Here are the ballots in EM format:

1: Approval > STAR > ApprovalRunoff > Benham = SchwartzWoodall = Woodall

CondorcetBorda = CopelandBorda = DoubleDefeatHare = MSA = MSMLV = MSTB =
Raynaud = RCIPE = SmithApprovalExplicit = SmithDAC = SmithScore > MJ >
IRV > Plurality
1: IRV > STAR > ApprovalRunoff > Approval > Baldwin = Benham =
CondorcetBorda = CopelandBorda = DoubleDefeatHare = Minmax = MJ = MSA =
MSMLV = MSTB = RankedPairs = Raynaud = RCIPE = Schulze = SchwartzWoodall
= SmithApprovalExplicit = SmithApprovalImplicit = SmithDAC = SmithScore
= Woodall > Plurality
1: MSA > SmithApprovalExplicit = SmithApprovalImplicit = IRV = Benham =
DoubleDefeatHare > RankedPairs = Schulze > Approval > Minmax > Baldwin =
CondorcetBorda = CopelandBorda = MSMLV = MSTB = Raynaud = RCIPE =
SchwartzWoodall = SmithDAC = SmithScore = Woodall > MJ > STAR =
ApprovalRunoff = Plurality
1: Approval > RankedPairs > STAR > Woodall > SmithDAC > Minmax > RCIPE >
Benham > MSA > SmithApprovalExplicit > ApprovalRunoff > MSMLV >
SmithApprovalImplicit > DoubleDefeatHare > Raynaud > Schulze >
SchwartzWoodall > SmithScore > MJ > Plurality > IRV > CondorcetBorda >
Baldwin > CopelandBorda
1: STAR > SmithScore > Baldwin = Benham = CondorcetBorda = CopelandBorda
= Raynaud = Minmax = RankedPairs = Schulze = SchwartzWoodall =
SmithApprovalExplicit = SmithApprovalImplicit = SmithDAC = Woodall = MSA
= MSMLV = MSTB > ApprovalRunoff > Approval > RCIPE > DoubleDefeatHare >
MJ > IRV > Plurality
1: RankedPairs > Schulze = Benham > Woodall > Minmax > SchwartzWoodall >
SmithApprovalImplicit = SmithApprovalExplicit > SmithScore > Raynaud >
Baldwin > MJ > DoubleDefeatHare = MSTB = MSMLV = MSA > CopelandBorda >
SmithDAC > ApprovalRunoff > STAR > RCIPE > CondorcetBorda > Approval >
IRV > Plurality
1: CondorcetPlur > Minmax > RankedPairs > Schulze > BTRIRV > Baldwin =
Benham = CondorcetBorda = CopelandBorda = MSA = MSMLV = MSTB = Raynaud =
SchwartzWoodall = SmithApprovalExplicit = SmithApprovalImplicit =
SmithDAC = SmithScore = Woodall > IRV > Approval > STAR > Plurality > Score
1: RCIPE > Benham > Minmax > RankedPairs > Woodall > SchwartzWoodall >
Baldwin > CopelandBorda > CondorcetBorda > Schulze > SmithScore >
Raynaud > MSTB > MSMLV > SmithDAC > DoubleDefeatHare > IRV > MJ > STAR >
Approval > MSA > SmithApprovalExplicit > SmithApprovalImplicit >
Plurality > ApprovalRunoff
1: Approval > SmithScore > MSA > SmithApprovalExplicit > RankedPairs >
Benham > Minmax > STAR > ApprovalRunoff = Baldwin = CondorcetBorda =
CopelandBorda = DoubleDefeatHare = IRV = MJ = MSMLV = MSTB = Raynaud =
RCIPE = Schulze = SchwartzWoodall = SmithApprovalImplicit = SmithDAC =
Woodall > Plurality
1: STAR > SmithScore > Score > MJ > Approval = SmithApprovalExplicit =
SmithApprovalImplicit = MSA > ApprovalRunoff = RankedPairs = Schulze >
Baldwin = Benham = CopelandBorda = MSMLV = MSTB = Raynaud =
SchwartzWoodall = SmithDAC = Woodall > CondorcetBorda = Minmax > RCIPE >
IRV > Plurality
1: Benham > SchwartzWoodall > Woodall > RankedPairs > Schulze > MSTB >
Minmax > BTRIRV > Raynaud > Baldwin > RCIPE > IRV > SmithDAC > MSMLV >
MSA > SmithApprovalExplicit > SmithApprovalImplicit > SmithScore >
DoubleDefeatHare > CopelandBorda > CondorcetBorda > Approval > MJ >
Score > ApprovalRunoff > STAR > Plurality > Borda

