Difference between revisions of "Template:Comparison of Schulze to preferential voting systems"

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{| class="wikitable collapsible sortable" style="text-align:center"
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{| class="wikitable collapsible sortable" style="text-align:center;"
|+ Comparison of Preferential Electoral Systems
+
|+ Comparison of preferential electoral systems
 
|-
 
|-
! style="width:8%;" |
+
! style="width:8%;" | Sys­tem
! style="width:3%;" | [[Monotonicity criterion|Monotonic]]
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! style="width:3%;" | [[Monotonicity criterion|Mono­tonic]]
! style="width:3%;" | [[Condorcet criterion|Condorcet]]
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! style="width:3%;" | [[Condorcet criterion|Cond­orcet]]
! style="width:3%;" | [[Majority criterion|Majority]]
+
! style="width:3%;" | [[Majority criterion|Majo­rity]]
 
! style="width:3%;" | [[Condorcet loser criterion|Condorcet loser]]
 
! style="width:3%;" | [[Condorcet loser criterion|Condorcet loser]]
 
! style="width:3%;" | [[Majority loser criterion|Majority loser]]
 
! style="width:3%;" | [[Majority loser criterion|Majority loser]]
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! style="width:3%;" | [[Independence of Smith-dominated alternatives|ISDA]]
 
! style="width:3%;" | [[Independence of Smith-dominated alternatives|ISDA]]
 
! style="width:3%;" | [[Independence of irrelevant alternatives#Local independence|LIIA]]
 
! style="width:3%;" | [[Independence of irrelevant alternatives#Local independence|LIIA]]
! style="width:3%;" | [[Independence of clones criterion|Clone independence]]
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! style="width:3%;" | [[Independence of clones criterion|Independence of clones]]
 
! style="width:3%;" | [[Reversal symmetry]]
 
! style="width:3%;" | [[Reversal symmetry]]
! style="width:3%;" | [[Participation criterion|Participation]], [[consistency criterion|Consistency]]
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! style="width:3%;" | [[Participation criterion|Participation]], [[consistency criterion|consistency]]
 
! style="width:3%;" | [[Later-no-harm criterion|Later-no‑harm]]
 
! style="width:3%;" | [[Later-no-harm criterion|Later-no‑harm]]
 
! style="width:3%;" | [[Later-no-help criterion|Later-no‑help]]
 
! style="width:3%;" | [[Later-no-help criterion|Later-no‑help]]
 
! style="width:3%;" | [[Polynomial time]]
 
! style="width:3%;" | [[Polynomial time]]
! style="width:3%;" | [[Resolvability criterion|Resolvability]]
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! style="width:3%;" | [[Resolvability criterion|Resol­vability]]
 
|-
 
|-
 
! [[Schulze method|Schulze]]
 
! [[Schulze method|Schulze]]
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! [[Nanson's method|Nanson]]
 
! [[Nanson's method|Nanson]]
 
| {{no}}  || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{no}}  || {{no}}  || {{no}}  || {{yes}} || {{no}} || {{no}} || {{no}} || {{yes}} || {{yes}}
 
| {{no}}  || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{no}}  || {{no}}  || {{no}}  || {{yes}} || {{no}} || {{no}} || {{no}} || {{yes}} || {{yes}}
 +
|-
 +
! [[Black's method|Black]]
 +
| {{yes}}  || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{no}} || {{no}} || {{no}}  || {{no}}  || {{no}}  || {{yes}} || {{no}} || {{no}} || {{no}} || {{yes}} || {{yes}}
 
|-
 
|-
 
! [[Instant-runoff voting]]
 
! [[Instant-runoff voting]]
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| {{no}}  || {{no}}  || {{yes}} || {{yes}} || {{yes}} || {{no}}  || {{no}}  || {{no}}  || {{no}}  || {{no}}  || {{no}} || {{no}} || {{yes}} || {{yes}} || {{yes}}  || {{yes}}
 
| {{no}}  || {{no}}  || {{yes}} || {{yes}} || {{yes}} || {{no}}  || {{no}}  || {{no}}  || {{no}}  || {{no}}  || {{no}} || {{no}} || {{yes}} || {{yes}} || {{yes}}  || {{yes}}
 
