Difference between revisions of "Condorcet//Approval"

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'''Condorcet//Approval''' is an election method according to which the [[Condorcet criterion|Condorcet]] winner is elected if one exists, otherwise the [[Approval voting]] winner is elected. Approval can be designated by a cutoff placed within the ranking by the voter. Alternatively, all explicitly ranked candidates on a ballot could be considered approved.
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'''Condorcet//Approval''' is an election method by which the [[Condorcet criterion|Condorcet]] winner is elected if one exists, otherwise the [[Approval voting|approval]] winner is elected. Also see Smith//Approval below.
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===Explicit/Implicit Approval===
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Approval can be designated by a cutoff ranked among alternatives (explicit approval). Alternatively, if truncation is allowed, all explicitly ranked candidates could be considered to be approved (implicit approval).
  
 
===Burial resistance===
 
===Burial resistance===
 
[[Condorcet method|Condorcet methods]] are generally vulnerable to [[Tactical voting|burying strategy]]. One faction ''buries'' a candidate by ranking him insincerely below other candidates. This is an attempt to give this candidate new or stronger pairwise defeats.
 
[[Condorcet method|Condorcet methods]] are generally vulnerable to [[Tactical voting|burying strategy]]. One faction ''buries'' a candidate by ranking him insincerely below other candidates. This is an attempt to give this candidate new or stronger pairwise defeats.
  
When all explicitly ranked candidates are considered approved, Condorcet//Approval makes burying strategy less likely to succeed than in other Condorcet methods. Burying is only effective when it prevents the targeted candidate from being the Condorcet winner. But a faction can't succeed in this task without then being counted as approving the candidate(s) beneath which the targeted candidate was insincerely ranked. This makes it quite likely that burying strategy will backfire, and cause a candidate to be elected who is actually liked less than the targeted candidate.
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When all explicitly ranked candidates are considered approved, Condorcet//Approval makes burying strategy more risky than in other Condorcet methods. Burying is only effective when it prevents the targeted candidate from being the Condorcet winner. But a faction can't succeed in this task without then being counted as approving the candidate(s) beneath which the targeted candidate was insincerely ranked. This makes it quite likely that burying strategy will backfire, and cause a candidate to be elected who is actually liked less than the targeted candidate.
  
 
One drawback in proposing implicit approval of all explicitly ranked alternatives is that, in general elections, many "sincere" (naive) voters will feel entitled to rank all alternatives. Many may then bristle at the assertion that they approve of unsavory candidates by exercising their franchise to distinguish between lesser and greater "evils". This perception may be mitigated somewhat by a change in terminology. Even so, voters or legislators may balk at reform if they anticipate voter frustration.
 
One drawback in proposing implicit approval of all explicitly ranked alternatives is that, in general elections, many "sincere" (naive) voters will feel entitled to rank all alternatives. Many may then bristle at the assertion that they approve of unsavory candidates by exercising their franchise to distinguish between lesser and greater "evils". This perception may be mitigated somewhat by a change in terminology. Even so, voters or legislators may balk at reform if they anticipate voter frustration.
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[[Approval voting]]'s satisfaction of the [[Favorite Betrayal criterion]] can be preserved in Condorcet//Approval by using the [[tied at the top]] rule. This results in the [[Improved Condorcet Approval]] method. However, this variant technically isn't [[Condorcet criterion|Condorcet]]-compliant.
 
[[Approval voting]]'s satisfaction of the [[Favorite Betrayal criterion]] can be preserved in Condorcet//Approval by using the [[tied at the top]] rule. This results in the [[Improved Condorcet Approval]] method. However, this variant technically isn't [[Condorcet criterion|Condorcet]]-compliant.
  
==Satisfied criteria==
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==Satisfied Criteria==
  
Condorcet//Approval satisfies [[Condorcet criterion|Condorcet]] and always elects a majority favorite, but doesn't satisfy [[Smith set|Smith]] or the [[Majority criterion for solid coalitions]]. It satisfies [[Minimal Defense criterion|Minimal Defense]] (and the [[Strong Defensive Strategy criterion]]), the [[Plurality criterion]], and [[Monotonicity criterion|monotonicity]].
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Condorcet//Approval satisfies [[Condorcet criterion|Condorcet]] and always elects a majority favorite, but doesn't satisfy [[Smith set|Smith]] or the [[Majority criterion for solid coalitions]]. It satisfies [[Monotonicity criterion|monotonicity]] and, when truncation is permitted, [[Minimal Defense criterion|Minimal Defense]] (and the [[Strong Defensive Strategy criterion]]) and the [[Plurality criterion]].
  
