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@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@gmail.com
wrote:

@ 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@gmail.com
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@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@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@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@t-online.de wrote:

On 08.11.2022 18:02, Richard, the VoteFair guy wrote:

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

President Biden on the Mid-terms, kept mentioning "democracy". With that in mind, I previously recommended the best of a bad job would be Senate 2-member STV/PR elections.

Regards,
Richard Lung.

On 9 Nov 2022, at 10:07 pm, Forest Simmons forest.simmons21@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

Election-Methods mailing list - see https://electorama.com/em for list info

In this blog post (new today), Foley describes what he thinks is the
relationship between "total vote runoff" and Baldwin:

https://electionlawblog.org/?p=133027

He seems to be saying (I think) that the two methods are computationally
different but always get the same answer.

--Bob Richard

------ Original Message ------
From: "Bob Richard (lists)" lists001@robertjrichard.com
To: "election-methods@lists.electorama.com"
election-methods@lists.electorama.com
Sent: 11/7/2022 6:06:59 AM
Subject: Re: [EM] Fwd: Election-methods messages not being posted

On 10.11.2022 18:07, Toby Pereira wrote:

There have been so many voting methods proposals lately, so I think some
kind of simulator would be needed to winnow them out. Either that or a
lot of meticulous theoretical work so that we could classify the methods
in groups for which VSE/strategy resistance would be known.

I have something that kind of looks like such a strategy simulator, but
the code is incredibly ugly. It needs to be rewritten or redone, but I
haven't had the time.

So until someone writes an extensible simulator where it's easy to chain
together components to get e.g. Friendly Cover, QCBRS or GLE... the
uncertainty remains.

On a bit of a side note: I don't think any Condorcet method that only
uses the Condorcet matrix can satisfy weak immunity to burial (DMTCBR).
I have no proof of this, but neither did my exploration (that found
fpA-fpC) find any such method.

-km

On 11/9/2022 12:05 AM, Forest Simmons wrote:

Should the "only two steps" be interpreted as "two or fewer steps?" or
"two or more steps?" or "exactly two steps?"

I'm still trying to understand the "uncovered" (and "covered") concept.
Especially, what is its relationship to the Smith set?

Thanks,

Richard Fobes

On 11/9/2022 12:05 AM, Forest Simmons wrote:

There is no consensus, but Robert's Rules say to use Sequential Pairwise
Elimination ... starting from the least approval end of the agenda.

If you want a complete finish order, continue bubble sorting with priority
to the low approval end out of order pairs.

If you want a monotonically chosen uncovered candidate, I recommend the
following sort:

While any candidate X is covered by any lower approval candidate Y, insert
immediately ahead of the highest such X the highest such Y.

Once this subroutine is completed, bubble sort the resulting list ... with
priority to pairs closest to the bottom end.

This will yield a solid beat path through the candidates where no early
candidate in the path is covered by any later member. The monotonicity of
approval (or score or Borda or the Kemeny Young order) is preserved.

Of course neither Borda nor K-Y is clone free, so I recommend Score, Grade,
Approval, etc for the agenda ... or just get the agenda by Asset Voting or
VPA (Vote for a Published Agenda) as a kind of primary.

If you don't need the whole finish order and you consider chain building to
be simpler than covering, I recommend chain building rather tha chain
Climbing, since climbing is not IPDA, but chain building from the top is:

Initialize a chain with the top two score candidates in the form of a list
with the pairwise winner of the two listed s ove the other.

Then while the chain list will accommodate another candidate, among those
who would fit in, insert the one with the highest score. (A candidate fits
in if it can be inserted into the list in a position where it is defeated
by every candidate listed above it,  while defeating every candidate listed
below it.)

This may be easier for some election folk to tally than dealing with
covering or two step beat paths. But the two step beatpath matrix is easily
obtained by squaring the defeat matrix.

Hope that helps!

-Forest

-Forest

This can be used to improve

On Thu, Nov 10, 2022, 8:27 AM Andy Dienes andydienes@gmail.com wrote:

On Fri, Nov 11, 2022, 1:18 AM Forest Simmons forest.simmons21@gmail.com
wrote:

But I have posted, from time to time how to de-clone them.

so I recommend Score, Grade, Approval, etc for the agenda ... or just get

Since almost all RCV implementations limit the number of candidates that
can be ranked on a ballot, the simplest decent  RCV method is ... Elect the
uncovered candidate that is unranked on the fewest ballots.

Apparently, the biggest defect of this method is that voters cannot believe
in an RCV method that is not based on one-by-one eliminations.

But you can complicate it into an Elimination formulation ... if the
candidate with the fewest truncations is covered , then eliminate it.  Keep
eliminating candidates until you come to one that is uncovered. Keep that
one, and eliminate the rest!

This method has the mildest kind of non-monotonicity that cannot possibly
bother anyone that believes in methods like IRV based on one-at-a-time
elimination. .I say "mild", because decreasing its truncations will not
depose the winner However it is barely possible, though extremely unlikely,
that mono-raise can uncover a candidate with fewer truncations than the
erstwhile winner ... nothing that can show up as an embarrassing
electograph in a Yee/Bolson Diagram like IRV's non-monotonicity does.

If you are using an elimination method finish order or some other
non-monotone agenda, then simply elect the uncovered candidate in the most
favorable agenda position. It won't make the non-monotonicity worse, and it
will get rid of the most egregious kind ...  "Bolsonaro Nonmonotonicity"
... that produces a pathological Yee/Bolson electo-graph.

I recommend chain building over chain climbing, since climbing is not IPDA,

Chain building on an agenda is only partially monotone .... upgrading the
winner in the agenda will not make her lose ... however it is possible (but
not likely) that mono-raise could change the win matrix in a way that
allows someone beaten by the winner to be incorporated soon enough after
the winner to prevent a certain later addition, and thereby change the
order from that point on ... it could not happen with a Smith set of only
three members.

Nor would it be the egregious, embarrassing kind of non-monotonicity that
shows up so glaringly on a Yee/Bolson diagram of IRV. Anybody who has even
casually examined IRV under the Yee/Bolson electoscope would be crazy to
continue recommending it!

For a completely monotone version of chain building, instead of a fixed
agenda order, use a random ballot favorite order. Then elect the candidate
that has the biggest probability of winning. A computer is needed for this
version ... run this random ballot version a thousand times, and elect the
candidate that wins most of the time. (Most of the time the same candidate
will win all thousand trials).

Note that the start of chain building is the precise finish of STAR ... in
other words Score Based Chain Building is STAR carried to its logical
conclusion.

To make covered/uncovered easier to discern, take the win matrix WN (whose
k_th entry in the j_th row is one or zero depending on whether or not
candidate j outranks k on more ballots than not), insert ones down the
diagonal, and then square it.

The resulting matrix (WN+I)^2 will have a zero in the k_th column of row j
iff candidate j is covered by candidate k.

The row of an uncovered candidate will have no zeroes in it.