[EM] Easy fix to Alaska's ranked-choice voting

[Forest Simmons]

On Thu, Nov 10, 2022, 9:40 PM Richard, the VoteFair guy <
electionmethods at votefair.org> wrote:

> On 11/9/2022 12:05 AM, Forest Simmons wrote:
>
>  > A candidate is uncovered iff it has a beatpath of
>  > only two steps to each candidate (if any) that beats it.
>
> Should the "only two steps" be interpreted as "two or fewer steps?" or
> "two or more steps?" or "exactly two steps?"
>
In this context, exactly two, because when a candidate beats it, it cannot
beat that candidate in one step, since it is not possible for X to outrank
Y on more ballots than Y outranks X, and at the same time have Y out rank X
on more ballots than X outranks Y.

A candidate X has a beatpath to every other candidate if and only if X is
in the Smith set.

So the Landau is a subset of the Smith set.

You see Landau is more special because it requires shorter beatpaths. Any
length beatpath will do for Smith.

Suppose the cycle ABCA is augmented with a candidate D that beats only A,
and is beaten by B and C.

Then all four candidates are in Smith because the beat cycle  DABCD
includes a beatpath from each candidate to each of the other candidates.

Is D a Landau candidate? Well C beats it. So does it have a two-step path
back to C? No. So it is covered by C, and covered means not in Landau.

Is A a Landau candidate? Yes. Only D and C beat it, and ABD and ABC are the
respective required two-step beatpaths that get back to D and C,
respectively.

Does that help?



> I'm still trying to understand the "uncovered" (and "covered") concept.
> Especially, what is its relationship to the Smith set?
>
> Thanks,
>
> Richard Fobes
>
>
> On 11/9/2022 12:05 AM, Forest Simmons wrote:
> > In this context the most relevant question is what do we mean by
> > "uncovered", since that's the word used in the method definition ...
> >
> > Repeatedly eliminate the (remaining) candidate with fewest votes until
> > there remains only one uncovered candidate to elect.
> >
> > No need to know what covering means, although you can figure it out
> > indirectly from the definition of "uncovered:"
> >
> > A candidate is uncovered iff it has a beatpath of only two steps to each
> > candidate (if any) that beats it.
> >
> > Any candidate X who complains that they should have won because they
> > beat the winner W pairwise will get this truthful and obviously relevant
> > rejoinder:
> >
> > When you were eliminated, you had fewer transferred votes than I.
> >
> > I fact, I beat every candidate pairwise that was not already eliminated
> > (like you) on the basis of two few (transferred) votes.
> >
> > It is very easy to discern if some candidate X is uncovered:
> >
> > Just check each candidate Y that beats it (X) to see if it has a two
> > step beatpath via some Z, back to Y:
> >
> > X beats Z beats Y
> >
> > Only Smith candidates can be uncovered because only Smith candidates
> > have beatpaths back to the candidates that beat them. So the candidates
> > you have to check are the Smith candidates ... at most three, and rarely
> > more than one, in a public election.
> >
> > If you want, you can run IRV all the way through ... then if the IRV
> > winner is uncovered, you are done. If not, back up until you cone to an
> > uncovered candidate ... that's your winner!
> >
> > It's just a matter of doing regular IRV, and backing up (if necessary)
> > until you get to an uncovered candidate.
> >
> > Forest
> >
> >
> > On Tue, Nov 8, 2022, 11:18 AM Kristofer Munsterhjelm
> > <km_elmet at t-online.de <mailto:km_elmet at t-online.de>> wrote:
> >
> >     On 08.11.2022 18:02, Richard, the VoteFair guy wrote:
> >      > Forest, what do you mean by "covered"?  Is there a Wikipedia or
> >      > Electowiki article (or section of an article) that explains it?
> >     Or is
> >      > there a dictionary reference you can point to?
> >      >
> >      > Yes, you've used the words "covered" and "uncovered" many times
> >     but I
> >      > don't recall ever seeing a clear explanation of what you mean.  I
> >      > presume it involves pairwise counts, but that's as far as I can
> >     guess.
> >
> >     The short answer is: A covers B if A pairwise beats everybody B
> >     pairwise
> >     beats and then some.
> >
> >     An uncovered candidate is someone who is not covered by anyone else.
> >
> >     This definition works when there are no pairwise ties. Things get
> >     trickier with pairwise ties, as I found out when generalizing
> Friendly
> >     Cover.
> >
> >     -km
> >     ----
> >     Election-Methods mailing list - see https://electorama.com/em
> >     <https://electorama.com/em> for list info
> >
> ----
> Election-Methods mailing list - see https://electorama.com/em for list
> info
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20221112/4f100e59/attachment.htm>