It fails [[Strategic nomination|Clone-Winner]], [[Participation criterion|Participation]], and [[Later-no-harm]].
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It fails [[Strategic nomination|Clone-Winner]], [[Participation criterion|Participation]], and [[Later-no-harm criterion|Later-no-harm]].
  
 
[[Category:Condorcet method]]
 
[[Category:Condorcet method]]
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== Smith//Approval ==
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The approval winner may be limited to the [[Smith set]]. This variation perforce satisfies the [[Smith set|Smith criterion]] and the [[Majority criterion for solid coalitions]]. It satisfies [[strategic nomination|clone independence]] at least when clones are defined such that every voter approves either all or no members of a clone set.
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== Explicit, Fully Ranked Smith//Approval ==
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: If this deserves a concise name, then use mine -- [[User:Jrfisher|Jrfisher]]
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::Voters ''must'' rank all but one alternative, (disallow ties or truncation).
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::Therefore, use an approval cutoff (explicit approval).
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::Pick the [[Condorcet Criterion|Condorcet Winner]] (CW) if there is one. Otherwise...
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::Find the smallest set of alternatives having no defeats outside the set ([[Smith set]]).
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::Within that set, the alternative with the most winning votes against the approval bar is the winner.
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== See Also ==
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[[Definite Majority Choice]] (DMC)

Latest revision as of 21:26, 10 October 2005

Condorcet//Approval is an election method by which the Condorcet winner is elected if one exists, otherwise the approval winner is elected. Also see Smith//Approval below.

Explicit/Implicit Approval

Approval can be designated by a cutoff ranked among alternatives (explicit approval). Alternatively, if truncation is allowed, all explicitly ranked candidates could be considered to be approved (implicit approval).

Burial resistance

Condorcet methods are generally vulnerable to burying strategy. One faction buries a candidate by ranking him insincerely below other candidates. This is an attempt to give this candidate new or stronger pairwise defeats.

When all explicitly ranked candidates are considered approved, Condorcet//Approval makes burying strategy more risky than in other Condorcet methods. Burying is only effective when it prevents the targeted candidate from being the Condorcet winner. But a faction can't succeed in this task without then being counted as approving the candidate(s) beneath which the targeted candidate was insincerely ranked. This makes it quite likely that burying strategy will backfire, and cause a candidate to be elected who is actually liked less than the targeted candidate.

One drawback in proposing implicit approval of all explicitly ranked alternatives is that, in general elections, many "sincere" (naive) voters will feel entitled to rank all alternatives. Many may then bristle at the assertion that they approve of unsavory candidates by exercising their franchise to distinguish between lesser and greater "evils". This perception may be mitigated somewhat by a change in terminology. Even so, voters or legislators may balk at reform if they anticipate voter frustration.

Favorite Betrayal criterion compliance

Approval voting's satisfaction of the Favorite Betrayal criterion can be preserved in Condorcet//Approval by using the tied at the top rule. This results in the Improved Condorcet Approval method. However, this variant technically isn't Condorcet-compliant.

Satisfied Criteria

Condorcet//Approval satisfies Condorcet and always elects a majority favorite, but doesn't satisfy Smith or the Majority criterion for solid coalitions. It satisfies monotonicity and, when truncation is permitted, Minimal Defense (and the Strong Defensive Strategy criterion) and the Plurality criterion.

It fails Clone-Winner, Participation, and Later-no-harm.

Smith//Approval

The approval winner may be limited to the Smith set. This variation perforce satisfies the Smith criterion and the Majority criterion for solid coalitions. It satisfies clone independence at least when clones are defined such that every voter approves either all or no members of a clone set.

Explicit, Fully Ranked Smith//Approval

If this deserves a concise name, then use mine -- Jrfisher
Voters must rank all but one alternative, (disallow ties or truncation).
Therefore, use an approval cutoff (explicit approval).
Pick the Condorcet Winner (CW) if there is one. Otherwise...
Find the smallest set of alternatives having no defeats outside the set (Smith set).
Within that set, the alternative with the most winning votes against the approval bar is the winner.

See Also

Definite Majority Choice (DMC)