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

Sat Nov 12 18:28:40 PST 2022

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.  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.

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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