In a democracy, Bayrou would have won. Application of the Borda Fixed Point method to the 2007 French presidential elections

Colignatus, Thomas (2007): In a democracy, Bayrou would have won. Application of the Borda Fixed Point method to the 2007 French presidential elections.

Abstract

Democratic nations are advised to have parliaments select the chief executive by the Borda Fixed Point method. The current practice of having direct popular elections using systems that have originated in history is inoptimal and actually quite undemocratic since winners are selected who don’t reflect the national sentiment. The paper gives the example of the 2007 French presidential elections. Under the currently and historically grown system of run-off plurality Sarkozy got elected while the more democratic method of Borda Fixed Point would have generated Bayrou. The example uses reasonable assumptions on underlying micro preferences. The parliamentary vote that followed the presidential vote and that annihilated Bayrou increased the paradox but not the principles involved.

• Item Type: MPRA Paper
• Institution: Thomas Cool Consultancy & Econometrics
• Language: English
• Keywords: voting theory; voting systems; elections; public choice; political economy; run-off plurality; Borda Fixed Point; democracy
• Subjects: D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice ; Clubs ; Committees ; Associations; A - General Economics and Teaching > A2 - Economic Education and Teaching of Economics; H - Public Economics > H0 - General

References

Thomas Colignatus is the preferred name of Thomas Cool in science.

EWP references are to the Economics Working Papers Archive at the Washington University at St. Louis: http://econwpa.wustl.edu. See also http://www.dataweb.nl/~cool.

To enhance completeness, the following lists the literature in Colignatus (2007b) as well (which in itself need not be complete).

Ancot & Hughes Hallet (1984), “Establishing public preferences for coalition government: an empirical study in economic planning behavior”, De Economist, p153-170

Aronson, E. (1972, 1992a), “The social animal”, Freeman, sixth edition 1992

Aronson, E. (ed) (1973, 1992b), Readings about The Social Animal”, Freeman, sixth edition 1992

Arrow, K, & T. Scitovsky eds. (1969), “Readings in welfare economics”, Allen & Unwin

Arrow, K. & F. Hahn (1971), “General competitive analysis”, North Holland

Arrow, K. (1950), “A difficulty in the concept of social welfare”, J. of political economy, pp328-346, reprinted in Arrow & Scitovsky (1969) pp147-168

Arrow, K. (1951, 1963), “Social choice and individual values”, J. Wiley

Barrow, J.D. (1998), “Impossibility. The limits of science and the science of limits”, Vintage

Bernstein (1992), “Capital ideas”, The Free Press

Bernstein (1996), “Against the gods”, Wiley

Blanchard, O. & S. Fischer (1989), “Lectures on macroeconomics”, MIT

Bochenski (1956, 1970), “A history of formal logic”, 2nd edition, Chelsea

Csikszentmihalyi (1997), “Finding flow”, Basic Books

Colignatus (1990c), “Why a social welfare (meta) function does exit: The Arrow Impossibility Theorem for Social Choice resolved, A better analysis suggested,” internal note Central Planning Bureau, The Hague, reprinted in Colignatus (1992b) pp57-104

Colignatus (1992a), “On the reasonableness and the moral desirability of the conditions of Arrow’s Theorem”, published in Colignatus (1992b) pp273-285

Colignatus (1992b), “Definition and Reality in the general theory of political economy; Some background papers 1989-1992”, ISBN 905518-207-9, Magnana Mu Publishing and Research, Rotterdam

Colignatus (1996b), “A constitutional amendment for an Economic Supreme Court”, ewp-get/9604003

Colignatus (1997b) “The solution to Arrow’s difficulty in social welfare”, ewp-get/9707001

Colignatus (1999a), “Proper definitions for risk and uncertainty”, EconWPA ewp-get/9902002

Colignatus (2000), "Definition and Reality in the General Theory of Political Economy", Samuel van Houten Genootschap, ISBN 90-802263-2-7, JEL 2000-1325

Colignatus (2000a), "Aspects of testing (matching, ranking and rating)", ewp-get/0004004

Colignatus (2000b), "The choice on sustainability: information or the meta-SWF approach to a shift of preferences", ewp-othr/0004004

Colignatus (2000c), "The seminal contribution of Roefie Hueting to economic science: Theory and measurement of Sustainable National Income", November 16 2000, see the internet

Colignatus (2001), "Voting Theory For Democracy", first edition, ISBN-90-804774-3-5

Colignatus (2005), "Definition and Reality in the General Theory of Political Economy", 2nd edition, Dutch University Press

Colignatus (2007a), "A Logic of Exceptions", ISBN 978-90-804774-4-5

Colignatus (2007b), “Voting theory for democracy”, 2nd edition, Thomas Cool Econometrics & Consultancy

Cool (1999, 2001), “The Economics Pack, Applications for Mathematica”, Scheveningen, JEL-99-0820, ISBN 90-804774-1-9 (website update 2007)

Cullis, J. & P. Jones (1992), "Public finance & public choice", McGraw-Hill

Dahl & Lindblom (1976), “Politics, economics and welfare”, Chicago

Dahl, R (1956), “A preface to democratic theory”, Chicago

Dasgupta, A.K. & D.W. Pearce (1980), “Cost-benefit analysis”, Macmillan

DeLong, H. (1971), “A profile of mathematical logic”, Addison Wesley

Doel, J. van den, and B.C.J. van Velthoven (1990), “Democratie en welvaartstheorie”, Samson

Dopp (1969), “Formale Logik”, Benziger Verlag, Einsiedeln

Eatwell c.s. (1998), “The New Palgrave”, Macmillan (entries risk, risk aversion, Arrow' Theorem, Social Welfare)

Elo, A.E. (1978), "The Rating of Chess Players, Past and Present", Arco Publishing, Inc., New York.

