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Topic: Voting paradox

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	Voting paradox Summary
		Voting paradoxes can arise in any election involving three or more candidates; though they come in many different forms, they can all be summed up in a single statement: Even if every voter is individually rational, society as a whole is not.
		The most commonly used voting method in the United States is the plurality vote: Each voter casts a ballot for one candidate, and the winner is the candidate who gets the most votes (even if this is less than 50 percent).
		The voting paradox (also known as Condorcet's paradox or the paradox of voting) is a situation noted by the Marquis de Condorcet in the late 18th century, in which collective preferences can be cyclic (i.e.
	www.bookrags.com /Voting_paradox (848 words)

	[No title]
		Voting directly for coalitions would be facilitated by being able to vote for the combinations themselves, not just their components, which is a possibility we consider later.
		To establish an isomorphism between the paradox of voting and the vote-aggregation paradox, assume that the eight votes actually taken on the proviso in the House on August 8, 1846, can be reduced to three hypothetical pairwise contests between (1) a and b, (2) b and c, and (3) c and a.
		The significance of this discrepancy is underscored by the linkage of the vote-aggregation paradox to the paradox of voting.
	bcn.boulder.co.us /government/approvalvote/paradox.html (8994 words)

	Paradoxes and Dilemmas
		While such paradoxes may be resolved in time with better understanding, it is unlikely that the paradoxes mentioned here will be so easily resolved.
		This paradox is quite representative of the general problem of the Social Dilemmas which I discuss here and has to do with the fact that an individual's vote has no significant impact on the outcome of an election.
		The paradox is important in theory since some philosophers claim that Newcomb's Paradox and the Prisoner's Dilemma are essentially the same phenomenon.
	perspicuity.net /paradox/paradox.html (2955 words)

	Vote Aggregation Methods
		Voting systems that elect multiple representatives may be evaluated in terms of the correspondence between the number of representatives elected from each party and the support for each party in the electorate.
		Plurality voting is classified at the first level of Nurmi's preference misrepresentation hierarchy and is generally considered to be one of the easiest voting systems to manipulate [78].
		However, approval voting has a higher Condorcet efficiency than plurality voting, selecting the Condorcet winner in all cases where it is selected by plurality voting as well as in other cases where it it may not be selected by plurality voting [17].
	lorrie.cranor.org /pubs/diss/node4.html (8348 words)

	Voting paradox - Wikipedia, the free encyclopedia
		The voting paradox (also known as Condorcet's paradox or the paradox of voting) is a situation noted by the Marquis de Condorcet in the late 18th century, in which collective preferences can be cyclic (i.e.
		This is paradoxical, because it means that majority wishes can be in conflict with each other.
		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.
	en.wikipedia.org /wiki/Voting_paradox (318 words)

	[No title]
		The alternative vote procedure also aggregates in the manner of plurality voting, but only the alternative with the fewest number of votes is eliminated at each stage; thus m -1 votes are required altogether.
		A sequential binary procedure is a voting procedure of the parliamentary type, in which a sequence of binary choices (e.g., yes or no) is put to the voters.
		Under plurality voting, C is selected (with 9 votes, as opposed to 6 for B, 4 for A, and none for D).
	research.umbc.edu /~nmiller/RESEARCH/VOTING.htm (3944 words)

	Social Choice: The Impossible Dream
		If a new election were held and a single voter were to change his or her ballot from being a vote for the loser of the previous election, and everyone else voted exactly as before, then the outcome of the new election would be the same as the outcome of the previous election.
		A voting method that assigns points in a non-increasing manner to each voter’s subsequent ranking and then sums these points to arrive at a group’s final ranking is called a rank method.
		We have shown that there is a best voting method when talking about two alternatives, however we have not answered if there is a best voting method that satisfies the properties for three alternatives.
	www.math.okstate.edu /~millerd/Socialchoice.htm (1758 words)

