Difference between revisions of "Condorcet//Approval"

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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]] winner is elected. The approval winner may (Smith//Approval) or may not be limited to the [[Smith set]].
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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.
  
Approval could be designated by a cutoff ranked among alternatives by the voter (explicit approval). Alternatively, if truncation is allowed, all explicitly ranked candidates could be considered to be approved (implicit approval).
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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===
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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]].
 
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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[[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.
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== Explicit, Fully Ranked Smith//Approval ==
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: If this deserves a 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)

Revision as of 15:14, 22 August 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 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.

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 Minimal Defense (and the Strong Defensive Strategy criterion), the Plurality criterion, and monotonicity.

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.

Explicit, Fully Ranked Smith//Approval

If this deserves a 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)