The Condorcet paradox is after Marie Jean Antoine Nicolas a Caritat, Marquis de Condorcet designated paradox with choice procedure, which affects itself particularly with the Condorcet method. It reads as follows:

It is possible that a majority prefers the option A in relation to an option B preferentially, at the same time a majority the option B give over an option C preferentially and nevertheless a majority the option C in relation to the option A.

Explanation

We accept, it give three persons x, y and z.x have thereby dearest option A, secondarydearest option B and to few gladly option C. y have dearest option B, then option C and last A. Person z finally have the desire list C, A, B.

In tabular form:

{|

! width= " 100px " |! width= " 50px " |x! width= " 50px " |y! width= " 50px " |z | - |align= |Erstwunsch |align= " center " " left " |A |align= " centers " |B |align= " centers " |C | - |align= " left " |Zweitwunsch |align= " centers " |B |align= " centers " |C |align= " centers " |A | - |align= |Drittwunsch |align= " center " " left " |C |align= " centers " |A |align= " centers " |B |} 

Two of three (x and z) prefer the option A to the option B. Zwei of three (x and y) prefer also the option B to the option C. however it give likewise two (y and z), which prefers the option C of the option A. In order to set up a common rank list in accordance with the Condorcet method, one would have to thus arrange both A before B and B before C and C before A, because in the direct comparison A before B, B before C and C before A has the majority. Such a common rank list is however not possible.

This applies naturally also, if x, y and z, but (approximately) equal large groups represent a person not only in each case.

In the reality it can come by this paradox even to the fact that the tuning leader can determine the result: It is given the above situation, and it is well-known the tuning leader. Then it, if it prefers alternative A, can let co-ordinate first between B and C: here B. thereby wins explains it C for separated and lets between A and B co-ordinate, where now A wins. It looks now in such a way, as if an overwhelming majority behind A would stand, finally this clearly over B and B clearly over C triumphed. A tuning between A and C, which would not have shown that the preference is not by any means clear, have taken place. There (particularly over requests) in the described way, affects themselves the problem is very often co-ordinated quite practically. It is not provable, but probable the fact that even in the highest committees resolutions would differently have read if after other order had been co-ordinated.

Meaning

The Condorcet paradox is a simple example for the fact that from several individual transitiven preference lists without arbitrary preference always transitive preference lists cannot collective be provided. In particular it is a special case of the impossibility set of Arrow, which proves the impossibility in principle of a "“democratic"” collective preference list. This raises some questions in the democracy theory; in particular it points to opinion of some that a democratization of economic or political decisions does not lead always to optimal results. The social choice theory examines the Condorcet paradox and other aggregation problems with tunings and elections.

Discovery

Probably first Condorcet described this paradox in its Essai sur l'application de l'analyse la dcisions the rendues la voix (Paris 1785). It came practically into oblivion, until Kenneth Arrow rediscovered it when its investigations independently of it and only some time admits of late Condorcets "„authority "“became.

Related links

• http://www.wahlrecht.de/lexikon/arrow.html

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