|-
 
|-
! [[Coombs' method|Coombs]]<ref name=truncation>Anti-plurality, Coombs and Dodgson are assumed to receive truncated preferences by apportioning possible rankings of unlisted alternatives equally; for example, ballot A&nbsp;>&nbsp;B&nbsp;=&nbsp;C is counted as <math>\tfrac{1}{2}</math>&nbsp;A&nbsp;>&nbsp;B&nbsp;>&nbsp;C and <math>\tfrac{1}{2}</math>&nbsp;A&nbsp;>&nbsp;C&nbsp;>&nbsp;B.  If these methods are assumed not to receive truncated preferences, then [[Later-no-harm criterion|Later-no-harm]] and [[Later-no-help criterion|Later-no-help]] are not applicable.</ref>
+
! [[Coombs' method|Coombs]]<ref name=truncation>Anti-plurality, Coombs and Dodgson are assumed to receive truncated preferences by apportioning possible rankings of unlisted alternatives equally; for example, ballot A&nbsp;>&nbsp;B&nbsp;=&nbsp;C is counted as <math>\tfrac{1}{2}</math>&nbsp;A&nbsp;>&nbsp;B&nbsp;>&nbsp;C and <math>\tfrac{1}{2}</math>&nbsp;A&nbsp;>&nbsp;C&nbsp;>&nbsp;B.  If these methods are assumed not to receive truncated preferences, then [[later-no-harm criterion|later-no-harm]] and [[later-no-help criterion|later-no-help]] are not applicable.</ref>
 
| {{no}}  || {{no}}  || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{no}}  || {{no}}  || {{no}}  || {{no}}  || {{no}} || {{no}} || {{no}} || {{no}} || {{yes}}  || {{yes}}
 
| {{no}}  || {{no}}  || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{no}}  || {{no}}  || {{no}}  || {{no}}  || {{no}} || {{no}} || {{no}} || {{no}} || {{yes}}  || {{yes}}
 
|-
 
|-

Latest revision as of 11:40, 27 November 2020

Comparison of preferential electoral systems
Sys­tem Mono­tonic Cond­orcet Majo­rity Condorcet loser Majority loser Mutual majority Smith ISDA LIIA Independence of clones Reversal symmetry Participation, consistency Later-no‑harm Later-no‑help Polynomial time Resol­vability
Schulze Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes No No No Yes Yes
Ranked pairs Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No No No Yes Yes
Tideman's Alternative No Yes Yes Yes Yes Yes Yes Yes No Yes No No No No Yes Yes
Kemeny–Young Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes No No No No Yes
Copeland Yes Yes Yes Yes Yes Yes Yes Yes No No Yes No No No Yes No
Nanson No Yes Yes Yes Yes Yes Yes No No No Yes No No No Yes Yes
Black Yes Yes Yes Yes Yes No No No No No Yes No No No Yes Yes
Instant-runoff voting No No Yes Yes Yes Yes No No No Yes No No Yes Yes Yes Yes
Borda Yes No No Yes Yes No No No No No Yes Yes No Yes Yes Yes
Baldwin No Yes Yes Yes Yes Yes Yes No No No No No No No Yes Yes
Bucklin Yes No Yes No Yes Yes No No No No No No No Yes Yes Yes
Plurality Yes No Yes No No No No No No No No Yes Yes Yes Yes Yes
Contingent voting No No Yes Yes Yes No No No No No No No Yes Yes Yes Yes
Coombs[1] No No Yes Yes Yes Yes No No No No No No No No Yes Yes
MiniMax Yes Yes Yes No No No No No No No No No No No Yes Yes
Anti-plurality[1] Yes No No No Yes No No No No No No Yes No No Yes Yes
Sri Lankan contingent voting No No Yes No No No No No No No No No Yes Yes Yes Yes
Supplementary voting No No Yes No No No No No No No No No Yes Yes Yes Yes
Dodgson[1] No Yes Yes No No No No No No No No No No No No Yes
  1. 1.0 1.1 1.2 Anti-plurality, Coombs and Dodgson are assumed to receive truncated preferences by apportioning possible rankings of unlisted alternatives equally; for example, ballot A > B = C is counted as <math>\tfrac{1}{2}</math> A > B > C and <math>\tfrac{1}{2}</math> A > C > B. If these methods are assumed not to receive truncated preferences, then later-no-harm and later-no-help are not applicable.