[EM] Help me understand some notation

[Forest Simmons]

In the case of a three candidate Smith set, the simplest way to get the
Smih,X winner is to use X finish order as the (reverse) agenda for SPE
(Sequential Pairwise Elimination): start at the least promising end of the
agenda (i.e. the last candidate in the finish order) and make one pass of
Bubble Sort. The candidate who ends up on top is the highest Smith
candidate (provided cardinality(Smith)=3).

The beauty of this is its seamless-ness ... no need to even construct or
even mention Smith.

Another Seamless (but not as simple) way is Agenda Based Landau applied to
the same finish order:

Initialize a variable w as the highest finish order candidate. Then ...

While w is covered, let t be the highest finish order candidate that covers
w. Store t in w: (t---->w).

The final value of w is the candidate we want.


El jue., 20 de ene. de 2022 2:22 a. m., Kristofer Munsterhjelm <
km_elmet at t-online.de> escribió:

> 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
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>
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