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Topic: Monotonicity criterion

Related Topics

Approval voting

Tactical voting

Voting system criterion

Borda count

WestVirginia

Cambridge, Massachusetts

Hawaii

Nebraska

	Monotonicity criterion - Wikipedia, the free encyclopedia
		In mathematics, monotonicity usually refers to the different concept of a monotonic function.
		Furthermore, although all voting systems are vulnerable to tactical voting, systems which fail the monotonicity criterion suffer an unusual form, where voters might try to elect their candidate by voting against that candidate.
		Range voting and approval voting are monotonic as you never help a candidate by reducing or removing support for them, but require a slightly different definition as they are not preferential systems.
	en.wikipedia.org /wiki/Monotonicity_criterion (527 words)

	[No title]
		Condorcet methods satisfy the Condorcet criterion, which says that if there is a candidate who could beat any other candidate in a one-on-one election (i.e., if there is a candidate who "pairwise beats" every other candidate), this candidate must be elected.
		Sincere Favorite criterion: Lowering a candidate from the top rank can't cause another top rank candidate to pairwise beat the lowered candidate, because "tied at the top" rankings are counted as votes for each side over the other.
		The Plurality criterion says that C must be elected with no greater probability than A. If C is elected, it could be viewed as an obvious mistake, as there is no way to adjust the ballots voting for C so that there are as many C first preferences as A first preferences.
	nodesiege.tripod.com /elections (7779 words)

	L28
		Criterion 3 (monotonicity): Suppose X is the winner and suppose that in another election some voters are able to rank X higher, with no change for the other candidates, then X should still win.
		Criterion 4: if C drops out, then B would win 22 first place votes and supercede A. Suppose the winner is decided by a single runoff.
		Criterion 4: if A, D, and E drop out, C would win a match between B and C. Suppose the winner is decided by sequential runoffs.
	www.math.wisc.edu /~meyer/math141/L28.html (377 words)

	Quantitative Methods in Public Administration, Measures of Association
		By the criterion of accord there would be a null relationship, whereas by the criterion of independence there would be a relationship.
		When the value categories of both variables are ordered and crosstabulated, by this criterion a null relationship is said to exist when the number of cases on the right-sloping diagonal(s) is equal to the number of cases on the left-sloping diagonal(s).
		By this criterion, a null relationship exists when the number of cases associated with each category of the independent variable is split evenly among the dependent variable categories.
	www2.chass.ncsu.edu /garson/pa765/association.htm (2442 words)

	Vote Aggregation Methods
		The first consequence of the independence criterion can also be understood by considering Vickrey's definition: ``The social choice between any two alternatives shall not be affected by the removal or addition of other alternatives to the field of feasible alternatives under consideration'' [103].
		This criterion is similar to the monotonicity criterion, but is more often satisfied by the voting systems that have been proposed.
		Furthermore, this procedure is not monotonic and thus may result in perverse outcomes in which a candidate would be better off with fewer votes [18, 38].
	lorrie.cranor.org /pubs/diss/node4.html (8348 words)

	Chapter 1 The Mathematics of Voting
		Monotonicity Criterion: If a candidate wins an election, and then we change some of the ballots, but only so as to increase the ratings on those ballots of the winning candidate, then that candidate should still win.
		Criterion of Independence of Irrelevant Alternatives: If a candidate wins, and then one of the losing candidates is eliminated, then the original winner still wins.
		This criterion can be violated by all of the voting methods discussed in the text.
	www.math.hawaii.edu /~les/m100/lecture2.htm (623 words)

	On the Behaviour of Zeros of Jacobi Polynomials - Dimitrov, Rodrigues (ResearchIndex) (Site not responding. Last check: 2007-10-21)
		4 a conjecture concerning monotonicity of zeros of ultraspheri..
		3 A monotonic property for the zeros of ultraspherical polynom..
		3 Monotonicity properties of the zeros of ultraspherical polyn..
	citeseer.ist.psu.edu /491667.html (479 words)

	Glossary for Voting
		A voting system violates monotonicity if a voter can raise a candidate in the social ordering by lowering that candidate in his individual ordering.
		Condorcet winner criterion: If there is an alternative X which could obtain a majority of votes in pairwise contests against every other alternative, a voting rule should choose X as the winner.
		Pareto criterion: If every voter prefers as alternative X to an alternative Y, a voting rule should not produce Y as a winner.
	accuratedemocracy.com /docs/z_words.doc (1088 words)

	Approval voting - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-21)
		Approval voting passes a form of the monotonicity criterion, in that voting for a candidate never lowers that candidate's chance of winning.
		When all voters use this tactic, there is a good chance that the Condorcet winner will be elected.
		It should be noted that Approval voting does not satisfy the Condorcet criterion.
	www.bonneylake.us /project/wikipedia/index.php/Approval_voting (1419 words)

