Colignatus, Thomas (2011): Arrow’s Impossibility Theorem and the distinction between Voting and Deciding.
Download (141kB) | Preview
Arrow’s Impossibility Theorem in social choice finds different interpretations. Bordes-Tideman (1991) and Tideman (2006) suggest that collective rationality would be an illusion and that practical voting procedures do not tend to require completeness or transitivity. Colignatus (1990 and 2011) makes the distinction between voting and deciding. A voting field arises when pairwise comparisons are made without an overall winner, like in chess or basketball matches. Such (complete) comparisons can form cycles that need not be transitive. When transitivity is imposed then a decision is made who is the best. A cycle or deadlock may turn into indifference, that can be resolved by a tie-breaking rule. Since the objective behind a voting process is to determine a winner, then it is part of the very definition of collective rationality that there is completeness and transitivity, and then the voting field is extended with a decision.
|Item Type:||MPRA Paper|
|Institution:||Thomas Cool Consultancy & Econometrics|
|Original Title:||Arrow’s Impossibility Theorem and the distinction between Voting and Deciding|
|Keywords:||economic crisis; voting theory; democracy; economics and mathematics;|
|Subjects:||D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice; Clubs; Committees; Associations
A - General Economics and Teaching > A1 - General Economics > A10 - General
P - Economic Systems > P1 - Capitalist Systems > P16 - Political Economy
|Depositing User:||Thomas Colignatus|
|Date Deposited:||21. Nov 2011 16:00|
|Last Modified:||19. Feb 2013 00:01|
Thomas Colignatus is the preferred name of Thomas Cool in science.
Arrow, K. (1951, 1963), “Social choice and individual values”, J. Wiley
Arrow, K. (1988), entry on his theorem in The New Palgrave, Macmillan
Bordes, G. and N. Tideman (1991), “Independence of Irrelevant Alternatives in the Theory of Voting” Theory and Decision 30 (1991), 163-86.
Colignatus, Th. (1990), “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 90-III-37, The Hague
Colignatus, Th. (2011a), “Voting Theory for Democracy”, 3rd edition, T. Cool (Consultancy & Econometrics), http://www.dataweb.nl/~cool/Papers/VTFD/Index.html
Colignatus, Th. (2011b), “Yes we can, in Cannes”, http://www.dataweb.nl/~cool/Papers/Drgtpe/Crisis-2007plus/2011-10-28-YesWeCan-in-Cannes.html
Colignatus, Th. (2011c), “Response to a review of Voting Theory for Democracy, in the light of the economic crisis and the role of mathematicians”, http://mpra.ub.uni-muenchen.de/34615
Schulze, M. (2011), “Review “Voting Theory for Democracy””, Voting Matters, Issue 29, October 2011, http://www.votingmatters.org.uk/ISSUE29/INDEX.HTM and http://www.votingmatters.org.uk/ISSUE29/I29P5.pdf
Sen, A. (1970), “Collective choice and social welfare”, North Holland
Stavrou, P. (2011), “Chaos in Europe, the G20 in Cannes and the need for constitutional changes – Interview with Thomas Colignatus”, November 3, http://protes-stavrou.blogspot.com/2011/11/chaos-in-europe-g20-in-cannes-and-need.html
Tideman, N. (2006), “Collective Decisions and Voting: The Potential for Public Choice”, Ashgate Publishing