Composite method: Difference between revisions
m
Added cn as I couldn't find any sources for this term.
(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...") |
m (Added cn as I couldn't find any sources for this term.) |
||
| (6 intermediate revisions by 2 users not shown) | |||
Line 1:
Common compositions include:
Two common method compositions used on the [[election-methods list]] are the comma and double slash (or slash) compositions. These are as follows:▼
* '''Condorcification''', which modifies the base method by electing the Condorcet winner (if one exists) as the first step.
* '''Smithification''',{{cn}} which begins by eliminating all candidates outside the [[Smith set]].
▲Two common method compositions used on the [[election-methods list]] are the comma and double slash (or slash) compositions.
==Comma==
Line 14 ⟶ 19:
The [[first past the post]] ordering is L>R>C>A=B and the Smith set is {A, B, C}. Thus the method Smith,Plurality would return the ordering C>A=B>L>R.
This composition was first defined by Woodall in 2003.<ref>{{cite journal|last=Woodall|first=D. R.|date=2003|title=Properties of single-winner preferential election rules II: examples and problems (draft)}}</ref>
==Double-slash==
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]].
This composition was first defined on the [[EM list]] by Bruce Anderson in 1996.<ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/1996-April/065516.html|title=Reply on EM to Mike's Reply on ER|website=Election-methods mailing list archives|date=1996-04-03|last=Anderson|first=B.}}</ref><ref group="fn">In Anderson's post, "Condorcet" refers not to the [[Condorcet winner]] but to Minimax Condorcet, which was called [[plain Condorcet]] in the early days of EM.</ref>
==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.
{{stub}}
==Footnotes==
<references group="fn" />
==References==
<references />
[[Category:Electoral_systems]][[Category:Glossary]]
| |||