	Single-Winner Electoral Methods FAQ
		The Smith Criterion says that the winner should be from the Smith set.
		For methods meeting the Majority Criterion, this can be done if the majority ranks their chosen candidate first.
		The important point is that A won because of a change in the ballots that only demonstrated a reduction in A's support, or an increase of that of B and C. Non-monotonicity (the property of having monotonicity violations) is common in methods that use elimination of candidates.
	www.condorcet.org /emr/singfaq.shtml (4064 words)

	Evaluating Voting Methods
		In general, voting schemes which use a runoff procedure fail the Monotonicity criterion.
		Although this system uses most of the information in the preference ballot, it still fails the Monotonicity criterion, since it is held in several rounds with elimination in between.
		This states that, for a given set of criteria, it is impossible for a voting method to satisfy all simultaneously.
	theorem.ca /~mvcorks/code/voting_methods.html (2289 words)

	CDTT - Electowiki
		Limiting an election method's selection to the CDTT members can permit it to satisfy the Minimal Defense criterion (and thus the Strong Defensive Strategy criterion) and the Majority criterion for solid coalitions, while coming close to satisfying the Later-no-harm criterion.
		When the paired method is used to generate a ranking of the candidates which is not influenced by which candidates make it into the CDTT, then compliance with the Monotonicity criterion can be preserved when the paired method already satisfies this criterion.
		When the CDTT is paired with a method which satisfies Later-no-harm, the combined method fails the Plurality criterion and Condorcet criterion.
	wiki.electorama.com /wiki/CDTT (545 words)

	Articles - Borda count (Site not responding. Last check: 2007-10-21)
		The Borda count satisfies the monotonicity criterion, the summability criterion, the consistency criterion, the participation criterion, the Plurality criterion (trivially), Reversal symmetry, and the Condorcet loser criterion.
		It does not satisfy the Condorcet criterion, the Independence of irrelevant alternatives criterion, or the Independence of Clones criterion.
		The third way is to employ a uniformly truncated ballot obliging the voter to rank a certain number of candidates, while not ranking the remainder, who all receive 0 points.
	www.worldhammock.com /articles/Borda_count (1390 words)

	Information and Computation Bibliography (Site not responding. Last check: 2007-10-21)
		The paper explores language learning in the limit under various constraints on the number of mindchanges, memory, and monotonicity.
		We define language learning with limited (long term) memory and prove that learning with limited memory is exactly the same as learning via set driven machines (when the order of the input string is not taken into account).
		A surprising result is that there are families of languages that can be monotonically learned with at most one mindchange, but can neither be weak-monotonically nor conservatively learned.
	theory.lcs.mit.edu /~iandc/References/kinbers1995:224.html (355 words)

	Monotonicity Of Zeros Of Orthogonal Laurent Polynomials (ResearchIndex)
		Monotonicity Of Zeros Of Orthogonal Laurent Polynomials (ResearchIndex)
		Abstract: Monotonicity of zeros of orthogonal Laurent polynomials associated with a strong distribution with respect to a parameter is discussed.
		Recent results of Ismail and Muldoon based on the Hellman-Feynman theorem are also extended to a monotonicity criterion for zeros of Laurent polynomials.
	citeseer.ist.psu.edu /498800.html (394 words)

	Learning Module 1 - Concepts
		The majority criterion: If a majority (remember, a majority is more than half; a plurality is just the largest number, even if not a majority) of voters rank a candidate first, that candidate should always win the election.
		Sadly, most of our systems fail the Condorcet criterion - which means we can make up examples where there is a Condorcet winner but that candidate doesn't win the election under Plurality, or under Borda, or under instant run-off.
		Instant Run-Off fails the monotonicity criterion, because changing the votes can lead to different candidates being eliminated - and the final (2 candidate) showdown might have a different pair of candidates and a different result.
	voyager.dvc.edu /~sneedham/06concepts.html (1024 words)

	CONDORCET'S METHOD for Single-Winner elections
		Still, SD's violation of Monotonicity is an embarrassment, and could be used against it when SD is being considered as an alternative to Plurality or Borda.
		Monotonicity is defined at the Academic Criteria page, but, briefly, a method meets Monotonicity if voting a candidate higher will never make him lose, and if voting a candidate lower will never make him win.
		Another reason to measure them as we do is because of the criterion complicances that it confers.
	www.barnsdle.demon.co.uk /vote/condor2.html (2608 words)

	Math 250
		Lecture 2 (June 24) We discussed the plurality-with-elimination method, the pairwise comparison method, the monotonicity criterion and the independence-of-irrelevant-alternatives criterion.
		Examples showed that the Borda count method may violate the Condorcet criterion, that the pairwise comparison method may violate the monotonicity criterion and that the plurality-with-elimination method may violate the monotonicity criterion.
		If it is desired to rank the candidates in order (instead of just determining a winner) there are extended versions of each of the four methods we discussed (plurality, Borda count, pairwise comparison, plurality-with-elimination).
	www.math.rutgers.edu /~rwilson/math103.html (1635 words)

