Template:Comparison of voting systems: Difference between revisions

Content deleted Content added

Inline

Revision as of 04:38, 20 June 2024

Comparison of single-winner voting systems
Criterion Method	Majority	Majority loser	Mutual majority	Condorcet winner^{[Tn 1]}	Condorcet loser	Smith^{[Tn 1]}	Smith-IIA^{[Tn 1]}	LIIA	IIA^{[Tn 1]}	Cloneproof	Monotone	Participation	Later-no-harm^{[Tn 1]}	Later-no-help^{[Tn 1]}	No favorite betrayal^{[Tn 1]}
Anti-plurality	No	Yes	No	No	No	No	No	No	No	No	Yes	Yes	No	No	Yes
Approval	Yes	No	No	No	No	No	No	Yes	Yes^{[Tn 2]}	Yes	Yes	Yes	No	Yes	Yes
Baldwin	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Black	Yes	Yes	No	Yes	Yes	No	No	No	No	No	Yes	No	No	No	No
Borda	No	Yes	No	No	Yes	No	No	No	No	No	Yes	Yes	No	Yes	No
Bucklin	Yes	Yes	Yes	No	No	No	No	No	No	No	Yes	No	No	Yes	No
Coombs	Yes	Yes	Yes	No	Yes	No	No	No	No	No	No	No	No	No	Yes
Copeland	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	Yes	No	No	No	No
Dodgson	Yes	No	No	Yes	No	No	No	No	No	No	No	No	No	No	No
Highest median	Yes	Yes^{[Tn 3]}	No^{[Tn 4]}	No	No	No	No	Yes	Yes^{[Tn 2]}	Yes	Yes	No^{[Tn 5]}	No	Yes	Yes
Instant-runoff	Yes	Yes	Yes	No	Yes	No	No	No	No	Yes	No	No	Yes	Yes	No
Kemeny–Young	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	Yes	No	No	No	No
Minimax	Yes	No	No	Yes^{[Tn 6]}	No	No	No	No	No	No	Yes	No	No^{[Tn 6]}	No	No
Nanson	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No
Plurality	Yes	No	No	No	No	No	No	No	No	No	Yes	Yes	Yes	Yes	No
Random ballot^{[Tn 7]}	No	No	No	No	No	No	No	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Ranked pairs	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	Yes	Yes	No^{[Tn 5]}	No	No	No
Runoff	Yes	Yes	No	No	Yes	No	No	No	No	No	No	No	Yes	Yes	No
Schulze	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	Yes	Yes	No^{[Tn 5]}	No	No	No
Score	No	No	No	No	No	No	No	Yes	Yes^{[Tn 2]}	Yes	Yes	Yes	No	Yes	Yes
Sortition^{[Tn 8]}	No	No	No	No	No	No	No	Yes	Yes	No	Yes	Yes	Yes	Yes	Yes
STAR	No	Yes	No	No	Yes	No	No	No	No	No	Yes	No	No	No	No
Tideman alternative	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	Yes	No	No	No	No	No
Table Notes	^ ^a ^b ^c ^d ^e ^f ^g \|Condorcet, Smith and Independence of Smith-dominated alternatives criteria are incompatible with Independence of irrelevant alternatives, Consistency, Participation, Later-no-harm, Later-no-help, and Favorite betrayal^{[clarification needed]} criteria. ^ ^a ^b ^c Approval voting, score voting, and majority judgment satisfy IIA if it is assumed that voters rate candidates independently using their own absolute scale. For this to hold, in some elections, some voters must use less than their full voting power despite having meaningful preferences among viable candidates. ^ Majority Judgment may elect a candidate uniquely least-preferred by over half of voters, but it never elects the candidate uniquely bottom-rated by over half of voters. ^ Majority Judgment fails the mutual majority criterion, but satisfies the criterion if the majority ranks the mutually favored set above a given absolute grade and all others below that grade. ^ ^a ^b ^c In Highest median, Ranked Pairs, and Schulze voting, there is always a regret-free, semi-honest ballot for any voter, holding all other ballots constant and assuming they know enough about how others will vote. Under such circumstances, there is always at least one way for a voter to participate without grading any less-preferred candidate above any more-preferred one. ^ ^a ^b A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm. ^ A randomly chosen ballot determines winner. This and closely related methods are of mathematical interest and included here to demonstrate that even unreasonable methods can pass voting method criteria. ^ Where a winner is randomly chosen from the candidates, sortition is included to demonstrate that even non-voting methods can pass some criteria.