	Social Choice and Beyond - History
		The Paradox of Voting states that, given the distribution of voter’s preferences, in certain cases there may be no solution which obeys certain common sense rules.
		This is known as the paradox of voting.
		For instance, if A is preferred to B by a vote of 100 to 50, B is preferred to C by a vote of 90 to 60 and C is preferred to A by a vote of 80 to 70, then C would be dropped, and A would be the winner.
	www.socialchoiceandbeyond.com /scabpage2.html (2492 words)

	Untitled Document
		Voting on B and C gives B a victory over C. But then they all vote on A vs C. Here a problem arises because C wins.
		What this voting paradox illustrates is that when preferences for public goods differ for individuals, any system for adding up those preferences can often lead to inconsistencies and results which just don't seem to make much sense.
		The voter's paradox also shows us that when there are more than 2 alternatives, we should not make paired comparisons, to avoid mistakenly assuming that a chosen alternative is preferred to one that is not chosen.
	www.mtholyoke.edu /~hkwarner/PublicFinancePage12.html (689 words)

	ThoughtStorms: ParadoxOfVoting (Site not responding. Last check: 2007-11-03)
		The paradox of voting is the bane of rational choice theorists.
		If voting is generalised to 'contributing' this is the PublicGoodProblem, where the public good is the desired election result.
		For older people in particular, voting is a chance to make a statement or express solidarity with all those who ‘fought and died to win the right to vote.’ Voting itself is virtually costless, even enjoyable for some.
	www.nooranch.com /synaesmedia/wiki/wiki.cgi?ParadoxOfVoting (328 words)

	Research - Citizens Get Satisfaction from Voting - Stanford GSB
		If voting is associated with a payoff that is higher than that person's aspiration (or hoped-for outcome), then he or she is satisfied and will become more likely to vote next time.
		And it's equally important to look at the reverse side of the theory: If someone doesn't vote and is unhappy with the results, then he or she will subsequently become more likely to change behavior and vote.
		This helps to buoy the voting statistics: Non-voters who are dissatisfied with the way the elections turn out may then come back to the polls and try again.
	www.gsb.stanford.edu /news/research/pubpolicy_voting.shtml (943 words)

	Notes on the Voting Paradox
		H: H wins (A and B will vote for H) That is, society prefers M to L and H to M. Consistency then requires that it should also prefer H to L (i.e.
		- this feature of majority voting is known as Condorcet’s paradox, after the Marquis de Condorcet, who was the first to discover it, in 1785.
		Rather, what it means is that there may be some arbitrariness about these decisions – it undermines the idea that decisions made by voting have a particular legitimacy – has had a vast influence on political science and philosophy.
	www.sp.uconn.edu /~langlois/dhammika.html (630 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		This paradox of voting was first discovered by a French nobelman, Marie Jean Antoine Nicolas Caritat - bett e r known as the Marquis de Condorcet.
		In this case, if the committee uses the "king of the hill" method of voting where two policies are paired for a vote and then the winner is paired with the third policy for a final vote, the policy selected by the committee will depend on who controls the agenda.
		Other terms that are sometimes used to describe }{\f1\ul Condorcet's paradox}{\f1 are }{\f1\ul voting cycles}{\f1 or }{\f1\ul preference cycles}{\f1 because the social choice tends to cycle through all the alternatives: \par \par A is preferred to B which is preferred to C which is preferred to A which is preferred to B...
	www.towson.edu /~roberts/339/A12socprf.doc (2182 words)

	manipulability of voting systems, The American Mathematical Monthly, The - Find Articles (Site not responding. Last check: 2007-11-03)
		When one speaks of a mathematical analysis of voting, two results spring to the forefront: the voting paradox of Condorcet [7] and Arrow's Impossibility Theorem [1].
		Intuitively, it means that there is at least one situation in which this voter prefers the election outcome resulting from his submission of a disingenuous ballot to the outcome resulting from his submission of a ballot corresponding to his true preferences.
		Thus, we are assuming that the voter in question has complete knowledge of how everyone else voted (or perhaps better: will vote), and we are asking if he can take advantage of this knowledge to secure a better outcome-better, that is, from his point of view-by submitting an insincere ballot.
	www.findarticles.com /p/articles/mi_qa3742/is_200204/ai_n9041706 (848 words)

