Composite method

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, for the following ballot set:

10: L>A>B>C>R
 8: R>B>C>A>L
 5: C>A>B>L>R

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.

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.

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