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

Thu Nov 10 09:07:03 PST 2022

 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
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