	Voting Paradox
		The paradox of voting was discovered over 200 years ago by M. Condorcet, a French mathematician, philosopher, economist, and social scientist.
		The importance of the voting paradox was not fully realized until several years after Kenneth Arrow published Social Choice and Individual Values in 1951, which contained his General Possibility Theorem.
		Note that in all votes, each voter casts their vote for the candidate they like most who is on the ballot (as a result of the voting paradox, this doesn't always maximize the chance that a candidate they like will be elected).
	www.cs.umd.edu /Outreach/hsContest97/questions/node6.html (582 words)

	Social Choice and Beyond - Papers
		The Paradox of Voting states that, given the distribution of voter's preferences, in certain cases there may be no solution which obeys certain common sense rules.
		Finally, the voting paradox is resolved by the BC when the most likely individual profiles are used.
		By means of a proper treatment of tie solutions, Condorcet's method of determining the outcome of an election is extended to cases that have previously produced a "paradox of voting." Our method is based on pairwise comparisons of candidates by voters and meets Arrow's five criteria and his axioms 1 and 2.
	www.socialchoiceandbeyond.com /scabpage3.html (2885 words)

	Pursuit of Liberty: The Voter's Paradox [Free Republic]
		The second paradox is that, "while it is true that the outcome of a group effort is made up of the sum of the individual efforts, in many cases a particular individual's contribution makes no significant and/or measurable impact on the outcome".
		The act of voting that I have chosen to be representative of the social dilemmas, seems to be an irrational act for the individual.
		If I vote for B and B wins, I don't get freedom, and I probably won't get the loot that B had promised, but at least I would be in a better position compared to those who voted for A. So, I vote for B. The bumps are brought to you by Elvis Presley.
	www.freerepublic.com /forum/a3a7e0ec3409b.htm (8731 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		Plurality Rule, Majority Rule and Scoring Methods A voting rule we encounter most often in elections is the plurality rule: Each voter casts a vote for his or her preferred candidate.
		Third, because a strategic vote often requires voting against a desirable policy proposal, legislators may be forced to choose between taking the preferred "position" of less informed constituents and voting strategically to promote the best policy outcome for those constituents: "Although helpful in producing a final result desired by constituents, a strategic vote...
		That is, one MP can vote for a project that has a negative net benefit to him or her in return for a vote from the other MP on this MP’s most preferred project.
	web.uvic.ca /~egugl/indexpf_files/voting.doc (3056 words)

	Voting paradox (Site not responding. Last check: 2007-11-03)
		Suppose a department of 15 people is voting for the beverage to be served at the picnic (this example is from D. Saari's text Geometry of Voting); 6 prefer milk to wine to beer; 5 prefer beer to wine to milk; 4 prefer wine to beer to milk.
		The organizer saw a plurality for milk; orders milk, but when it turned out to be unavailable, ordered beer (next in line - 5 preferred beer over anything else).
		At the picnic, the wine-lovers discussed the votes and discovered that 10 people preferred wine over beer.
	www.math.virginia.edu /~cfd5z/voting.html (340 words)

	Saari: Voting Paradox (Site not responding. Last check: 2007-11-03)
		A voting paradox is where the election outcome is not what we think it should be.
		During this election year, we can expect to find all sorts of voting paradoxes which are direct consequences of the lousy election procedure we currently use.
		Readers interested in the problems of voting, some history, and the properties of the Borda Count might be interested in my recently published book Basic Geometry of Voting.
	www.colorado.edu /education/DMP/voting_a.html (376 words)

