[EM] Help me understand some notation

[Kristofer Munsterhjelm]

On 20.01.2022 01:05, Daniel Carrera wrote:
> I just read this sentence:
> 
> "And going from Copeland//Borda to Copeland,Borda shouldn't make the
> method that much harder to understand.">
> I remember seeing Kristofer say "Smith//IRV" and "Smith,IRV". Evidently
> "//" and "," have particular meanings. Can someone explain what they
> are? At least one of those must mean "Restrict to the Smith set then
> apply IRV".

Smith,IRV is the method where you first do IRV and then you pick the
highest ranked candidate in the resulting social ordering that's in the
Smith set. (In IRV's case this means: the last eliminated candidate
who's in the Smith set.)

Smith//IRV is the method where you first eliminate everybody not in the
Smith set and *then* do IRV. This is your "restrict to the Smith set
then apply IRV".

Smith//X methods are often nonmonotone because raising A might insert
someone else into (or kick someone else out of) the Smith set. If this
candidate is say, ranked in the middle in the social ordering of X, then
the whole social ordering can change and turn the winner from A to
someone else. Smith,X methods don't have that (unless X itself already
fails).

Maybe I should add a note about this somewhere on electowiki, but I'm
not sure where I would put it so that people who don't know about the
notation would know where to look.

-km