Composite method: Difference between revisions
Added some monotonicity implications.
(Created page with "Composite methods are voting methods constructed by combining multiple other methods. Usually sets like the Smith set or uncovered set are considered to be methods in this context. Two common method compositions used on the election-methods list are the comma and double slash (or slash) compositions. These are as follows: ==Comma== The composition M1,M2 denotes taking the result of method M1, then breaking any ties in the ordering by using M2. For instance...") |
(Added some monotonicity implications.) |
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The composition M1//M2 denotes taking the result of method M1, eliminating everybody but the winners according to that method, and then giving the outcome of M2 on the reduced ballot set. For instance, the method that first eliminates every candidate not in the [[Smith set]], then runs IRV on the remaining candidates, is [[Smith//IRV]].
==Criterion compliances==
If M1 and M2 are two methods, then M1,M2 is monotone if:
* M1 and M2 are both monotone
* Raising a candidate X can't add another candidate Y into the M1 set (or make Y tie for first if M1 is a method).
M1//M2 is monotone if:
* M1 and M2 are both monotone
* Raising a candidate X can neither add nor remove another candidate Y from the M1 set (or tied for first).
These are sufficient conditions: methods can be monotone even if they fail these conditions. For instance, Copeland//Borda ([[Ranked Robin]]) is monotone even though the conditions are not met.
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