Ferguson, Th. (1967), “Mathematical statistics”, Academic Press

Freeman, J. (1994), "Simulating neural networks with Mathematica", Addison-Wesley

French Government (2007), “Resultats des elections legislatives”, June 17, http://www.interieur.gouv.fr/sections/a_votre_service/resultats-elections/LG2007/FE.html, retrieved from source

Good, A. & F. Graybill (1950, 1963), "Introduction to the theory of statistics", McGraw-Hill

Hart (1961, 1997), “The concept of law”, Oxford

Hicks (1981), “Collected essays on economic theory, volume I; Wealth and welfare”, Blackwell

Hornby (1985), “Oxford advanced learner’s dictionary of current English”, Oxford

Huang, C. & P. Crooke (1997), "Mathematics and Mathematica for economists", Blackwell

Johansen (1969), “An examination of the relevance of Kenneth Arrow’s general possibility theorem for economic planning”, Economics of planning 9, pp5-41

Jorgenson, D. (1990), “Aggregate consumer behavior and the measurement of social welfare”, Econometrica 58 no 5 pp1007-1040

Luce & Raiffa (1957), “Games & decisions”, J. Wiley

Luenberger, D. (1998), “Investment science”, Oxford

Maeder, R. (1991), "Programming in Mathematica", Addison-Wesley

Mas-colell, A., M. Whinston and J. Green (1995), “Microeconomic theory”, Oxford

Moulin, H. (1988), "Axioms of cooperative decision making", Econometric Society monographs ; 15, CUP

Mueller (1989), “Public Choice II”, Cambridge

Noguchi, Asahi (1993), “General Equilibrium models”, in Varian (ed), “Economic and financial modeling with Mathematica”, Springer Telos 1993 pp 104-123

NRC-Handelsblad (2007a), “In permanente staat van ontbinding”, June 9 2007

NRC-Handelsblad (2007b), “Franse oppositie strijdt voor pluralisme”, June 11 2007

Paulus, J.A. (1990), "Ik denk, dus ik lach", Ooievaar pockets ("I think, therefore I laugh", Columbia University Press 1985)

Pikkemaat, A. (1990), “Arrow’s significance for economic science in the Netherlands”, De Economist 138 No 3 p235-255

Rafiei, D. & A. Mendelzon (2000), "What is this Page Known for? Computing Web Page Reputations", http://www9.org/w9cdrom/index.html

Rijken van Olst, H. (1969), "Inleiding tot de statistiek", Part I-II-III, Van Gorcum

Ruckeer, R. (1988), "Mind tools", Penguin

Saari, D, (internet), "The symmetry and complexity of elections" (S&C)

Saari, D, (internet), "Explaining all three alternative voting outcomes" (E3)

Saari, D, (internet), "Connecting and resolving Sen's and Arrow's theorems" (C&R)

Saari, D. (2001a), Chaotic elections, AMS, 2001, www.ams.org

Saari, D. (2001b), Decisions and Elections. Explaining the unexpected, CUP

Schrijver (1987), “Analyse van macro-economische beleidspreferenties met behulp van optimale besturingstheorie”, Research memorandum 35, CPB

Sen, A. (1970), "Collective choice and social welfare", North Holland

Sen, A. (1986), “Social choice theory,” p1073-1181 in Arrow & Intrilligator eds. (1986), “Handbook of mathematical economics, Volume III”, North Holland

Sen, A. (1999a), “Development as freedom”, Knopf

Sen, A. (1999b), “The possibility of social choice”, AER p349-366 (excluding literature)

Shone, R. (1998), "Economic dynamics", Cambridge (uses Mathematica)

Sudgen, R. (1999), “Book review: On voting. A public choice approach. By Gordon Tullock”, JEL 1715-1716 (December)

Swank, O. (1989). “The objectives of Democrats and Republicans In the United States, 1956—1984”, Rotterdam

Takayama, A. (1974), “Mathematical economics”, The Dryden Press

The Economist (2000),

The New Palgrave, Macmillan 1988 - see Eatwell

Theil, H. (1971), “Principles of econometrics”, John Wiley

Tinbergen, J. (1956), “Economic policy: principles and design”, North-Holland

Tinbergen, J. (1985), “Production, income and welfare: the search for an optimal social order”, Weatsheaf books, Harvester press

Tobin, J. (1990), “On the theory of macroeconomic policy”, Tinbergen Lecture, De economist 138 pp1-14

Varian, H. (ed) (1993), “Economic and financial modeling with Mathematica”, Springer Telos

Varian, H. (ed) (1996), “Computational economics and finance”, Springer Telos

Weingast B.R. and D. Wittman (2006), "The Oxford Handbook of Political Economy", OUP

Wikipedia (2007a), Data on the French presidential elections, http://en.wikipedia.org/wiki/Politics_of_France (Retrieved May 9 2007)

Wikipedia (2007b), Data on the French parliamentary elections, http://en.wikipedia.org/wiki/French_legislative_election%2C_2007 (Retrieved June 27 2007)

Wilson, J.Q. (1993), “The moral sense”, The Free Press

Wolfram, S. (1992), “Mathematica”, Addison-Wesley

Wolfram, S. (1996), “Mathematica 3.0”, Cambridge