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Definite Majority Choice: Difference between revisions

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Revision as of 19:12, 14 April 2005

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→‎Tallying Votes: method clarification
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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 score. This kind of defeat is also called an ''Approval-consistent defeat''.
 
To determine the winner, the candidates are divided into two groups:
# Definitively defeated candidates.
# Eliminate all definitively defeated candidates. We call the remaining candidates the '''definite majority set'''.
# TheCandidates winner is the single candidate whothat pairwise defeatsdefeat (winsall headhigher-to-headapproved contestscandidates. with) allWe othercall candidatesthis ingroup the '''definite majority set'''.
The least-approved candidate in the definite majority set pairwise defeats ''all'' higher-approved candidates, including all other members of the definite majority set, and is declared the winner.
 
DMC always selects the [[Condorcet Criterion|Condorcet Winner]], if one exists, and otherwise selects a member of the [[Smith set]]. StepEliminating 1the 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 has some interesting properties:
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