View source for Descending Acquiescing Coalitions

'''Descending Acquiescing Coalitions''' (or '''DAC''') is a [[voting system]] devised by Douglas Woodall for use with ranked ballots. It is a variation of [[Descending Solid Coalitions]] (DSC), another [[voting system]] devised by Woodall.

== Procedure ==

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.

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 [[Independence of clone alternatives|Clone Independence]].

DAC fails the [[Condorcet criterion]], the [[Smith set|Smith criterion]] and the [[Later-no-harm criterion]]. It is (along with [[Descending Solid Coalitions|DSC]]) the most complicated method satisfying the [[Participation criterion]].

Like [[Descending Solid Coalitions]], DAC can be considered a [[Plurality voting|First-Preference Plurality]] variant that satisfies [[Independence of clone alternatives|Clone Independence]]. However, its coalition counting rule makes it depart from Plurality more than DSC does. For instance, in this example given by Chris Benham:

{{ballots|46: A
44: B>C
10: C}}

DAC elects C, while Plurality and DSC elect A.

===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. Since DAC satisfies the [[Later-no-help criterion]], however, 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 methods]]
[[Category:Monotonic electoral systems]]
[[Category:Clone-independent electoral systems]]