	Making Sense out of Consensus
		The Marquis de Condorcet---the founder of voting theory---suggested in 1785 that the winner of an election should be the candidate who defeats all the others in a head-to-head match-up.
		What's more, he says, he can now identify "all possible paradoxes" in voting theory, and thereby tell which method is least likely to elect a wildly unpopular candidate.
		All the action---all the voting paradoxes, and all the disagreements between methods---thus boils down to the orthogonal component of the kernel and basic subspaces.
	www.siam.org /siamnews/10-00/consensus.htm (2414 words)

	Introduction
		The "Voting Paradox", described herein, is an excellent representation of this class of phenomena.
		The voting example is a particularly good example of this phenomena in that it can easily be shown that one vote is highly unlikely to do any good whatsoever while there is cost to the person making the vote (admittedly small, usually).
		One way to better understand the insignificance of one vote is to imagine that you are an active supporter of a certain candidate and you are out on the trail soliciting votes.
	www.spectacle.org /995/sd.html (10527 words)

	Social Choice The Voting Paradox
		The voting paradox highlights the problem with majority rule voting.
		Another problem with majority-rule voting is that it leads to logrolling, which occurs when representatives trade votes (I vote for your program if you vote for mine).
		Also, choices are almost always limited to bundles of public goods, and we vote infrequently.
	wps.prenhall.com /bp_casefair_econf_7e/0,8233,2031397-,00.html (389 words)

	Voting Paradox (Site not responding. Last check: 2007-11-03)
		Answer: This is an example of a voting paradox, specifically a majority circle.
		Voting paradoxes are also studied in part because of their implications for practical politics.
		For instance, the instructor can manipulate the class to choose between the Republican and the Third, and then ask the class to choose between the winner of that contest (the Republican) and the Democrat.
	members.cox.net /srice1/profdeley/math/voteprdx.html (142 words)

	Democracy Science.
		Simple examples of how to conduct an election by the single transferable vote.
		Former reforms: Reversible STV and the Re-transferable Vote.
		Keep-value averaged STV answer to apology for anarchy of voting methods.
	www.voting.ukscientists.com (515 words)

	Political Science 1100: American Government (Site not responding. Last check: 2007-11-03)
		The three cast their votes between asparagus and broccoli and asparagus wins, two votes to one (Huey and Louis vote for asparagus, while Dewey votes for broccoli).
		In effect, Huey, Dewey and Louie are in a voting cycle or paradox.
		The paradox of voting demonstrates that we can't count on the will of the people or majority rule.
	cdis.missouri.edu /previews/2163/lesson01.htm (3334 words)

	CEPR Discussion Paper Abstracts (Site not responding. Last check: 2007-11-03)
		paradox of voting, rational voter hypothesis, Poisson gamex
		In this Paper, we take stock of existing empirical regularities and argue that we can use them to improve the model of instrumental voting.
		Once this is done, we show that purely rational/instrumental factors actually explain a large fraction of turnout variations.
	www.cepr.org /pubs/dps/DP3126.asp (228 words)

	VoltInsider » The Voting Paradox Interview Question at Microsoft, Part II (Site not responding. Last check: 2007-11-03)
		VoltInsider » The Voting Paradox Interview Question at Microsoft, Part II VoltInsider
		The Voting Paradox Interview Question at Microsoft, Part II
		In other words, by removing an irrelevant candidate (B), we affected the outcome of the voting.
	voltinsider.com /?p=9 (219 words)

	Introduction to American Politics, Fall 2001 Study Guide (Site not responding. Last check: 2007-11-03)
		Is this because of a change in registration laws, levels of voter turnout, the size of the voting-age electorate?
		What three factors influence how peole vote in election, according to the Lowi et al.
		In particular, you should focus on how the way we count the votes influences the outcome.
	www.siu.edu /~mcclurg/courses/pols114/guide6.html (543 words)

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