CDTT: Difference between revisions
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== Uses == |
== Uses == |
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Limiting an election method's selection to the CDTT members can permit it to satisfy the [[Minimal Defense criterion]] (and thus the [[Strong Defensive Strategy criterion]]) and [[Mutual majority criterion|Majority]], while coming close to satisfying the [[Later-no-harm criterion]]. Specifically, the CDTT completely satisfies [[Later-no-harm criterion|Later-no-harm]] in the three-candidate case, and failures can only occur in the general case when there are majority-strength cycles. |
Limiting an election method's selection to the CDTT members can permit it to satisfy the [[Minimal Defense criterion]] (and thus the [[Strong Defensive Strategy criterion]]) and the [[Mutual majority criterion|Majority criterion for solid coalitions]], while coming close to satisfying the [[Later-no-harm criterion]]. Specifically, the CDTT completely satisfies [[Later-no-harm criterion|Later-no-harm]] in the three-candidate case, and failures can only occur in the general case when there are majority-strength cycles. |
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(Please see the articles on the [[Minimal Defense criterion]] and [[Later-no-harm criterion]] for commentary on the significance of these criteria.) |
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| ⚫ | The CDTT's [[Later-no-harm criterion|Later-no-harm]] performance can be preserved by pairing the CDTT with a method which itself fully satisfies [[Later-no-harm criterion|Later-no-harm]]. When the paired method is used to generate a ranking of the candidates which is ''not'' influenced by which candidates make it into the CDTT, then compliance with the [[Monotonicity criterion]] can be preserved when the paired method already satisfies this criterion. Then the CDTT member who appears first in this ranking would be elected. |
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Some methods which can be paired in this way with the CDTT: |
Some methods which can be paired in this way with the CDTT: |
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*'''[[Random Ballot]]''': This can be very indecisive, but it is conceptually simple, and it satisfies [[Monotonicity criterion|Mono-raise]] and Clone Independence. |
*'''[[Random Ballot]]''': This can be very indecisive, but it is conceptually simple, and it satisfies [[Monotonicity criterion|Mono-raise]] and Clone Independence. |
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*'''[[Plurality voting|First-Preference Plurality]]''': This is decisive, simple, and [[Monotonicity criterion|monotone]], but fails Clone Independence. |
*'''[[Plurality voting|First-Preference Plurality]]''': This is decisive, simple, and [[Monotonicity criterion|monotone]], but fails Clone Independence. |
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*'''[[Instant-runoff voting|Instant Runoff Voting]]''': This is more complicated. It satisfies Clone Independence but not [[Monotonicity criterion|monotonicity]]. |
*'''[[Instant-runoff voting|Instant Runoff Voting]]''': This is more complicated. It satisfies Clone Independence but not [[Monotonicity criterion|monotonicity]]. The IRV ranking would be the reverse of the candidates' elimination order. |
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*'''[[Descending Solid Coalitions]]''': This is also somewhat complicated, but it's the only non-random option which satisfies Clone Independence and [[Monotonicity criterion|Mono-raise]]. |
*'''[[Descending Solid Coalitions]]''': This is also somewhat complicated, but it's the only non-random option which satisfies Clone Independence and [[Monotonicity criterion|Mono-raise]]. |
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*'''[[Minmax|MinMax (Pairwise Opposition)]]''': This has the advantage that it is calculated based on the pairwise matrix, just as the CDTT itself is. However, it is somewhat indecisive and fails Clone Independence. It satisfies [[Monotonicity criterion|Mono-raise]]. |
*'''[[Minmax|MinMax (Pairwise Opposition)]]''': This has the advantage that it is calculated based on the pairwise matrix, just as the CDTT itself is. However, it is somewhat indecisive and fails Clone Independence. It satisfies [[Monotonicity criterion|Mono-raise]]. |
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