Difference between revisions of "CDTT"
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Revision as of 19:07, 22 March 2005
The Condorcet doublyaugmented top tier or CDTT is defined by Douglas Woodall as the union of all minimal nonempty sets of candidates such that no candidate in each set has a majoritystrength pairwise loss to any candidate outside of the set.
Equivalently it can be defined as the set containing each candidate A who has a majoritystrength beatpath to every other candidate B who has a majoritystrength beatpath to A. That is, a candidate A is in the CDTT unless some candidate B has a majoritystrength beatpath to A while A has no such beatpath to B.
Uses
Limiting an election method's selection to the CDTT members can permit it to satisfy the Strong Defensive Strategy criterion (or Minimal Defense) and Majority, while coming close to satisfying the Laternoharm criterion. Specifically, the CDTT completely satisfies Laternoharm in the threecandidate case, and failures can only occur in the general case when there are majoritystrength cycles.
In order to maximize Laternoharm compliance, the CDTT should be paired with a method that itself fully satisfies Laternoharm. In order to ensure that Monoraise is not failed, the paired method should be used to generate a ranking of the candidates which is not influenced by which candidates make it into the CDTT. Then the CDTT member who appears first in this ranking is elected.
Some methods which can be paired in this way with the CDTT:
 Random Ballot: This can be very indecisive, but it is conceptually simple, and it satisfies Monoraise and Clone Independence.
 FirstPreference Plurality: This is decisive, simple, and monotone, but fails Clone Independence.
 Instant Runoff Voting: This is more complicated. It satisfies Clone Independence but not monotonicity.
 Descending Solid Coalitions: This is also somewhat complicated, but it's the only nonrandom option which satisfies Clone Independence and Monoraise.
 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 Monoraise.
Regardless of the method paired with the CDTT, it should be noted that the combined method necessarily fails the Plurality criterion and Condorcet criterion.