<div dir="auto">In the 11 ballots initially posted, doesn’t Benham pairbeat RP 6 to 5? … unless I made the same miscount twice.</div><div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Fri, May 17, 2024 at 16:36 Kristofer Munsterhjelm <<a href="mailto:km_elmet@t-online.de">km_elmet@t-online.de</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Here are the ballots in EM format:<br>
<br>
1: Approval > STAR > ApprovalRunoff > Benham = SchwartzWoodall = Woodall <br>
> RankedPairs > Minmax > SmithApprovalImplicit > Schulze > Baldwin = <br>
CondorcetBorda = CopelandBorda = DoubleDefeatHare = MSA = MSMLV = MSTB = <br>
Raynaud = RCIPE = SmithApprovalExplicit = SmithDAC = SmithScore > MJ > <br>
IRV > Plurality<br>
1: IRV > STAR > ApprovalRunoff > Approval > Baldwin = Benham = <br>
CondorcetBorda = CopelandBorda = DoubleDefeatHare = Minmax = MJ = MSA = <br>
MSMLV = MSTB = RankedPairs = Raynaud = RCIPE = Schulze = SchwartzWoodall <br>
= SmithApprovalExplicit = SmithApprovalImplicit = SmithDAC = SmithScore <br>
= Woodall > Plurality<br>
1: MSA > SmithApprovalExplicit = SmithApprovalImplicit = IRV = Benham = <br>
DoubleDefeatHare > RankedPairs = Schulze > Approval > Minmax > Baldwin = <br>
CondorcetBorda = CopelandBorda = MSMLV = MSTB = Raynaud = RCIPE = <br>
SchwartzWoodall = SmithDAC = SmithScore = Woodall > MJ > STAR = <br>
ApprovalRunoff = Plurality<br>
1: Approval > RankedPairs > STAR > Woodall > SmithDAC > Minmax > RCIPE > <br>
Benham > MSA > SmithApprovalExplicit > ApprovalRunoff > MSMLV > <br>
SmithApprovalImplicit > DoubleDefeatHare > Raynaud > Schulze > <br>
SchwartzWoodall > SmithScore > MJ > Plurality > IRV > CondorcetBorda > <br>
Baldwin > CopelandBorda<br>
1: STAR > SmithScore > Baldwin = Benham = CondorcetBorda = CopelandBorda <br>
= Raynaud = Minmax = RankedPairs = Schulze = SchwartzWoodall = <br>
SmithApprovalExplicit = SmithApprovalImplicit = SmithDAC = Woodall = MSA <br>
= MSMLV = MSTB > ApprovalRunoff > Approval > RCIPE > DoubleDefeatHare > <br>
MJ > IRV > Plurality<br>
1: RankedPairs > Schulze = Benham > Woodall > Minmax > SchwartzWoodall > <br>
SmithApprovalImplicit = SmithApprovalExplicit > SmithScore > Raynaud > <br>
Baldwin > MJ > DoubleDefeatHare = MSTB = MSMLV = MSA > CopelandBorda > <br>
SmithDAC > ApprovalRunoff > STAR > RCIPE > CondorcetBorda > Approval > <br>
IRV > Plurality<br>
1: CondorcetPlur > Minmax > RankedPairs > Schulze > BTRIRV > Baldwin = <br>
Benham = CondorcetBorda = CopelandBorda = MSA = MSMLV = MSTB = Raynaud = <br>
SchwartzWoodall = SmithApprovalExplicit = SmithApprovalImplicit = <br>
SmithDAC = SmithScore = Woodall > IRV > Approval > STAR > Plurality > Score<br>
1: RCIPE > Benham > Minmax > RankedPairs > Woodall > SchwartzWoodall > <br>
Baldwin > CopelandBorda > CondorcetBorda > Schulze > SmithScore > <br>
Raynaud > MSTB > MSMLV > SmithDAC > DoubleDefeatHare > IRV > MJ > STAR > <br>
Approval > MSA > SmithApprovalExplicit > SmithApprovalImplicit > <br>
Plurality > ApprovalRunoff<br>
1: Approval > SmithScore > MSA > SmithApprovalExplicit > RankedPairs > <br>
Benham > Minmax > STAR > ApprovalRunoff = Baldwin = CondorcetBorda = <br>
CopelandBorda = DoubleDefeatHare = IRV = MJ = MSMLV = MSTB = Raynaud = <br>
RCIPE = Schulze = SchwartzWoodall = SmithApprovalImplicit = SmithDAC = <br>
Woodall > Plurality<br>
1: STAR > SmithScore > Score > MJ > Approval = SmithApprovalExplicit = <br>
SmithApprovalImplicit = MSA > ApprovalRunoff = RankedPairs = Schulze > <br>
