Score Then Automatic Runoff (STAR) elects the pairwise winner between the
two candidates with the highest score totals.

One of the biggest problems with this method is that there is an
appreciable likelihood that the winner W will be a candidate that is
pairwise dominated by some other candidate C, which means that C not only
scores higher than W on more ballots than not, but if there even exists  a
beatpath from W back to C, it will take at least three steps.

Most other extant methods have this same defect, but almost all of them are
hard to fix compared to STAR. This fact makes it easy for a tweaked version
of STAR to become arguably superior to any of these other methods.

1. Initialize a set S of candidates with the STAR winner.
2. If any candidate pairwise dominates the newest member of S, from among
   such candidates add in to S the one with the highest score.
3. Repeat step 2 until the set S cannot be enlarged any further in this way.
4. Elect the last candidate to be added to the set.

Usually step 2 will be invoked only one or two times if at all ... so this
is not a big tweak.

With this tweak STAR becomes arguably superior to any method currently in
use.

The only other method currently in use that always elects pairwise
undominated candidates is Copeland.  But Copeland suffers from two fatal
defect that STAR does not have ... Copeland is neither Decisive nor Clone
Independent.

Will STAR proponents take advantage of this opportunity? ... or will they
pass it up?

fws

Wouldn't it be simpler (and better?) to start with the score winner rather than the STAR winner?
What do you mean by pairwise dominate in this context? I presume from the context (when you talk about Copeland) it's not the same as pairwise beat. Are you talking about covering in the Landau sense?
On Friday, 11 August 2023 at 01:19:30 BST, Forest Simmons forest.simmons21@gmail.com wrote:

Score Then Automatic Runoff (STAR) elects the pairwise winner between the two candidates with the highest score totals.
One of the biggest problems with this method is that there is an appreciable likelihood that the winner W will be a candidate that is pairwise dominated by some other candidate C, which means that C not only scores higher than W on more ballots than not, but if there even exists  a beatpath from W back to C, it will take at least three steps.
Most other extant methods have this same defect, but almost all of them are hard to fix compared to STAR. This fact makes it easy for a tweaked version of STAR to become arguably superior to any of these other methods.

1. Initialize a set S of candidates with the STAR winner. 2. If any candidate pairwise dominates the newest member of S, from among such candidates add in to S the one with the highest score.3. Repeat step 2 until the set S cannot be enlarged any further in this way.4. Elect the last candidate to be added to the set.
   Usually step 2 will be invoked only one or two times if at all ... so this is not a big tweak.
   With this tweak STAR becomes arguably superior to any method currently in use.
   The only other method currently in use that always elects pairwise undominated candidates is Copeland.  But Copeland suffers from two fatal defect that STAR does not have ... Copeland is neither Decisive nor Clone Independent.
   Will STAR proponents take advantage of this opportunity? ... or will they pass it up?
   fws----
   Election-Methods mailing list - see https://electorama.com/em for list info

Forest
I'm not sure it would be undiplomatic to start with the score winner. The top two run-off in STAR is the second stage to complete the method after doing score voting. By saying that it needs further completion is doing away with STAR's completion anyway, and to have three stages seems unnecessarily unwieldy and more likely to throw out strange results. STAR is also not clone independent, so this goes against your stated preference. This is just another way to complete the method instead of STAR, so I think it makes sense to start with the score winner, rather than the STAR winner.
Toby
On Sunday, 13 August 2023 at 00:12:21 BST, Forest Simmons forest.simmons21@gmail.com wrote:

That would be simpler, but not as diplomatic.
You could initialize the chain with the winner of anybody's favorite method, but ideally it would be a monotone clone independen method.
Pairwise Dominate is another (more descriptive way to say "cover" ... which I defined as the opposite of not being Pairwise Dominated.... we want our winner to be undominsted pairwise ... which can be easily checked as I suggested by the existence of a short return beatpath to any challenger. 
On Fri, Aug 11, 2023, 5:19 AM Toby Pereira tdp201b@yahoo.co.uk wrote:

Wouldn't it be simpler (and better?) to start with the score winner rather than the STAR winner?
What do you mean by pairwise dominate in this context? I presume from the context (when you talk about Copeland) it's not the same as pairwise beat. Are you talking about covering in the Landau sense?
On Friday, 11 August 2023 at 01:19:30 BST, Forest Simmons forest.simmons21@gmail.com wrote:

Score Then Automatic Runoff (STAR) elects the pairwise winner between the two candidates with the highest score totals.
One of the biggest problems with this method is that there is an appreciable likelihood that the winner W will be a candidate that is pairwise dominated by some other candidate C, which means that C not only scores higher than W on more ballots than not, but if there even exists  a beatpath from W back to C, it will take at least three steps.
Most other extant methods have this same defect, but almost all of them are hard to fix compared to STAR. This fact makes it easy for a tweaked version of STAR to become arguably superior to any of these other methods.

