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

[Andy Dienes]

@ Forest but also anyone who has answer:

If we have some prior ordering over candidates, what is the best way to
deliver a winner given pairwise prefs? I have seen a few options like Chain
Climbing, a single Bubble Sort pass, Friendly Cover, etc.
Let's say the way to generate this prior ordering is fixed and exogenous to
the method; it might be something like sorted by approvals collected
separately. What is current consensus on state-of-the-art?

On Wed, Nov 9, 2022 at 5:07 PM Forest Simmons <forest.simmons21 at gmail.com>
wrote:

> I forgot to mention that Gross Loser Elimination is just as burial
> resistant and Chicken resistant as IRV, and is less susceptible to
> compromise than IRV, because unlike IRV, it has no  Central Squeeze
> pathology.
>
> Imagine candidates X and Y close to the left and right of Center Z.  Under
> sincere ranked ballots Z will have few first choice votes compared to X and
> Y, so it will be eliminated, unless one of the factions compromises and
> votes its second choice Z over its favorite.
>
> Which one would benefit by that insincere order reversal?
>
> Answer: the pairwise loser in the final runoff step between X and Y.
>
> A note on counting GLE.... a rectangular table of pairwise counts is
> projected on the screen in the public counting room.
>
> The k_th entry in the j_th row of the table is the number of ballots on
> which the j_th candidate out ranks the k_th candidate.
>
> As the ballots are opened and the candidate rankings carefully compared
> one-by-one, the respective table entries for row j are incremental for each
> candidate k that candidate j outranks on that ballot.
>
> When the ballots have been fully tabulated, the elimination steps begin.
>
> At each step the smallest entry in the table is circled. All viewers must
> agree that it is indeed the smallest entry before continuing the step.
>
> Once all observers are in agreement that the smallest entry is the k_th
> entry of row j, then candidate j is declared to be the Gross Loser of this
> step, and so is eliminated by crossing out both the j_th row and the j_th
> column of the table.
>
> The remaining table has one fewer row and one fewer column.
>
> Find the Gross Loser of this smaller table by identifying which row has
> the smallest entry, etc.
>
> The last candidate standing is the GLE winner.
>
> If you want the frosting on the cake, have a representative for each
> candidate announce if they claim to have the highest uncovered candidate in
> the finish order.
>
> Process these claims in the reverse order, beginning with the GLE winner,
> then the runner up, etc until either a claim is verified, or all have been
> checked and refuted.
>
> To check a claim X, those who challenge X must produce a candidate Y who
> beats X, but is not at the end of a two step beat path from X to Y.
>
> If the challengers cannot successfully refute the claim in this manner,
> then the claim stands approved, and X is the winner.
>
> In other words, elect the candidate with the first unrefutted claim in the
> order of claim processing ... which (as we have already specified) is the
> reverse of the elimination order.
>
> Anybody have a better suggestion?
>
> Nobody?
>
> OK, then...how do we get the proposal ball rolling?
>
> -Forest
>
>
> On Wed, Nov 9, 2022, 8:50 AM Forest Simmons <forest.simmons21 at gmail.com>
> wrote:
>
>> 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
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>> 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
>>>>
>>> ----
> Election-Methods mailing list - see https://electorama.com/em for list
> info
>
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