are easy but will be helpful to those who are new in this field. The preference relations will give idea in individual’s and social choices according to their budget. Economists want to create maximum utility in society and the paper indicates how the maximum utility can be obtained. Arrow’s theorem indicates that the aggregate of individuals’ preferences will not satisfy transitivity, indifference to irrelevant alternatives and non-dictatorship simultaneously so that one of the individuals becomes a dictator. The Combinatorial and Geometrical approach facilitate understanding of Arrow’s theorem in an elegant manner.

Item Type: | MPRA Paper |
---|---|

Original Title: | Preference of Social Choice in Mathematical Economics |

English Title: | Preference of Social Choice in Mathematical Economics |

Language: | English |

Keywords: | Utility Function, Preference Relation, Indifference Hypersurface, Social Choice, Arrow’s Theorem. |

Subjects: | C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C65 - Miscellaneous Mathematical Tools |

Item ID: | 50665 |

Depositing User: | Haradhan Kumar Mohajan |

Date Deposited: | 16 Oct 2013 06:57 |

Last Modified: | 28 Sep 2019 04:57 |

References: | Arrow, K. J. 1959. Rational Choice Functions and Orderings: Economica, 26(102):121-127 Arrow, K. J. 1963. Social Choice and Individual Values (2nd ed.) New York: John Wiley & Sons. Barbera, S. 1980. Pivotal voters: A New Proof of arrow’s Theorem. Economics letter, 6(1): 13-16 Breton Le M. and Weymark J. 2006. Arrovian Social Choice Theory on Economics Domains: In Arrow K. J., A. K. Sen and K. Suzumura. A Handbook of social Choice and Welfare, Volume-2, North Holland: Amsterdam. Cassels, J.W.S. 1981. Economics for the Mathematicians. Cambridge, UK: Cambridge University Press. Feldman M.A. and R. Serrano. 2006. Welfare Economics and Social Choice Theory, (2nd Ed.). New York: Springer. Feldman M.A. and R. Serrano. 2007. Arrow’s Impossibility Theorem: Preference Diversity in a Single-Profile World. Working Paper No. 2007-12: Brown University Department of Economics. Feldman M.A. and R. Serrano. 2008. Arrow’s Impossibility Theorem: Two Simple Single-Profile Version. Working Paper: Brown University Department of Economics. Geonokoplos John. 2005. The Three Brief Proof of Arrow’s Impossibility Theorem. Economic Theory, 26(1):211-215. Islam, J.N. 1997. Aspects of Mathematical Economics and Social Choice Theory. Proceedings of the Second Chittagong Conference on Mathematical Economics and its Relevance for Development (Ed.) J.N. Islam. Chittagong, Bangladesh: Chittagong. University of Chittagong. Islam, J.N. 2008. An Introduction to Mathematical Economics and Social Choice Theory.Book to appear. Miller M.K., 2009. Social Choice theory without Pareto: The pivotal voter approach. Mathematical Social Sciences (Accepted 20 Feb.2009). Myerson R.B. 1996. Fundamentals of Social Choice Theory. Discussion Paper-1162, Centre for Mathematical Studies in Economics and Management Science, Northwestern University. Pahlaj M. 2002. Theory and Applications of Classical Optimization to Economic Problems. M. Phil. Thesis. Chittagong: University of Chittagong, Bangladesh. Sato S. 2009. Strtegy-Proof Social Choice with exogenous Indifference classes: Mathematical Social Sciences Vol:57. pp.48-57. Sen, A. K. 1970. Collective Choice and Social Welfare. Holden Day: Oliver and Boyd. Suzumura K. 2007. Choice, Opportunities, and Procedures: Collected Papers of Kotaro Suzumura. Institute of Economic Research, Hitotsubashi University, Kunitatchi, Tokyo, Japan. Ubeda, Luis. 2003. Neutrality in Arrow and Other Impossibility Theorems. Economic Theory, 23(10):195-204 |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/50665 |