1. Initialize a set S of candidates with the STAR winner. 2. If any candidate pairwise dominates the newest member of S, from among such candidates add in to S the one with the highest score.3. Repeat step 2 until the set S cannot be enlarged any further in this way.4. Elect the last candidate to be added to the set.
   Usually step 2 will be invoked only one or two times if at all ... so this is not a big tweak.
   With this tweak STAR becomes arguably superior to any method currently in use.
   The only other method currently in use that always elects pairwise undominated candidates is Copeland.  But Copeland suffers from two fatal defect that STAR does not have ... Copeland is neither Decisive nor Clone Independent.
   Will STAR proponents take advantage of this opportunity? ... or will they pass it up?
   fws----
   Election-Methods mailing list - see https://electorama.com/em for list info

By the way, if you started with the score winner, would it just be Landau//Score?

Toby
On Saturday, 19 August 2023 at 21:37:23 BST, Toby Pereira tdp201b@yahoo.co.uk wrote:

Forest
I'm not sure it would be undiplomatic to start with the score winner. The top two run-off in STAR is the second stage to complete the method after doing score voting. By saying that it needs further completion is doing away with STAR's completion anyway, and to have three stages seems unnecessarily unwieldy and more likely to throw out strange results. STAR is also not clone independent, so this goes against your stated preference. This is just another way to complete the method instead of STAR, so I think it makes sense to start with the score winner, rather than the STAR winner.
Toby
On Sunday, 13 August 2023 at 00:12:21 BST, Forest Simmons forest.simmons21@gmail.com wrote:

That would be simpler, but not as diplomatic.
You could initialize the chain with the winner of anybody's favorite method, but ideally it would be a monotone clone independen method.
Pairwise Dominate is another (more descriptive way to say "cover" ... which I defined as the opposite of not being Pairwise Dominated.... we want our winner to be undominsted pairwise ... which can be easily checked as I suggested by the existence of a short return beatpath to any challenger. 
On Fri, Aug 11, 2023, 5:19 AM Toby Pereira tdp201b@yahoo.co.uk wrote:

Wouldn't it be simpler (and better?) to start with the score winner rather than the STAR winner?
What do you mean by pairwise dominate in this context? I presume from the context (when you talk about Copeland) it's not the same as pairwise beat. Are you talking about covering in the Landau sense?
On Friday, 11 August 2023 at 01:19:30 BST, Forest Simmons forest.simmons21@gmail.com wrote:

Score Then Automatic Runoff (STAR) elects the pairwise winner between the two candidates with the highest score totals.
One of the biggest problems with this method is that there is an appreciable likelihood that the winner W will be a candidate that is pairwise dominated by some other candidate C, which means that C not only scores higher than W on more ballots than not, but if there even exists  a beatpath from W back to C, it will take at least three steps.
Most other extant methods have this same defect, but almost all of them are hard to fix compared to STAR. This fact makes it easy for a tweaked version of STAR to become arguably superior to any of these other methods.

1. Initialize a set S of candidates with the STAR winner. 2. If any candidate pairwise dominates the newest member of S, from among such candidates add in to S the one with the highest score.3. Repeat step 2 until the set S cannot be enlarged any further in this way.4. Elect the last candidate to be added to the set.
   Usually step 2 will be invoked only one or two times if at all ... so this is not a big tweak.
   With this tweak STAR becomes arguably superior to any method currently in use.
   The only other method currently in use that always elects pairwise undominated candidates is Copeland.  But Copeland suffers from two fatal defect that STAR does not have ... Copeland is neither Decisive nor Clone Independent.
   Will STAR proponents take advantage of this opportunity? ... or will they pass it up?
   fws----
   Election-Methods mailing list - see https://electorama.com/em for list info