Английская Википедия:Descending solid coalitions
Шаблон:Short description Шаблон:Multiple issues Шаблон:Electoral systemsDescending Solid Coalitions (DSC) is a ranked-choice voting system designed to preserve all the advantages of instant-runoff voting while still satisfying monotonicity.[1] It was developed by the famed voting theorist Douglas Woodall as an improvement on (and replacement for) the use of the single transferable vote in some countries.
A minor variant, Descending Acquiescing Coalitions (DAC), treats equal-ranked ballots slightly differently.[1]
Procedure
DSC assigns every coalition (i.e., set) of candidates a score equal to their total number of supporters; a supporter is a voter who ranks every member of the coalition higher than every non-member. Coalitions are ranked by their number of supporters (in descending order); at each step, we eliminate all candidates who are not supported by the coalition (unless doing so would eliminate all candidates). When only one candidate is still eligible to win, that candidate is elected.[1]
DAC differs in defining a supporter as a voter who ranks every member of the coalition higher than or equal to every non-member; when equal-ranked ballots are not permitted (as with most implementations of instant-runoff voting), both methods are identical.[1]
Properties
DSC satisfies majority, monotonicity, participation, plurality, later-no-harm,Шаблон:NoteTag later-no-help,Шаблон:NoteTag and independence of clones.[1]
It fails the Condorcet criterion, independence of irrelevant alternatives, and independence of Smith-dominated alternatives.
Comparison to instant-runoff
DSC was intended to serve as a practical alternative to instant-runoff voting, preserving all the positive attributes of IRV while mitigating many of its downsides. Unlike IRV, DSC satisfies both monotonicity and participation, meaning that candidates cannot lose because they have "too much support."[1]
At the same time, it maintains the most important advantages of IRV: independence of clones, later-no-harm, and later-no-help.[1]
Example
The possible coalitions have the following strengths:
- 58 {N, C, K}
- 42 {M}
- 42 {M, N}
- 42 {M, N, C}
- 32 {C, K}
- 26 {N, C}
- 26 {N}
- 17 {K}
- 15 {C}
(Where ties have been broken by ordering sets from fewest to most candidates.)
Going step-by-step:
- {N, C, K} has the largest coalition, so Memphis is eliminated (as it is not in the largest possible coalition).
- The next-strongest set is {M}, which would eliminate all candidates, so it is ignored.
- The next-strongest set is {M, N}, which would eliminate candidates {C, K}.
All candidates other than Nashville have been eliminated, leaving N the winner.
From this example we can see that DSC tends to select more moderate alternatives than IRV (Nashville, instead of Chattanooga) because it considers all the coalitions that might support of a candidate, instead of only considering the highest-ranked candidate who has not been eliminated.
Notice that more than half of the votes held Memphis to be the worst alternative, yet the Memphis supporters' votes were still useful in securing their second choice, Nashville. If the Memphis voters had not listed any preferences after Memphis, the winner would have been Chattanooga.
References
Шаблон:Reflist Шаблон:Voting systems
