The Voter's Paradox
in [Logic]
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From: Immortalista on 8 Jun 2010 20:10 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
From: C3 on 9 Jun 2010 00:20 On Jun 8, 5:10 pm, Immortalista <extro...(a)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. > > 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_paradoxhttp://en.wikipedia.org/wiki/Voting_system#Foundations_of_voting_theoryhttp://www.google.com/search?hl=en&q=define%3ATransitivity Vote prolife. C3+ What about antipsychiatry?! C3
From: russ bertrand on 9 Jun 2010 12:12 On Tue, 8 Jun 2010 17:10:50 -0700 (PDT), Immortalista <extropy1(a)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.
From: George Greene on 9 Jun 2010 15:19 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/wiki/Voting_system#Foundations_of_voting_theoryhttp://www.google.com/search?hl=en&q=define%3ATransitivity The link you ACUTALLY wanted was to Arrow's Impossibility Theorem.
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