The voting paradox …is a situation noted by the Marquis de Condorcet
in the late 18th century, in which collective preferences can be
cyclic …even if the preferences of individual voters are not. This
is paradoxical, because it means that majority wishes can be in
conflict with each other. When this occurs, it is because the
conflicting majorities are each made up of different groups of
individuals. For example, suppose we have three candidates, A, B and
C, and that there are three voters with preferences as follows
(candidates being listed in decreasing order of preference):
Voter 1: A B C
Voter 2: B C A
Voter 3: C A B
If C is chosen as the winner, it can be argued that B should win
instead, since two voters (1 and 2) prefer B to C and only one voter
(3) prefers C to B. However, by the same argument A is preferred to B,
and C is preferred to A, by a margin of two to one on each occasion.
The requirement of majority rule then provides no clear winner.
Also, if an election were held with the above three voters as the only
participants, nobody would win under majority rule, as it would result
in a three way tie with each candidate getting one vote. However,
Condorcet’s paradox illustrates that the person who can reduce
alternatives can essentially guide the election. For example, if Voter
1 and Voter 2 choose their preferred candidates (A and B
respectively), and if Voter 3 was willing to drop his vote for C, then
Voter 3 can choose between either A or B – and become the agenda-
setter.
When a Condorcet method is used to determine an election, a voting
paradox among the ballots can mean that the election has no Condorcet
winner. The several variants of the Condorcet method differ on how
they resolve such ambiguities when they arise to determine a winner.
Note that there is no fair and deterministic resolution to this
trivial example because each candidate is in an exactly symmetrical
situation.
The phrase "Voter’s Paradox" is sometimes used for the rational choice
theory prediction that voter turnout should be 0.
http://en.wikipedia.org/wiki/Voting_paradox
http://en.wikipedia.org/wiki/Voting_system#Foundations_of_voting_theory
http://www.google.com/search?hl=en&q=define%3ATransitivity
On Tue, 8 Jun 2010 17:10:50 -0700 (PDT), Immortalista
- Hide quoted text — Show quoted text -
<extro…@hotmail.com> wrote:
>The voting paradox …is a situation noted by the Marquis de Condorcet
>in the late 18th century, in which collective preferences can be
>cyclic …even if the preferences of individual voters are not. This
>is paradoxical, because it means that majority wishes can be in
>conflict with each other. When this occurs, it is because the
>conflicting majorities are each made up of different groups of
>individuals. For example, suppose we have three candidates, A, B and
>C, and that there are three voters with preferences as follows
>(candidates being listed in decreasing order of preference):
>Voter 1: A B C
>Voter 2: B C A
>Voter 3: C A B
>If C is chosen as the winner, it can be argued that B should win
>instead, since two voters (1 and 2) prefer B to C and only one voter
>(3) prefers C to B. However, by the same argument A is preferred to B,
>and C is preferred to A, by a margin of two to one on each occasion.
>The requirement of majority rule then provides no clear winner.
>Also, if an election were held with the above three voters as the only
>participants, nobody would win under majority rule, as it would result
>in a three way tie with each candidate getting one vote. However,
>Condorcet’s paradox illustrates that the person who can reduce
>alternatives can essentially guide the election. For example, if Voter
>1 and Voter 2 choose their preferred candidates (A and B
>respectively), and if Voter 3 was willing to drop his vote for C, then
>Voter 3 can choose between either A or B – and become the agenda-
>setter. ………….
And this so-called "paradox" not surprisingly has generated no
little philosophical and mathematical analysis/discussion – more than
more than enough to keep lots of graduate students and even professors
employed – although almost all of it including its classical
formulation above has almost no practical effect on the real world in
which a variety of proportional representation schemes or, for that
matter, majority-rules voting actually takes place.
This – ie., the lack of practical connection between the
formalistic logic referred to above and life experience – is so
because the "However, … etc." in the last para. above does not go
far enough in pointing as a *practical* matter to the lack of the
asserted paradox in real life – f’r'ex, if there is an election in
which there are only three voters who do not have the preferences so
arbitrarily hypothesized above *or* an election with a fourth voter
who selects *any* preference in any order of A and B and C other than
the rigidly constricted one first stated above *or* (and, as a
practical matter, more basically) an election in which the only
candidates are A and B and C but for which there are substantially
more than four voters.
As a practical matter, in other words, the matter of logic
narrowly hypothesized above for the very purpose of creating a
(strictly abstract) logical paradox disappears if one takes a
realistically probabilistic-statistical approach to a variety of forms
of proportional selection or instant run-off voting.
Also as a practical matter, a matter of Real Politik, compare the
majority/winner-takes-all approach – even if one assumes, but, if so,
probably unrealistically, that all voters who want and try to vote in
compliance with whatever are the rules for the election are
non-discriminatorily permitted to do so and also that all votes cast
are honestly and accurately counted bearing in mind that, under such
an alternative, someone might win by only one vote among zillions
counted – with what would be more *fair* over-all – even if one
allowed for the (mere) possibility that a paradox of the sort first
assumed above were to occur – of proportional voting or instant
run-off voting alternatives.
In summary, a *factual* – that is, *probable* – connection
between the hypothesized formalistic paradox an fairly described
*practicality* remains to be demonstrated.
Those of you who think you know it all are highly annoying to those of
us who do.
> http://en.wikipedia.org/wiki/Voting_paradoxhttp://en.wikipedia.org/wi...
The link you ACUTALLY wanted was to Arrow’s Impossibility Theorem.