Definite Majority Choice: Difference between revisions
Content added Content deleted
imported>Araucaria (Moved ''least-approved'' definition to top of article) |
imported>Araucaria (→Tallying Votes: method clarification) |
||
Line 136: | Line 136: | ||
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''. |
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, |
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'''. |
|||
# |
# Candidates that pairwise defeat all higher-approved candidates. We call this group 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]]. |
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. 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: |
DMC has some interesting properties: |