	Raynaud - Electowiki
		Defeat strength is usually measured as either the absolute number of votes cast for the winning side (winning votes), or the number of votes for the winning side minus those for the losing side (margins).
		Even when winning votes are used as the measure of defeat strength, Raynaud fails the Plurality criterion and the Strong Defensive Strategy criterion.
		A variant called Raynaud(Gross Loser) does satisfy the Plurality criterion.
	wiki.electorama.com /wiki/Raynaud (178 words)

	Definitions and Criteria (Site not responding. Last check: 2007-10-21)
		If there is a single majority of the voters who rank every candidate in a set over every candidate outside that set, then the winner should always be a member of the set.
		A method that always chooses from the minimal dominant set is Smith-efficient, and passes the Smith criterion.
		All resolvable voting methods that satisfy the mutual majority criterion have a compromising incentive when there is a majority rule cycle.
	fc.antioch.edu /~james_green-armytage/vm/define.htm (2163 words)

	Re: EVENT: Join "Make Poverty History" riders to Edinburgh, Fri 1
		monotonicity criterion with that of: unanimity or Pareto efficiency: if
		alternatives is an unreasonably strong criterion, and therefore Arrow's
		suggested replacements for this criterion, but none have become largely
	www.sportinfos.net /spo100d/050818033932.shtml (758 words)

	I. What do we mean by fair?
		If candidate C is not declared the winner, this would be a violation of the Condorcet Criterion.
		If an election is held and a winner is declared, this winning candidate should remain the winner in any revote in which all preference changes are in favor of the winner of the original election.
		This illustrates a violation of the Monotonicity Criterion.
	www.ctl.ua.edu /math103/Voting/whatdowe.htm (1229 words)

	monotonicity - OneLook Dictionary Search
		Tip: Click on the first link on a line below to go directly to a page where "monotonicity" is defined.
		monotonicity : Merriam-Webster's Online Dictionary, 10th Edition [home, info]
		Phrases that include monotonicity: monotonicity criterion, downward monotonicity, left downward monotonicity, left upward monotonicity, proof of monotonicity criterion, more...
	www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=monotonicity (137 words)

	Taditional Criteria for methods of Single-Winner Elections (Site not responding. Last check: 2007-10-21)
		It's topic is the least important of this series of articles, so feel free to skip it for now, and maybe come back to it later, perhaps, for reference.
		The 1st 3 and Monotonicity are the ones most often encountered.
		This is the very familiar criterion that says that if a majority of all the voters vote X alone in 1st place (or vote for him in 1-vote Plurality), then X should win.
	www.barnsdle.demon.co.uk /vote/akadem.html (493 words)

	Electoral Methods: Standards and Criteria
		Criteria are phrased in such a way that all methods will either pass or fail the criterion, and it can be proved which.
		Methods that fall outside this area are not scored as passing or failing.
		This is so as not to mislead the reader by claiming that a method passes or fails a criterion that was not intended to apply.
	www.condorcet.org /emr/criteria.shtml (749 words)

	Participating Sites (Site not responding. Last check: 2007-10-21)
		The participation criterion is a voting system criterion for evaluating voting systems.
		The addition of a further ballot should not, for any positive whole number ''k'', reduce the probability that at least one candidate is elected out of the first ''k'' candidates listed on that ballot.
		Plurality voting, Approval voting, cardinal ratings, and Borda count satisfy the Participation Criterion.
	www.blownspeakers.com /pages3/65/participating-sites.html (991 words)

	RCPS Math Curriculum
		DM.3 Discuss how to break ties and how the four voting methods relate to fairness criteria, such as majority criterion, Condorcet criterion, monotonicity criterion, and independence of irrelevant alternatives criterion.
		DM.3 The student will be able to discuss how to break ties and how the four voting methods relate to fairness criteria, such as majority criterion, Condorcet criterion, monotonicity criterion, and independence of irrelevant alternatives criterion.
		DM.4 The student will be able to describe a weighted voted system and identify its associated notation and terminology.
	www.rockingham.k12.va.us /RCPS_Math/discrete.html (946 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		We prove that the converse is true: any entropy flux vector splitting can be interpreted by a kinetic model, and we obtain an explicit characterization of entropy satisfying flux vector splitting schemes.
		We deduce a new proof of discrete entropy inequalities under a sharp CFL condition that generalizes the monotonicity criterion in the scalar case.
		In particular, this gives a stability condition for numerical kinetic methods with noncompact velocity support.
	www.dma.ens.fr /~fbouchut/publications/bgk-fvs_abs.html (152 words)

	Lesson I - Voting (Site not responding. Last check: 2007-10-21)
		In MAS election, A has 14 first place votes, B has 4 votes, C has 11 votes, and D has 8 votes, so A is the winner.
		The Plurality Method fails to use all the information in the preference schedule (and equivalently, all the voters' preferences.) It satisfies the Majority Criterion.
		Plurality with Elimination satisfies the Majority Criterion (Example 1.5) but violates the Monotonicity Criterion (Example 1.6).
	www.vsg.edu.au /frames/x/lesson1.html (465 words)

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