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Definite Majority Choice: Difference between revisions
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'''Definite Majority Choice''' (DMC) is a single-winner [[voting method]] that
uses ballots expressing both
* The [[Pairwise Sorted Approval]] equivalent was first proposed by Forest Simmons in [http://lists.electorama.com/pipermail/election-methods-electorama.com/2001-March/005448.html March 2001].
* The [[Ranked Approval Voting]] equivalent was first proposed by Kevin Venzke in [http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-September/010799.html September 2003].
The [http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/015144.html philosophical basis]
We call a candidate [[Techniques_of_method_design#Defeats_and_defeat_strength|definitively defeated]] when that candidate is defeated in a head-to-head contest against any other candidate with higher Approval
To find the DMC winner
# Eliminate all definitively defeated candidates. The remaining candidates are called the '''definite majority set'''. We also call these candidates the '''provisional set''' (or '''P-set'''), since the winner will be found from among that set.
# Among P-set candidates, eliminate any candidate who is defeated by a lower-rated P-set opponent.
# When there are no pairwise ties, there will be one remaining candidate.
If there is a candidate who, when compared in turn with each of the others, is preferred over the other candidate, DMC guarantees that candidate will win. Because of this property, DMC is (by definition) a '''[[Condorcet method]]'''. Note that this is different from some other preference voting systems such as [[Borda count|Borda]] and [[Instant-runoff voting]], which do not make this guarantee.
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:The Definite Majority Choice winner is the ''least-approved'' candidate who, when compared in turn with each of the other ''higher-approved'' candidates, is preferred over the other candidate.
The main difference between DMC and Condorcet methods such as [[Ranked Pairs]] (RP), [[Schulze method|Cloneproof Schwartz Sequential Dropping]] (Beatpath or Schulze) and [[River]] is the use of the additional Approval
* DMC is a strong majority rule method.
* When defeat strength is measured by the approval rating of the defeating candidate, DMC is the only possible immune ([[Condorcet_method#Key_terms_in_ambiguity_resolution|cloneproof]]) method.
DMC is also equivalent to [[Ranked Approval Voting]] (RAV) (also known as
Approval Ranked Concorcet), and [[Pairwise Sorted Approval]] (PSA): DMC always selects the [[Condorcet Criterion|Condorcet Winner]], if one exists, and otherwise selects a member of the [[Smith set]]. Eliminating the definitively defeated candidates from consideration has the effect of successively eliminating the least approved candidate
Some believe that DMC is currently the best candidate for a Condorcet Method that meets the [[Public Acceptability Criterion|Public Acceptability "Criterion"]].
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