Baldwin = Benham = CopelandBorda = MSMLV = MSTB = Raynaud = <br>
SchwartzWoodall = SmithDAC = Woodall > CondorcetBorda = Minmax > RCIPE > <br>
IRV > Plurality<br>
1: Benham > SchwartzWoodall > Woodall > RankedPairs > Schulze > MSTB > <br>
Minmax > BTRIRV > Raynaud > Baldwin > RCIPE > IRV > SmithDAC > MSMLV > <br>
MSA > SmithApprovalExplicit > SmithApprovalImplicit > SmithScore > <br>
DoubleDefeatHare > CopelandBorda > CondorcetBorda > Approval > MJ > <br>
Score > ApprovalRunoff > STAR > Plurality > Borda<br>
<br>
---------------------------------------------------------------------<br>
<br>
Ranked Pairs is the CW -- and Benham beats everybody but Ranked Pairs <br>
pairwise. This can be verified by going to Rob LeGrand's calculator <br>
(<a href="http://www.cs.angelo.edu/~rlegrand/rbvote/calc.html" rel="noreferrer" target="_blank">http://www.cs.angelo.edu/~rlegrand/rbvote/calc.html</a> with mirror <br>
<a href="https://munsterhjelm.no/km/rbvote/calc.html" rel="noreferrer" target="_blank">https://munsterhjelm.no/km/rbvote/calc.html</a> for people outside the US) <br>
and selecting "calculate all winners".<br>
<br>
Here are the Schulze results:<br>
<br>
1 Ranked Pairs (wv)<br>
2 Benham<br>
3 Approval<br>
Minmax (wv)<br>
Schulze<br>
STAR<br>
7 Smith//Score<br>
8 Margins-Sorted Approval<br>
Schwartz Woodall<br>
Smith//Approval (implicit)<br>
Woodall<br>
12 Smith//Approval (explicit)<br>
13 Raynaud<br>
14 Baldwin<br>
15 Max Strength Transitive Beatpath<br>
16 Margins-Sorted Minimum Losing Votes<br>
Smith//DAC<br>
18 Copeland//Borda (Ranked Robin)<br>
19 Condorcet//Borda (Black)<br>
20 Approval with manual runoff<br>
Double Defeat, Hare<br>
RCIPE<br>
23 Majority Judgement<br>
24 IRV<br>
25 Plurality<br>
26 BTR-IRV (write-in)<br>
27 Score (write-in)<br>
28 Borda (write-in)<br>
Condorcet//Plurality (write-in)<br>
<br>
The Approval voting results:<br>
<br>
1 Ranked Pairs (wv)<br>
2 Minmax (wv)<br>
3 Benham<br>
STAR<br>
Woodall<br>
6 Approval<br>
7 Approval with manual runoff<br>
Margins-Sorted Approval<br>
Schulze<br>
10 Schwartz Woodall<br>
Smith//Approval (explicit)<br>
Smith//Approval (implicit)<br>
Smith//Score<br>
14 Baldwin<br>
BTR-IRV (write-in)<br>
Condorcet//Borda (Black)<br>
Condorcet//Plurality (write-in)<br>
Copeland//Borda (Ranked Robin)<br>
Double Defeat, Hare<br>
IRV<br>
Majority Judgement<br>
Margins-Sorted Minimum Losing Votes<br>
Max Strength Transitive Beatpath<br>
Raynaud<br>
RCIPE<br>
Score (write-in)<br>
Smith//DAC<br>
28 Borda (write-in)<br>
Plurality<br>
<br>
and for fun, Schulze with ties broken by Approval:<br>
<br>
1 Ranked Pairs (wv)<br>
2 Benham<br>
3 Minmax (wv)<br>
4 STAR<br>
5 Approval<br>
6 Schulze<br>
7 Smith//Score<br>
8 Woodall<br>
9 Margins-Sorted Approval<br>
10 Schwartz Woodall<br>
Smith//Approval (implicit)<br>
12 Smith//Approval (explicit)<br>
13 Raynaud<br>
14 Baldwin<br>
15 Max Strength Transitive Beatpath<br>
16 Margins-Sorted Minimum Losing Votes<br>
Smith//DAC<br>
18 Copeland//Borda (Ranked Robin)<br>
19 Condorcet//Borda (Black)<br>
20 Approval with manual runoff<br>
21 Double Defeat, Hare<br>
RCIPE<br>
23 Majority Judgement<br>
24 IRV<br>
25 Plurality<br>
26 BTR-IRV (write-in)<br>
27 Score (write-in)<br>
28 Condorcet//Plurality (write-in)<br>
29 Borda (write-in)<br>
<br>
This should be accurate, but if you spot a typo or other mistake <br>
somewhere, let me know.<br>
<br>
-km<br>
----<br>
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</blockquote></div></div>