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

[Forest Simmons]

Grammatical correction...

On Sat, Nov 12, 2022, 6:28 PM Forest Simmons <forest.simmons21 at gmail.com>
wrote:

> I tried to state the most understandable description possible of Gross
> Loser Elimination ... is the following version an improvement? Anybody have
> a simpler or clearer description?
>
> Suppose there are seven candidates. Each candidate gets six cards with
> their name at the top and one of the other candidate names just below it.
>
> Each card is given to a different election worker.
>
> Pretend you are in charge of the card with Diane at the top and Jenny just
> below it.
>
> As the ballots are slowly opened one by one in a public ceremony so that
> everybody can see each ballot on an overhead projector screen, you put a
> hash mark on your Diane/Jenny card every time a ballot is opened that shows
> a vote for Diane over Jenny.
>
> After the ballots have been tallied in this way, you total the votes, and
> put that vote total to the left of her name on the top left of your card.
> This is the total of her votes in her matchup against one of the other
> candidates, namely Jenny.
>
> Then you hand in your card to the head vote counter, who sorts the cards
> in order of the vote totals in the upper left corner of each card.
>
> Now the Elimination steps:
>
> Remove the card from the bottom of the stack, the one with the smallest
> vote total next to the name at the top of that card. That name identifies
> the Gross Loser. Eliminate all of the cards
>
that have that name anywhere on it.
>

Should be "on them" not "on it"

That concludes one step of GLE, Gross Loser Elimination.
>
> Now remove the card from the bottom of the remaining deck. The name at
> the top of that card is the Gross Loser name for this step.. Eliminate all
> of the cards that have that name anywhere on it.  That concludes another
> step of GLE, Gross Loser Elimination.
>
> Now remove the card from the bottom of the remaining deck. The name at
> the top of that card is the Gross Loser name for this step.. Eliminate all
> of the cards that have that name anywhere on it.  That concludes another
> step of GLE, Gross Loser Elimination.
>
> Continue in this manner until all cards but two have been eliminated.
> Eliminate the bottom of these two, and elect the candidate whose name is at
> the top of the remaining card. This is the only candidate that was never at
> any stage the worst of the worst ... i.e. never the Gross Loser.
>
> -Forest
>
> On Sat, Nov 12, 2022, 12:13 PM Forest Simmons <forest.simmons21 at gmail.com>
> wrote:
>
>> Q&D was the simplest way to always get the same result (when the Smith
>> set was four or fewer members) as Implicit Approval Chain Climbing ... a
>> monotonic, clone free, burial resistant, Banks efficient method ... as
>> simple as possible for a method with those criteria compliances ....
>> compliances that no other method on record could truthfully claim.
>>
>> So why did it get no traction?
>>
>> According guys "in the trenches" it has to be an elimination method with
>> vote transfers between steps.
>>
>> No such method is monotonic, but the next best thing is Yee/Bolson
>> monotonic.
>>
>> That method is Gross Loser Elimination (GLE).
>>
>> The Gross Loser of a Round Robin tournament is the player whose worst
>> score (for any of her matchups) is worse than anybody elses's ... we could
>> call her the MinMin loser.
>>
>> GLM is the elimination method that at each stage eliminates the gross
>> loser of the remaing candidates ... after the gross losers from the
>> previous stages have already been removed.  The last candidate standing is
>> the winner.
>>
>> As a reminder, the gross loser is the candidate with the worst worst
>> score. Each candidate has several scores ... one against each of the other
>> players. The worst of these is that candidate's worst score. The candidate
>> whose worst score is worse than anybody elses's worst score is the gross
>> loser.  That is the one to be eliminated in the first step.
>>
>> In the second step each candidate has a worst score in any of its
>> matchups with the remaining candidates. The candidate whose worst score is
>> worse than any other remaining candidate's worst score is the gross loser
>> of that stage. That's the one to be eliminated at that stage.
>>
>> For example suppose that in 10th stage there are only four candidates
>> left ... candidates A B,C,&D with respective worst matchup scores of 15,
>> 13, 28, and 35.  Which one do you think would be eliminated at that stage?
>>
>> If you guessed candidate B, you guessed right: B's worst score (13) at
>> this stage is worse (smaller than) any of the other three scores 15, 28, or
>> 35.
>>
>> Each elimination step is that simple!
>>
>> Where do the matchup scores come from? In a sports tournament it is
>> obvious because each matchup is a completion for points.
>>
>> In an election each matchup is also a competition for points ... in the
>> form of ........ (you guessed it) votes!
>>
>> The scores we've been talking about are the votes in the head-to-head
>> matchups.
>>
>> The beauty of RCV ballots is that for each matchup you can figure out the
>> scores for both candidates from the RCV ballots.
>>
>> Suppose the matchup in question is between candidates X and Y.
>> Separate the ballots into three stacks.
>>
>> Pretend that all of the other candidates are out of the picture so that
>> all votes are transferred to X and Y. How many votes would X get? That is
>> X's score for this matchup.
>>
>> You don't have to actually deface the ballots by crossing out the
>> irrelevant candidates to find X's vote totals. Just count the number of
>> ballots on which candidate X outranks candidate Y.
>>
>> This can be done for each of X's matchups, giving a complete set of
>> matchup scores for X.
>>
>> Similarly we can get a completes set of matchup scores for each of the
>> other candidates.
>>
>> And the one whose worst score is worse than anybody elses's worst score
>> is the Gross Loser.
>>
>> So, to recap the method ... in the very first step eliminate the Gross
>> Loser.  In the next step eliminate the Gross Loser from among the remaining
>> candidates, those who were not eliminated in the first step.
>>
>> In all subsequent steps where more than two candidates remain, eliminate
>> the Gross Loser from among those remaining candidates.
>>
>> When it gets down to two candidates eliminate the Gross Loser,  the one
>> with the lowest score, i.e. the one with the fewest votes, i.e. elect the
>> one with the most votes in this final matchup.
>>
>> This spells it out as plainly as I can do in the abstract. But what we
>> all know is children do not learn how to play a game by reading the
>> instructions on the inside cover of the box. They learn by playing with
>> friends who already know the rules.
>>
>> This little card game (ballot counting game) is much simpler than
>> Monopoly, Poker, Uno, Clue, etc that kids feel pretty confident with after
>> a couple of dry runs with their friends.
>>
>> A YouTube video is the second best way to teach it.
>>
>> An EM text message is the worst way to teach it ... but you guys pick
>> things up faster than average!
>>
>> -Forest
>>
>>
>>
>>
>>
>>
>> On Thu, Nov 10, 2022, 9:07 AM Toby Pereira <tdp201b at yahoo.co.uk> wrote:
>>
>>> So do you have a nice and simple definition of this method that anyone
>>> can understand?
>>>
>>> Where do you now stand on your Quick and Clean Burial Resistant Smith
>>> method? At the time, it seemed to be the best thing since sliced bread, but
>>> amongst all the posts, it now it appears not to have resisted, er, burial.
>>>
>>> Toby
>>>
>>> On Wednesday, 9 November 2022 at 22:07:53 GMT, 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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