Definite Majority Choice: Difference between revisions
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'''Definite Majority Choice''' (DMC) is a [[voting method]] proposed by several (name suggested by [http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/015164.html Forest Simmons]) to select a single winner using ballots that express both ranked preferences and approval. |
'''Definite Majority Choice''' (DMC) is a [[voting method]] proposed by several (name suggested by [http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/015164.html Forest Simmons]) to select a single winner using ballots that express both ranked preferences and approval. |
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If there is a candidate who is preferred over the other candidates, |
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when compared in turn with each of the others, DMC guarantees that that candidate will win. |
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Because of this property, DMC is (by definition) a '''[[Condorcet method]]'''. |
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Note that this is different from some other preference voting systems such as [[Borda count|Borda]] and |
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[[Instant-runoff voting]], which do not make this guarantee. |
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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 DMC winner satisifies this variant of the [[Condorcet Criterion]]: |
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⚫ | The main difference between DMC and Condorcet methods such as [[Ranked Pairs]] (RP), [[Cloneproof Schwartz Sequential Dropping]] (Beatpath or Schulze) and [[River]] is the use of the additional Approval score to break |
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⚫ | The main difference between DMC and Condorcet methods such as [[Ranked Pairs]] (RP), [[Cloneproof Schwartz Sequential Dropping]] (Beatpath or Schulze) and [[River]] is the use of the additional Approval score to break cyclic ambiguities. If defeat strength is measured by the Total Approval score of the pairwise winner, all three other methods become equivalent to DMC (See [http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/015405.html proof]). |
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Some people believe that DMC is currently the best candidate for a Condorcet Method that meets the [[Public Acceptability Criterion|Public Acceptability "Criterion"]]. |
Some people 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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For example, the X2>X4 ("for X2 over X4") vote is entered in {row 2, column 4}. |
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When pairwise totals are completed, we determine the outcome of a particular pairwise contest as described [[Condorcet_method#Counting_with_Matrices|elsewhere]]. But in DMC, X2 definitively defeats X4 if the {row 2, column 4} (X2>X4) total votes exceed the {row 4, column 2} (X4>X2) total votes, and {row 2, column 2} (X2>X2 total approval score) exceeds {row 4, column 4} (X4>X4 total approval score). |
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The winner is then determined as described above. |
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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 in the Smith set and then recalculating the new Smith set until a single winner exists. But the definite majority set may also contain higher-approved candidates outside the Smith set. For example, the Approval Winner will always be a member of the definite majority set, because it cannot be definitively defeated. |
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 in the Smith set and then recalculating the new Smith set until a single winner exists. But the definite majority set may also contain higher-approved candidates outside the Smith set. For example, the Approval Winner will always be a member of the definite majority set, because it cannot be definitively defeated. |