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

[Forest Simmons]

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>
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
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>
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