Definite Majority Choice: Difference between revisions

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The rankings on a single ballot are added into a round-robin table using the standard [[Condorcet_method#Counting_with_matrices|Condorcet pairwise matrix]] method: the higher ranked candidates are given one vote in each of their pairwise contests with lower ranked candidates.

The Condorcet pairwise matrix can also be used to store each candidate's Approval point score, in the diagonal cell ~~which is unused in other Condorcet methods~~.

The Condorcet pairwise matrix can also be used to store each candidate's Approval point score, in the otherwise-unused diagonal cell.

We call a candidate '''Strongly defeated''' when that candidate is pairwise defeated by any other candidate with higher Approval rating. This kind of defeat is also called an Approval-consistent or [http://wiki.electorama.com/wiki/Techniques_of_method_design#Defeats_and_defeat_strength definitive defeat].

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# The winner is the candidate that pairwise defeats all other remaining candidates.

DMC always selects the Condorcet Winner, if it exists, and otherwise selects a member of the Smith Set. Step 1 has the effect of successively eliminating the least approved candidate in the Smith set, but allows higher-approved candidates outside the Smith set (such as the Approval Winner) to remain in the set of non-strongly-defeated candidates.

DMC always selects the Condorcet Winner, if one exists, and otherwise selects a member of the Smith Set. Step 1 has the effect of successively eliminating the least approved candidate in the Smith set, but allows higher-approved candidates outside the Smith set (such as the Approval Winner) to remain in the set of non-strongly-defeated candidates.

=== Handling Ties and Near Ties ===