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

[Forest Simmons]

This same simple tweak works on any method with a built in finish order,
including any one-at-a-time elimination method like IRV, BTR-IRV, Baldwin,
etc:

Elect the uncovered candidate highest in the finish order.

Why does our suggested tweak say to elect the highest uncovered candidate
in the finish order, instead of the highest unbeaten candidate in the
finish order?

Answer: because sometimes there is no unbeaten candidate, but there is
always an uncovered candidate.

The simplest and best one-by-one elimination method is Gross Loser
Elimination.

No other one-at-time elimination method can improve on it, much less the
uncovered version:

Elect the uncovered candidate highest in the Gross Elimination finish order.

Like IRV it is clone free. Unlike IRV it is precinct summable on one pass
through the ballots at each precinct.

Wouldn't that have been nice last night at the midterm election count?

Like IRV it is non monotonic, but unlike IRV it is Yee/Bolson monotonic:
the win regions are convex, not pathological fractals. [I almost wrote
Bolsonaro instead of Bolson ... sorry Brian!]

Pick any method X, and pair it with Gross Loser Elimination ... uncovered
version or not ... and do a pairwise runoff between the two winners.

Not only will Gross Loser Elimination almost always come out ahead, the
people who do the experiment will come away saying, "Why do we even bother
with method X? GLE is so much more simple and effective."

GLE is already Smith efficient without the uncovered tweak ... that's just
optional frosting on the cake.

It is the simplest Smith efficient method that does not require computing
pairwise wins or losses. No need to mention Smith or Condorcet or pairwise
defeats.

It automatically eliminates the Condorcet Loser at any stage when there is
one, because when there is a Condorcet Loser, it will also be the Gross
Loser.

The Gross Loser is the candidate with the fewest ballots preferring it over
any other candidate. In a tournament, it is the candidate with the single
most embarrassingly low score.

In fact, unlike IRV, Gross Loser Elimination can be used to get a finish
order for a Round Robin Tournament, so the uncovered tweak can be applied
to it if so desired.

Suppose when there are only three uneliminated teams, team Rock's scores
against the other two teams stand at 60 and 40,  while team Paper's scores
are 45 points against one team, and 72 against the other, and finally team
Scissors' scores stand at 35 and 90.

Which team will be eliminated at this stage of GLE?

Answer ... Scissors, because no other team scored as low as 35.

Note that we did not even need to know who the other team was that skunked
Scissors, or how much it scored in that game to know that Scissors was the
Gross Loser of that round.

Now tell me, who was the IRV loser of that round?

Answer: impossible to know, because IRV makes no sense in a tournament
context, unless it is a superficial popularity contest of some kind.

Is this the best RCV public proposal?

No other Universal Domain method this simple is anywhere near as good.

How about outside the UD? Do you think STAR is a better proposal? If so why?

-Forest










On Wed, Nov 9, 2022, 12:05 AM Forest Simmons <forest.simmons21 at gmail.com>
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
>
>
>
>
>
>
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>
>
> 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
>> ----
>> Election-Methods mailing list - see https://electorama.com/em for list
>> info
>>
>
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