Descending Acquiescing Coalitions: Difference between revisions
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imported>Kevin Lamoreau (mentioned DAC's satisfaction of the Later-no-help criterion) |
imported>Kevin Lamoreau (largely redid this page to model it after the page for Descending Solid Coalitions) |
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'''Descending Acquiescing Coalitions''' or ''' |
'''Descending Acquiescing Coalitions''' (or '''DSC''') 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. |
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== Procedure == |
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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. |
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When no voter uses equal rankings or truncation, then DSC and DAC give the same results. |
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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. |
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When only one candidate is still eligible to win, that candidate is elected. |
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== Properties == |
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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. |
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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]]. |
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===Example=== |
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{{Tenn_voting_example}} |
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The sets have the following strengths: |
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100 {M,N,C,K}<br> |
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58 {N,C,K}<br> |
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42 {M,N,C}<br> |
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42 {M,N}<br> |
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42 {M}<br> |
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32 {C,K}<br> |
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26 {N,C}<br> |
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26 {N}<br> |
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17 {K}<br> |
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15 {C}<br> |
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{N,C,K} is the strongest set that excludes a candidate. Memphis becomes ineligible. |
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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. |
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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. |
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[[Category:Single-winner voting systems]] |
[[Category:Single-winner voting systems]] |