Methods of voting system and manipulation of voting

Islam, Jamal and Mohajan, Haradhan and Moolio, Pahlaj (2010): Methods of voting system and manipulation of voting. Published in: International Journal of Management and Transformation , Vol. 5, No. 1 (30 June 2011): pp. 10-34.

Abstract

In this paper an attempt has been taken to describe various types of voting system and manipulation of them. French philosophers Marquis de Condorcet (1743-1794) and Jeans-Charles Borda (1733-1799) introduced modern voting system. Duncan Black first introduced the manipulation of voting in 1958 in his book “Theory of Committee and Elections”. Condorcet, Borda and even many modern politicians believe that elections are logically imperfect. In this paper this imperfection is analyzed in some detail. In this paper voting methods are discussed in very simple but in a detailed manner. Voting system is directly involved with Economics, Political Science and Social Science. So that if one has no proper knowledge of the voting system then he can not serve the society in proper way and cannot expect the economic development of the society. Some voting methods such as Arrow’s theorem, median voter theorem, randomized voting, Muller-Satterthwaite theorem and Gibbard-Satterthwaite theorem are apparently non-manipulable and are included in this paper.

• Item Type: MPRA Paper
• Language: English
• Keywords: Voting system, voting paradox, manipulation of voting, Condorcet winner, dictatorship, strategy-proofness.
• Subjects: C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables

References

Arrow, K.J. (1951), Social Choice and Individual Values, 1st ed., John Wiley & Sons, New York.

Arrow, K.J. (1963), Social Choice and Individual Values, 2nd ed., John Wiley & Sons, New York.

Austen-Smith, D. and Banks, J.S. (1999), Positive Political Theory I: Collective Preference, Ann Arbor, The University of Michigan Press.

Barbera, S. (1980), Pivotal Voters: A New Proof of Arrow’s Theorem. Economics Letters, 6(1): 13-16.

Black, D. (1948), On the Rationale of Group Decision-making, The Journal of Political Economy, 56(1): 23-34.

Black, D. (1958), The Theory of Committees and Elections, Cambridge: Cambridge University Press.

Blackorby, C., Bossert, W. and Donaldson, D. (2002), Utilitarianism and the Theory of Justice, In: Arrow, K.J., Sen, A.K. and Suzumura, K. (Eds.), Handbook of Social Choice and Welfare, 2, Elsevier, Amsterdam.

Blackorby, C., Donaldson, D. and Weymark, J.A. (1990), A Welfarist Proof of Arrow’s Theorem, Researches économiques de Louvain, 56: 259-286.

Borda, (1781), Mémoire sur les élections au scrutin, In: the Historie de l’Académie Royale des Sciences, Paris.

Bossert, W. and Weymark, J.A. (2004), Utility in Social Choice, In: Barbera, S., Hammond, P. and Seidl, C. (Eds.), Handbook of Utility Theory, 2: Extensions, Kluwer, Dordrecht.

Brams, S.J. and Fishburn, P.C. (1978), Approval Voting, American Political Science Review, 72 (3): 831-847.

Condorcet, M. (1785), Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix, Paris.

Congleton, R.D. (2004), The median voter model, In: Rowley, C.K. and Schneider, F. (Eds.), The Encyclopedia of Public Choice, 2, Kluwer, Dordrecht: 382-387.

Droop, H.R. (1881), On Methods of Electing Representatives, Journal of the Statistical Society of London, 44 (2): 141- 202.

Dummett, M. (1998), The Borda Count and Agenda Manipulation, Social Choice and Welfare, 15: 289-296.

Feldman, M.A. (1974), A Very Unsubtle Version of Arrow’s Impossibility Theorem, Economic Inquiry, 12 (4): 534-546.

Feldman, M.A. (1979), Manipulating Voting Procedures, Economic Inquiry, 17 (3): 452-474.

Feldman, M.A. and Serrano, R. (2006), Welfare Economics and Social Choice Theory, 2nd ed., Springer, New York.

Feldman, M.A. and Serrano, R. (2007), Arrow’s Impossibility Theorem: Preference Diversity in a Single-Profile World, Working Paper No. 2007-12: Department of Economics, Brown University.

Feldman, M.A. and Serrano, R. (2008), Arrow’s Impossibility Theorem: Two Simple Single-Profile Versions, Working Paper, Department of Economics, Brown University.

