Definite Majority Choice: Difference between revisions
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See also [[Proposed Statutory Rules for DMC]].
It can be extended to use [[Range voting]] instead of [[Approval voting]] as its base: in that case, the method eliminates the least-rated candidate.
Its elimination logic is the same as [[Benham's method]], and the method can thus be thought of as a rated version of it.
== [[Range voting]] implementation ==
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== Alternative implementation ==
This implementation is called '''Pairwise Sorted Approval'''. It is the simplest of a class of [[Pairwise Sorted Methods]].
A voter ranks candidates, and specifies approval, either by using an [[Approval Cutoff]] or by ranking above and below a fixed approval cutoff rank.
To determine the winner,
# sort candidates in descending order of approval.
# For each candidate, move it higher in the list as long as it pairwise beats the next-higher candidate, and only after all candidates above it have moved upward as far as they can.
This procedure can be used to produce a social ordering. It finds the same winner as the Benham-form implementation.
== Properties ==
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== Background ==
The name "DMC" was first suggested [http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/015164.html here]. Equivalent methods have been suggested several times on the EM mailing list:
* The
* The Ranked Approval Voting
The [http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/015144.html philosophical basis] of DMC is to eliminate candidates that the voters strongly agree should ''not'' win, using two strong measures, and choose the undefeated candidate from those remaining.
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== Example ==
Here's a set of preferences taken from Rob LeGrand's [https://www.
The ranked ballots:
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The pairwise matrix, with the victorious and approval scores highlighted:
|- align="center"
| colspan=2 rowspan=2 |
! colspan=5 | against
|- align="center"
! class="against" | Brad
! class="against" | Dave
! class="against" | Erin
|- align="center"
! rowspan=5 | for
! class="for" | Abby
| bgcolor="yellow" | 645
| class="loss" | 458
| bgcolor="yellow" | 511
|- align="center"
! class="for" | Brad
| bgcolor="yellow" | 463
| bgcolor="yellow" | 410
| bgcolor="yellow" | 461
|- align="center"
| class="loss" | 460
| class="loss" | 460
| bgcolor="yellow" | 460
| class="loss" | 460
|- align="center"
! class="for" | Dave
| bgcolor="yellow" | 609
| bgcolor="yellow" | 461
| bgcolor="yellow" | 311
|- align="center"
! class="for" | Erin
| class="loss" | 410
| class="loss" | 298
| bgcolor="yellow" | 461
| bgcolor="yellow" | 610
| bgcolor="yellow" | 708
|}
The candidates in descending order of approval are Erin, Abby, Cora, Brad, Dave.
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After reordering the pairwise matrix, it looks like this:
|- align="center"
| colspan=2 rowspan=2 |
! colspan=5 | against
|- align="center"
! class="against" | Brad
! class="against" | Dave
|- align="center"
! rowspan=5 | for
! class="for" | Erin
| bgcolor="yellow" | 708
| class="loss" | 410
| bgcolor="yellow" | 461
| class="loss" | 298
| bgcolor="yellow" | 610
|- align="center"
! class="for" | Cora
| class="loss" | 460
|- align="center"
! class="for" | Brad
| bgcolor="yellow" | 623
| bgcolor="yellow" | 463
| class="loss" | 312
|- align="center"
| class="loss" | 311
| class="loss" | 436
| bgcolor="yellow" | 461
| bgcolor="yellow" | 609
| bgcolor="yellow" | 311
|}
To find the winner,
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* [[Marginal Ranked Approval Voting]]: chooses the winner from a subset of the definite majority set.
[[Category:
[[Category:Smith-efficient Condorcet methods]]
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