Ranked Pairs is the CW -- and Benham beats everybody but Ranked Pairs
pairwise. This can be verified by going to Rob LeGrand's calculator
(http://www.cs.angelo.edu/~rlegrand/rbvote/calc.html with mirror
https://munsterhjelm.no/km/rbvote/calc.html for people outside the US)
and selecting "calculate all winners".

Here are the Schulze results:

1      Ranked Pairs (wv)
2      Benham
3      Approval
Minmax (wv)
Schulze
STAR
7      Smith//Score
8      Margins-Sorted Approval
Schwartz Woodall
Smith//Approval (implicit)
Woodall
12      Smith//Approval (explicit)
13      Raynaud
14      Baldwin
15      Max Strength Transitive Beatpath
16      Margins-Sorted Minimum Losing Votes
Smith//DAC
18      Copeland//Borda (Ranked Robin)
19      Condorcet//Borda (Black)
20      Approval with manual runoff
Double Defeat, Hare
RCIPE
23      Majority Judgement
24      IRV
25      Plurality
26      BTR-IRV (write-in)
27      Score (write-in)
28      Borda (write-in)
Condorcet//Plurality (write-in)

The Approval voting results:

1      Ranked Pairs (wv)
2      Minmax (wv)
3      Benham
STAR
Woodall
6      Approval
7      Approval with manual runoff
Margins-Sorted Approval
Schulze
10      Schwartz Woodall
Smith//Approval (explicit)
Smith//Approval (implicit)
Smith//Score
14      Baldwin
BTR-IRV (write-in)
Condorcet//Borda (Black)
Condorcet//Plurality (write-in)
Copeland//Borda (Ranked Robin)
Double Defeat, Hare
IRV
Majority Judgement
Margins-Sorted Minimum Losing Votes
Max Strength Transitive Beatpath
Raynaud
RCIPE
Score (write-in)
Smith//DAC
28      Borda (write-in)
Plurality

and for fun, Schulze with ties broken by Approval:

1      Ranked Pairs (wv)
2      Benham
3      Minmax (wv)
4      STAR
5      Approval
6      Schulze
7      Smith//Score
8      Woodall
9      Margins-Sorted Approval
10      Schwartz Woodall
Smith//Approval (implicit)
12      Smith//Approval (explicit)
13      Raynaud
14      Baldwin
15      Max Strength Transitive Beatpath
16      Margins-Sorted Minimum Losing Votes
Smith//DAC
18      Copeland//Borda (Ranked Robin)
19      Condorcet//Borda (Black)
20      Approval with manual runoff
21      Double Defeat, Hare
RCIPE
23      Majority Judgement
24      IRV
25      Plurality
26      BTR-IRV (write-in)
27      Score (write-in)
28      Condorcet//Plurality (write-in)
29      Borda (write-in)

This should be accurate, but if you spot a typo or other mistake
somewhere, let me know.

-km

In the 11 ballots initially posted, doesn’t Benham pairbeat RP 6 to 5? …
unless I made the same miscount twice.

On Fri, May 17, 2024 at 16:36 Kristofer Munsterhjelm km_elmet@t-online.de
wrote:

...

I can live with Tideman Ranked Pairs.

Now lets craft some credible legislative language for it.

--

r b-j . _ . _ . _ . _ rbj@audioimagination.com

"Imagination is more important than knowledge."

.
.
.

Good luck getting any substantial number of legislators — let alone voters
— to support it. Understanding will be hard enough.

On Sat, May 18, 2024 at 8:50 AM robert bristow-johnson <
rbj@audioimagination.com> wrote:

Well, there is a reason why I marked Condorcet/Plurality at top.  It has the most direct and understandable code to define the method.