Gans, J.S. and Smart, M. (1996), Majority Voting with Single-Crossing Preferences, Journal of Public Economics, Elsevier, 59 (2): 219-237.

Gibbard, A. (1973), Manipulation of Voting Schemes: A General Result, Econometrica, 41: 587-601.

Gibbard, A. (1978), Straightforwardness of Game Forms with Lotteries as Outcomes, Econometrica, 46(3): 595-614.

Islam, J.N. (1997), Aspects of Mathematical Economics and Social Choice Theory, In: Islam, J.N. (Ed.), Proceedings of the Second Chittagong Conference on Mathematical Economics and its Relevance for Development, University of Chittagong, Bangladesh.

Islam, J.N. (2008), An Introduction to Mathematical Economics and Social Choice Theory, Book to Appear.

Islam, J.N., Mohajan, H.K. and Moolio, P. (2009), Preference of Social Choice in Mathematical Economics, Indus Journal of Management & Social Sciences, 3(1): 17-38.

Islam, J.N., Mohajan, H.K. and Moolio, P. (2009), Political Economy and Social Welfare with Voting Procedure, KASBIT Business Journal, 2(1): 42-66 (spring and fall).

Le Breton, M. and Weymark, J.A. (2002), Arrovian Social Choice Theory on Economics Domains, In: Arrow, K.J., Sen, A.K. and Suzumura, K. (Eds.), Handbook of Social Choice and Welfare, 2, Elsevier, Amsterdam.

McLennan, A. (2008), Manipulation in Elections with Uncertain Preference, Unpublished Manuscript.

Miller, M.K. (2009), Social Choice Theory without Pareto: The Pivotal Voter Approach, Mathematical Social Sciences,58(2009): 251-255.

Myerson, R.B. (1985), An Introduction to Game Theory, Discussion Paper No. 623, Center for Mathematical Studies in Economics and Management Science, Northwestern University.

Myerson, R.B. (1993), Effectiveness of Electoral Systems for Reducing Government Corruption: A Game-Theoretic Analysis, Games and Economic Behavior, 5(1): 118-132.

Myerson, R.B. (1996), Fundamentals of Social Choice Theory, Discussion Paper No. 1162, Centre for Mathematical Studies in Economics and Management Science, Northwestern University.

Myerson, R.B. (2006), Federalism and Incentives for Success of Democracy, Quarterly Journal of Political Science, 1(1): 3-23.

Myerson, R.B. (2009), Constitutional Structures for a Strong Democracy: Considerations on the Government of Pakistan, Presentation Paper at Lahore University of Management Sciences.

Muller, E. and Satterthwaite, M.A. (1977), The Equivalence of Strong Positive Association and Strategy-proofness, Journal of Economic Theory, 14(2): 412-418.

Newland, R.A. and Britton, F.S. (1997), How to Conduct an Election by the Single Transferable Vote: ERS, 3rd edition.

O’Neill, J.C. (2004), Tie-Breaking with the Single Transferable Vote, Voting Matters, 18: 14-17.

Penn, E.M., Gailmard, S. and Patty J.W. (2008), Strategic Manipulation in Representative Institution: Conference Paper/Unpublished Manuscript.

Reny, P.J. (2000), Arrow’s Theorem and Gibbard-Satterthwaite Theorem: A Unified Approach, Mimeo, Department of Economics, University of Chicago.

Risse, M. (2005), Why the count de Borda cannot beat the Marquis de Condorcet, Social Choice and Welfare, 25(October): 95-113.

Robert, F. and Tsoukiàs, A. (2009), Voting Theory and Preference Modeling, Mathematical Social Sciences, 57(3): 289-291.

Saporiti, A. and Thomé, F. (2006), Single-Crossing, Strategic Voting and the Median Choice Rule, Social Choice and Welfare, 26(2): 363-383.

Saporiti, A. (2008), Strategy-Proof and Single-Crossing, Unpublished Manuscript, University of Manchester.

Sato, S. (2009), Strategy-Proof Social Choice with Exogenous Indifference Classes, Mathematical Social Sciences, 57(1): 48-57.

Satterthwaite, M.A. (1975), Strategy-Proofness and Arrow’s Conditions: Existence and Correspondence Theorems for Voting Procedures and Social Welfare Functions, Journal of Economic Theory, 10: 198-217.

Serais, J. (2002), Cloning Manipulation of the Borda Rule, Meeting SCW, GEMMA-CRÈME, University of Caen, France.

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.