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Definite Majority Choice: Difference between revisions
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Line 110:
X2 > X4 >> X1 > X3
where the ">>" indicates the approval cutoff --- candidates to the right of that sign receive no approval votes. This ballot is counted as
X2 > X4
X2 > X1
X2 > X3
X4 > X1
X4 > X3
▲ X4 > X4 (approval point)
X1 > X3
Line 141:
For example, the X2>X4 ("for X2 over X4") vote is entered in {row 2, column 4}.
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
* the {row 2, column 2} (X2>X2) total approval score exceeds the {row 4, column 4} (X4>X4) total approval score.
The winner is then determined as described above.
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, which is why DMC is equivalent to RAV. 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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