Definite Majority Choice: Difference between revisions
Content added Content deleted
imported>Araucaria No edit summary |
imported>Araucaria |
||
| Line 51: | Line 51: | ||
Since the diagonal cells in the Condorcet pairwise matrix are usually left blank, those locations can be used to store each candidate's Approval point score. |
Since the diagonal cells in the Condorcet pairwise matrix are usually left blank, those locations can be used to store each candidate's Approval point score. |
||
We call a candidate [[Techniques_of_method_design#Defeats_and_defeat_strength| |
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, |
||
# Eliminate all definitively defeated candidates. |
# Eliminate all definitively defeated candidates. We call the remaining candidates the '''definite majority set'''. |
||
# The winner is the single candidate who pairwise defeats (wins head-to-head contests with) all other candidates in the |
# The winner is the single candidate who pairwise defeats (wins head-to-head contests with) all other candidates in the definite majority set. |
||
DMC always selects the [[Condorcet Criterion|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 and then recalculating the new Smith set |
DMC always selects the [[Condorcet Criterion|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 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. |
||
DMC has some interesting properties: |
DMC has some interesting properties: |
||
* The DMC winner has the lowest total approval score of any candidate in the Definite Majority set. |
* The DMC winner has the lowest total approval score of any candidate in the Definite Majority set. |
||
* When defeat strength is measured by the approval of the defeating candidate, there is only one possible immune method, namely DMC. |
* When defeat strength is measured by the approval of the defeating candidate, there is only one possible immune method, namely DMC. |
||