Descending Acquiescing Coalitions: Difference between revisions

Descending Acquiescing Coalitions (view source)

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Line 1: '''Descending Acquiescing Coalitions''' (or '''~~DAC~~DSC''') is a [[voting system]] devised by Douglas Woodall for use with ranked ballots. It is ~~equivalent~~a tovariation of [[Descending Solid Coalitions]] (DSC), ~~except~~another ~~that~~[[voting ~~sets~~system]] ~~are scored not~~devised by the number of voters solidly committed to them, but by the number of voters ''acquiescing'' to them. A voter "acquiesces" to a set of candidates if he does not strictly prefer any candidate outside of the set to any candidate within the setWoodall. == Procedure == Unlike DSC, DAC does not satisfy the [[Later-no-harm criterion]], but it does, unlike DSC, satisfy the [[Later-no-help criterion]].▼ Every possible set of candidates is given a score equal to the number of voters who ''acquiesce'' to the candidates in that set. A voter "acquiesces" to a set of candidates if he or she does not rank any candidate outside of the set strictly above any candidate within the set. ~~When no voter uses equal rankings or truncation, then DSC and DAC give the same results.~~ Then 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. When only one candidate is still eligible to win, that candidate is elected. == Properties == DAC satisfies the [[Plurality criterion]], the [[Mutual majority criterion\|Majority criterion]], [[Monotonicity criterion\|Mono-raise]], [[Mono-add-top criterion\|Mono-add-top]], the [[Participation criterion]], the [[Later-no-help criterion]] and Clone Independence. ▲~~Unlike DSC,~~ DAC ~~does not satisfy~~fails the [[~~Later-no-harm~~Condorcet criterion]], ~~but~~the it[[Smith ~~does,~~set\|Smith ~~unlike DSC,~~criterion]] ~~satisfy~~and the [[Later-no-~~help~~harm criterion]]. DAC can be considered a [[Plurality voting\|First-Preference Plurality]] variant that satisfies Clone Independence. It is (along with [[Descending Solid Coalitions\|DSC]]) the most complicated method satisfying the [[Participation criterion]]. ===Example=== {{Tenn_voting_example}} The sets have the following strengths: 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> {N,C,K} is the strongest set that excludes a candidate. Memphis becomes ineligible. No matter in which order we consider the sets with 42% of the voters solidly committed to them, we will arrive at the same result, which is that Nashville will be the only candidate remaining. So Nashville is the winner. Since DAC fails the [[Later-no-harm criterion]], a voter can hurt the chances of a candidate already ranked by ranking additional candidates below that candidate, and can thus get a better result in some cases by witholding lower preferences. And since DAC satisfies the [[Later-no-help criterion]], a voter cannot increase the probability of election of a candidate already ranked by ranking additional candidates below that candidate, and cannot hurt the chances of a candidate already ranked by withholding or equalizing lower preferences. [[Category:Single-winner voting systems]]