Descending Solid Coalitions: Difference between revisions

Then theThe sets are then considered in turn, from those with the greatest score to those with the least. When a set is considered, every candidate not in the set becomes ineligible to win, unless this would cause all candidates to be ineligible, in which case that set is ignored.

A variation of this method is [[Descending Acquiescing Coalitions]] (DAC).

DSC satisfies the [[Plurality criterion]], the [[Mutual majority criterion|Majority criterion]], [[Monotonicity criterion|Mono-raise]], [[Mono-add-top criterion|Mono-add-top]], the [[Participation criterion]], [[Later-no-harm criterion|Later-no-harm]], and Clone Independence.

DSC fails the [[Condorcet criterion]], andthe [[Smith set|Smith criterion]] and the [[Later-no-help criterion]].

DSC can be considered a [[Plurality voting|First-Preference Plurality]] variant that satisfies Clone Independence. It is (along with [[Descending Acquiescing Coalitions|DAC]]) is the most complicated method satisfying the [[Participation criterion]].

* 100 {M,N,C,K}<br>

* 58 {N,C,K}<br>

* 42 {M,N,C}<br>

* 42 {M,N}<br>

* 42 {M}<br>

* 32 {C,K}<br>

* 26 {N,C}<br>

* 26 {N}<br>

* 17 {K}<br>

* 15 {C}<br>

Since DSC satisfies [[Later-no-harm criterion|Later-no-harm]], it's not possible for a voter to get a better result by withholding lower preferences, or to hurt the chances of a candidate already ranked by ranking additional candidates below that candidate. Since ItDSC isfails possiblethe [[Later-no-help criterion]], however, it is possible in some cases for a voter to get a better result for a candidate already ranked by ranking additional candidates below that candidate, or by changing the ranking of candidates ranked below that candidate such that at least one candidate is ranked above another candidate instead of being ranked the same as or below that candidate. The corrolarycorollary to this statement is that it is possible in some cases for a voter to get a worse result for a candidate by withholding preferences for candidates ranked below that candidate, or by changing the ranking of candidates ranked below that candidate such that at least one candidate is ranked the same as or below another candidate instead of being ranked above that candidate. If the Nashville voters had not listed any preferences after either Nashville or Chattanooga, or had ranked Memphis the same as or above either Knoxville or Chattanooga or both Knoxville and Chattanooga, the winner would have been Memphis, as the number of candidates strictly committed to the set {N,C,K} would have been only 32, which is less than the number of candidates strictly committed to at least the sets {M} and {M,N}, and. regardlessRegardless of the order in which those two sets (along with the set {M,N,C} if Nashville's voters had still all ranked Chattanooga ahead of Knoxville) were considered, Memphis would have been the only candidate remaining after those two or three sets were considered and so would have been the winner.

[[Category:Single-winner voting systemsmethods]]