But I would agree, as far as resistance to burying or some deliberate strategy, Condorcet/Plurality would be more vulnerable to burying than, say, Schulze or Ranked-Pairs.  And the latter is more credible as legislative language.

I think I can write something for RP that has an initially empty list of "defeators" for each candidate.  The defeators of a candidate are those candidates who have defeated this candidate and any other candidate who has defeated the winning candidate.

Beginning with the preference pairing having the greatest defeat strength (in this case, winning votes), first check to see if the candidate defeated in that pairing is in the list of defeators of the winning candidate in that pairing.  If the defeated candidate is in the list of defeators of the winning candidate, this pairing is ignored.  Otherwise the defeated candidate in the pairing is marked as defeated and all of the defeators of the winning candidate are merged with the existing list of defeators for the defeated candidate.

Do this for every pairing in order of the defeat strength.  Then elect the sole candidate who is not marked as defeated.

--

r b-j . _ . _ . _ . _ rbj@audioimagination.com

"Imagination is more important than knowledge."

.
.
.

Brief introductory definition:

Elect the candidate who isn’t beaten among all the strongest defeats that
don’t contradict (form any cycle(s) with) eachother.

A possible longer legislation wording:

List the pairwise-defeats one at a time, strongest ones first.

But if the next strongest one cycles with any listed defeats, then skip
that one.

When all defeats have been listed or skipped, elect the candidate not
beaten by any listed defeat.

Of course either would have to be preceded by the same preliminary
definitions as any pairwise-count method.

The short definition is probably unambiguous enough for a legislative
definition, but the longer one might be preferred.

Tideman RP?  It’s long been accepted that wv is better than margins, due to
Minimal-Defense compliance.  ..& the resulting reduction of strategy-need

In fact, it has been pointed-out here that the autodeterence of the wv.
Condorcet methods brings complete freedom from any defensive strategy at
all.

One could still use the defensive-truncation afforded by Minimal-Defense,
but that would be optional, for if one wants to further enhance deterrence
by adding that of Minimal-Defense’s defensive truncation.

The autodeterence is strong. But defensive-truncation provides certain,
inevitable penalty, in addition to the (strong) probabilistic autodeterence.

RP(margins), if that’s what Tideman RP implies, is a very different method
from RP(wv).

--

Offer RP(wv) to the Vermont legislature. I like RP because it’s prestige &
popularity likely make it more enactable, & because of its
criterion-compliances, which could matter in the rare spontaneous
circular-tie. But, if an even briefer definition is desired by legislators,
then offer MinMax(wv).

I’d offer both, pointing out that RP is more popular & prestigious with the
people who discuss single-winner methods, & might do better in the very
rare spontaneous circular-tie.

On Sat, May 18, 2024 at 00:32 robert bristow-johnson <
rbj@audioimagination.com> wrote:

Thanks for doing this Kristofer. If I counted correctly Ranked Pairs beat Benham 5-4 with two ties, so not a particularly significant result in that respect. But it must have had at least two more approvals given that Minmax is between them. Perhaps it would have been interesting to have the margins version on the ballot to see how it compared. I think people likely just saw Ranked Pairs on the ballot and left it at that. I'm not sure exactly what the difference between them would be in practice. I think it's been said that winning votes protects against burial better, but if it does that by punishing burial by causing a worse result for everyone, it's not necessarily a good thing. People won't necessarily know the optimum strategy when using a voting system. Ranked ballots all look the same after all.
Toby
On Saturday 18 May 2024 at 00:36:32 BST, Kristofer Munsterhjelm km_elmet@t-online.de wrote:

Here are the ballots in EM format:

1: Approval > STAR > ApprovalRunoff > Benham = SchwartzWoodall = Woodall

CondorcetBorda = CopelandBorda = DoubleDefeatHare = MSA = MSMLV = MSTB =
Raynaud = RCIPE = SmithApprovalExplicit = SmithDAC = SmithScore > MJ >
IRV > Plurality
1: IRV > STAR > ApprovalRunoff > Approval > Baldwin = Benham =
CondorcetBorda = CopelandBorda = DoubleDefeatHare = Minmax = MJ = MSA =
MSMLV = MSTB = RankedPairs = Raynaud = RCIPE = Schulze = SchwartzWoodall
= SmithApprovalExplicit = SmithApprovalImplicit = SmithDAC = SmithScore
= Woodall > Plurality
1: MSA > SmithApprovalExplicit = SmithApprovalImplicit = IRV = Benham =
DoubleDefeatHare > RankedPairs = Schulze > Approval > Minmax > Baldwin =
CondorcetBorda = CopelandBorda = MSMLV = MSTB = Raynaud = RCIPE =
SchwartzWoodall = SmithDAC = SmithScore = Woodall > MJ > STAR =
ApprovalRunoff = Plurality
1: Approval > RankedPairs > STAR > Woodall > SmithDAC > Minmax > RCIPE >
Benham > MSA > SmithApprovalExplicit > ApprovalRunoff > MSMLV >
SmithApprovalImplicit > DoubleDefeatHare > Raynaud > Schulze >
SchwartzWoodall > SmithScore > MJ > Plurality > IRV > CondorcetBorda >
Baldwin > CopelandBorda
1: STAR > SmithScore > Baldwin = Benham = CondorcetBorda = CopelandBorda
= Raynaud = Minmax = RankedPairs = Schulze = SchwartzWoodall =
SmithApprovalExplicit = SmithApprovalImplicit = SmithDAC = Woodall = MSA
= MSMLV = MSTB > ApprovalRunoff > Approval > RCIPE > DoubleDefeatHare >
MJ > IRV > Plurality
1: RankedPairs > Schulze = Benham > Woodall > Minmax > SchwartzWoodall >
SmithApprovalImplicit = SmithApprovalExplicit > SmithScore > Raynaud >
Baldwin > MJ > DoubleDefeatHare = MSTB = MSMLV = MSA > CopelandBorda >
SmithDAC > ApprovalRunoff > STAR > RCIPE > CondorcetBorda > Approval >
IRV > Plurality
1: CondorcetPlur > Minmax > RankedPairs > Schulze > BTRIRV > Baldwin =
Benham = CondorcetBorda = CopelandBorda = MSA = MSMLV = MSTB = Raynaud =
SchwartzWoodall = SmithApprovalExplicit = SmithApprovalImplicit =
SmithDAC = SmithScore = Woodall > IRV > Approval > STAR > Plurality > Score
1: RCIPE > Benham > Minmax > RankedPairs > Woodall > SchwartzWoodall >
Baldwin > CopelandBorda > CondorcetBorda > Schulze > SmithScore >
Raynaud > MSTB > MSMLV > SmithDAC > DoubleDefeatHare > IRV > MJ > STAR >
Approval > MSA > SmithApprovalExplicit > SmithApprovalImplicit >
Plurality > ApprovalRunoff
1: Approval > SmithScore > MSA > SmithApprovalExplicit > RankedPairs >
Benham > Minmax > STAR > ApprovalRunoff = Baldwin = CondorcetBorda =
CopelandBorda = DoubleDefeatHare = IRV = MJ = MSMLV = MSTB = Raynaud =
RCIPE = Schulze = SchwartzWoodall = SmithApprovalImplicit = SmithDAC =
Woodall > Plurality
1: STAR > SmithScore > Score > MJ > Approval = SmithApprovalExplicit =
SmithApprovalImplicit = MSA > ApprovalRunoff = RankedPairs = Schulze >
Baldwin = Benham = CopelandBorda = MSMLV = MSTB = Raynaud =
SchwartzWoodall = SmithDAC = Woodall > CondorcetBorda = Minmax > RCIPE >
IRV > Plurality
1: Benham > SchwartzWoodall > Woodall > RankedPairs > Schulze > MSTB >
Minmax > BTRIRV > Raynaud > Baldwin > RCIPE > IRV > SmithDAC > MSMLV >
MSA > SmithApprovalExplicit > SmithApprovalImplicit > SmithScore >
DoubleDefeatHare > CopelandBorda > CondorcetBorda > Approval > MJ >
Score > ApprovalRunoff > STAR > Plurality > Borda

Ranked Pairs is the CW -- and Benham beats everybody but Ranked Pairs
pairwise. This can be verified by going to Rob LeGrand's calculator
(http://www.cs.angelo.edu/~rlegrand/rbvote/calc.html with mirror
https://munsterhjelm.no/km/rbvote/calc.html for people outside the US)
and selecting "calculate all winners".