[condorcet-iia-incompatibility-1] ^ ^a ^b ^c ^d ^e ^f ^g |Condorcet, Smith and Independence of Smith-dominated alternatives criteria are incompatible with Independence of irrelevant alternatives, Consistency, Participation, Later-no-harm, Later-no-help, and Favorite betrayal^{[clarification needed]} criteria.

[IIA_rating_methods-2] Approval voting, score voting, and majority judgment satisfy IIA if it is assumed that voters rate candidates independently using their own absolute scale. For this to hold, in some elections, some voters must use less than their full voting power despite having meaningful preferences among viable candidates.

[3] Majority Judgment may elect a candidate uniquely least-preferred by over half of voters, but it never elects the candidate uniquely bottom-rated by over half of voters.

[mjmmc-4] Majority Judgment fails the mutual majority criterion, but satisfies the criterion if the majority ranks the mutually favored set above a given absolute grade and all others below that grade.

[semipc-5] In Highest median, Ranked Pairs, and Schulze voting, there is always a regret-free, semi-honest ballot for any voter, holding all other ballots constant and assuming they know enough about how others will vote. Under such circumstances, there is always at least one way for a voter to participate without grading any less-preferred candidate above any more-preferred one.

[MinimaxVarient-6] A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm.

[7] A randomly chosen ballot determines winner. This and closely related methods are of mathematical interest and included here to demonstrate that even unreasonable methods can pass voting method criteria.

[8] Where a winner is randomly chosen from the candidates, sortition is included to demonstrate that even non-voting methods can pass some criteria.

[Tn 1]

@@ Line 1: / Line 1: @@
 {{sticky header}}
+{{sort-under}}
 {| class="wikitable sortable mw-collapsible sticky-header sticky-header-scroll" style="text-align:center;"
 |+Comparison of single-winner voting systems
 ! style="vertical-align:middle;" style="border-bottom:2px solid #a0a0a0; rowspan=1{{diagonal split header|<br /><br />Method|Criterion}}
 ! style="border-bottom:2px solid #a0a0a0; |[[Majority]]
 ! style="border-bottom:2px solid #a0a0a0; |[[Majority loser criterion|Majority loser]]
@@ Line 12: / Line 13: @@
 ! style="border-bottom:2px solid #a0a0a0; |[[Independence of irrelevant alternatives#Local independence|LIIA]]
 ! style="border-bottom:2px solid #a0a0a0; |[[Independence of irrelevant alternatives|IIA]]<wbr><ref group=Tn name=condorcet-iia-incompatibility/>
-! style="border-bottom:2px solid #a0a0a0; |[[Independence of clones|Cloneproof]]
+! style="border-bottom:2px solid #a0a0a0; |[[Independence of clones|]]
-! style="border-bottom:2px solid #a0a0a0; |[[Monotonicity criterion|Monotone]]
+! style="border-bottom:2px solid #a0a0a0; |[[Monotonicity criterion|]]
 ! style="border-bottom:2px solid #a0a0a0; |[[Participation criterion|Participation]]<!-- ![[Reversal symmetry|Reversal]] -->
 ! style="border-bottom:2px solid #a0a0a0; |[[Later-no-harm]]<wbr><ref group=Tn name=condorcet-iia-incompatibility/>