Anonymous user
Definite Majority Choice: Difference between revisions
More rearrangement
imported>Araucaria No edit summary |
imported>Araucaria (More rearrangement) |
||
Line 15:
:The Definite Majority Choice winner is the ''least-approved'' candidate who, when compared in turn with each of the other ''higher-approved'' candidates, is preferred over the other candidate.
* DMC is a strong majority rule method.▼
* When defeat strength is measured by the approval of the defeating candidate,
DMC is the only one possible immune ([[Condorcet_method#Key_terms_in_ambiguity_resolution|cloneproof]])method.
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]).
DMC is also equivalent to [[Ranked Approval Voting]] (RAV) (also known as
Approval Ranked Concorcet), and [[Pairwise Sorted Approval]] (PSA): 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_voting|Approval]]
Some
== Procedure ==
Line 145 ⟶ 151:
* 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:
▲* When defeat strength is measured by the approval of the defeating candidate, there is only one possible immune method, namely DMC.
▲* DMC is a strong majority rule method.
==== A more intuitive ballot --- Ranking Candidates using Grades ====
| |||