Here are the Schulze results:

1      Ranked Pairs (wv)
2      Benham
3      Approval
        Minmax (wv)
        Schulze
        STAR
7      Smith//Score
8      Margins-Sorted Approval
        Schwartz Woodall
        Smith//Approval (implicit)
        Woodall
12      Smith//Approval (explicit)
13      Raynaud
14      Baldwin
15      Max Strength Transitive Beatpath
16      Margins-Sorted Minimum Losing Votes
        Smith//DAC
18      Copeland//Borda (Ranked Robin)
19      Condorcet//Borda (Black)
20      Approval with manual runoff
        Double Defeat, Hare
        RCIPE
23      Majority Judgement
24      IRV
25      Plurality
26      BTR-IRV (write-in)
27      Score (write-in)
28      Borda (write-in)
        Condorcet//Plurality (write-in)

The Approval voting results:

1      Ranked Pairs (wv)
2      Minmax (wv)
3      Benham
        STAR
        Woodall
6      Approval
7      Approval with manual runoff
        Margins-Sorted Approval
        Schulze
10      Schwartz Woodall
        Smith//Approval (explicit)
        Smith//Approval (implicit)
        Smith//Score
14      Baldwin
        BTR-IRV (write-in)
        Condorcet//Borda (Black)
        Condorcet//Plurality (write-in)
        Copeland//Borda (Ranked Robin)
        Double Defeat, Hare
        IRV
        Majority Judgement
        Margins-Sorted Minimum Losing Votes
        Max Strength Transitive Beatpath
        Raynaud
        RCIPE
        Score (write-in)
        Smith//DAC
28      Borda (write-in)
        Plurality

and for fun, Schulze with ties broken by Approval:

1      Ranked Pairs (wv)
2      Benham
3      Minmax (wv)
4      STAR
5      Approval
6      Schulze
7      Smith//Score
8      Woodall
9      Margins-Sorted Approval
10      Schwartz Woodall
        Smith//Approval (implicit)
12      Smith//Approval (explicit)
13      Raynaud
14      Baldwin
15      Max Strength Transitive Beatpath
16      Margins-Sorted Minimum Losing Votes
        Smith//DAC
18      Copeland//Borda (Ranked Robin)
19      Condorcet//Borda (Black)
20      Approval with manual runoff
21      Double Defeat, Hare
        RCIPE
23      Majority Judgement
24      IRV
25      Plurality
26      BTR-IRV (write-in)
27      Score (write-in)
28      Condorcet//Plurality (write-in)
29      Borda (write-in)

This should be accurate, but if you spot a typo or other mistake
somewhere, let me know.

-km

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

On 2024-05-18 21:20, Toby Pereira wrote:

That's a good point - I should post the Approval counts too :-)

Here they are:

Ranked Pairs (wv)                    8
Minmax (wv)                          7
Benham                              6
STAR                                6
Woodall                              6
Approval                            5
Approval with manual runoff          4
Margins-Sorted Approval              4
Schulze                              4
Schwartz Woodall                    3
Smith//Approval (explicit)          3
Smith//Approval (implicit)          3
Smith//Score                        3
Baldwin                              2
BTR-IRV (write-in)                  2
Condorcet//Borda (Black)            2
Condorcet//Plurality (write-in)      2
Copeland//Borda (Ranked Robin)      2
Double Defeat, Hare                  2
IRV                                  2
Majority Judgement                  1
Margins-Sorted Minimum Losing Votes  1
Max Strength Transitive Beatpath    1
Raynaud                              1
RCIPE                                1
Score (write-in)                    1
Smith//DAC                          1
Borda (write-in)                    0
Plurality                            0

-km

On Sun, May 19, 2024 at 09:40 Kristofer Munsterhjelm km_elmet@t-online.de
wrote: