Re: Preliminary Droop-fit proportionality results
Toby Pereira via Election-Methods <[email protected]> Tue, 2 Jun 2026 14:54:30 +0000 (UTC)
| Newsgroups | gmane.politics.election-methods |
|---|---|
| Message-ID | <[email protected]> |
--===============1183282871216801904==
Content-Type: multipart/alternative;
boundary="----=_Part_517332_1248802798.1780412070401"
------=_Part_517332_1248802798.1780412070401
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: quoted-printable
Interestingly Kristofer put the two methods together suggesting the simula=
tion ran them as if they were they same method. I don't really know the dif=
ference between all the STV methods, but QPQ also got a score 0f 0.998 for =
9 seats, suggesting it's up there as well. Do we know why Schulze outperfor=
med the others for 5 seats but not 9?
Toby
On Sunday, 31 May 2026 at 10:34:43 BST, Etjon Basha via Election-Method=
s <[email protected]> wrote: =20
=20
Thank you for sharing these Kristofer,
Always a pleasure to see one's biases reinforced by independent sources, wi=
th such a total Warren/Meek STV victory over Schultze. If only Warren had o=
utdone Meek, this would have been perfect.
Best regards,
Etjon
The only thing th
On Sun, 31 May 2026, 1:31=E2=80=AFam Kristofer Munsterhjelm via Election-Me=
thods, <[email protected]> wrote:
So I implemented a quick version of a spatial Droop proportionality measure=
:
The voters are drawn from a standard normal over a 1D opinion space, and=20
the candidates are drawn either from the same standard normal or a=20
uniform distribution (odd iterations use one, even iterations use the=20
other).[1] Each voter ranks the candidates in distance (and rates them=20
according to negative distance).
The "ideal" kth candidate is the k/(s+1)th quantile of the (drawn) voter=20
distribution; the error is then the square root of the sum of squares=20
between each ideal kth candidate and the kth candidate actually elected=20
(in order from leftmost to rightmost).
So, for instance, if it's a two-candidate election and the voters'=20
quantiles are -0.43 and +0.43, and method X elects candidates who are at=20
-0.27 and +0.34 respectively. Then the error for method X in that=20
election is the Euclidean distance between (-0.43, 0.43) and (-0.27,=20
0.34) ~=3D 0.184.[2]
I then calculated the VSE over this measure with 4096 voters, 10=20
candidates, and different numbers of seats. Here are some results with=20
some comments afterwards.
Note that a bad result (low VSE) only gives an indication that the=20
method doesn't select candidates close to the Droop quantiles, but not=20
*why*. It doesn't distinguish between that happening because the method=20
has a different notion of proportionality, or because it has no such=20
notion and is all over the place.
(I'd like to implement something that determines what that notion of=20
proportionality is if there is one. But I should read Ryan's post more=20
thoroughly before I do that.)
2 seats:
Name=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0VSE
Log-penalty voting=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 -1.47
Random ballots=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A00.29
Isoelastic (r=3D1)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A00.32
Isoelastic (r=3D10)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
0.37
Schulze STV=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 0.45
SNTV=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A00.46
QPQ (0.01)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A00.47
Psi voting (delta=3D0)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A00.52
Psi voting (Sainte-Lagu=C3=AB)=C2=A0 =C2=A0 =C2=A0 =C2=A0 0.55
Psi voting (d'Hondt)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A00.56
QPQ (Sainte-Lagu=C3=AB)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A00.59
Isoelastic (r=3D2)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A00.64
(Bloc) Normalized 0-20 Range=C2=A0 =C2=A0 =C2=A00.65
(Bloc) Borda=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A00.68
PSC-CLE=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 0.72
QPQ (d'Hondt)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0=
=C2=A0 0.79
Meek/Warren STV=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 0.80
STV=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 0.80
STV-ME(Schulze)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 0.80
Harmonic voting (delta=3D0.02)=C2=A0 =C2=A0 =C2=A00.80
Harmonic voting (d'Hondt)=C2=A0 =C2=A0 =C2=A0 =C2=A0 0.87
Harmonic voting (Sainte-Lagu=C3=AB)=C2=A0 =C2=A00.93
5 seats:
Name=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0VSE
Log-penalty voting=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 -1.36
Isoelastic (r=3D10)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0-=
0.30
Schulze STV=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 0.21
QPQ (0.01)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A00.32
Isoelastic (r=3D1)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A00.36
Psi voting (delta=3D0)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A00.39
Random ballots=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A00.38
Psi voting (Sainte-Lagu=C3=AB)=C2=A0 =C2=A0 =C2=A0 =C2=A0 0.40
Psi voting (d'Hondt)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A00.41
(Bloc) Normalized 0-20 Range=C2=A0 =C2=A0 =C2=A00.44
Isoelastic (r=3D2)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A00.44
(Bloc) Borda=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A00.49
Harmonic voting (delta=3D0.02)=C2=A0 =C2=A0 =C2=A00.59
SNTV=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A00.67
Harmonic voting (d'Hondt)=C2=A0 =C2=A0 =C2=A0 =C2=A0 0.76
PSC-CLE=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 0.81
QPQ (Sainte-Lagu=C3=AB)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A00.83
Harmonic voting (Sainte-Lagu=C3=AB)=C2=A0 =C2=A00.89
STV=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 0.94
QPQ (d'Hondt)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0=
=C2=A0 0.94
Meek/Warren STV=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 0.94
STV-ME(Schulze)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 0.96
9 seats:
Name=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0VSE
Log-penalty voting=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 -0.70
Schulze STV=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 0.00
Isoelastic (r=3D10)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
0.10
Isoelastic (r=3D1)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A00.19
Random ballots=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A00.41
SNTV=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A00.57
Harmonic voting (delta=3D0.02)=C2=A0 =C2=A0 =C2=A00.57
QPQ (0.01)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A00.57
Isoelastic (r=3D2)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A00.71
(Bloc) Normalized 0-20 Range=C2=A0 =C2=A0 =C2=A00.71
(Bloc) Borda=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A00.81
Psi voting (d'Hondt)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A00.82
Psi voting (Sainte-Lagu=C3=AB)=C2=A0 =C2=A0 =C2=A0 =C2=A0 0.82
Psi voting (delta=3D0)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A00.83
Harmonic voting (d'Hondt)=C2=A0 =C2=A0 =C2=A0 =C2=A0 0.90
QPQ (Sainte-Lagu=C3=AB)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A00.91
PSC-CLE=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 0.92
Harmonic voting (Sainte-Lagu=C3=AB)=C2=A0 =C2=A00.95
STV=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 0.98
STV-ME(Schulze)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 0.98
QPQ (d'Hondt)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0=
=C2=A0 0.998
Meek/Warren STV=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 0.998
("Random ballots" is the method where one repeatedly picks a random=20
voter and elects their favorite continuing candidate.)
The most surprising part, to me, is the bad fit of Schulze STV and how=20
little IRV's problems seem to generalize to STV, at least by this=20
measure. It's also a bit surprising that for most tunable methods,=20
d'Hondt does better than Sainte-Lagu=C3=AB, but for Harmonic the opposite i=
s=20
true.
Harmonic seems to do better than Psi, just as it did in the my earlier=20
simulations.
In retrospect, it's not that surprising that Harmonic is beaten by=20
ranked methods because it doesn't optimize the same thing (just like=20
single-winner Range has a different objective than majority rule).
If I were to guess, I'd imagine that there is some kind of property=20
that, if passed, leads to good performance here; and STV passes its due=20
to the way it works, but Schulze STV doesn't because it was designed=20
primarily to be strategy-resistant. But that's just a guess.
-km
[1] My point with doing this was to penalize methods that just make=20
assumptions about the voter distribution from the candidate distribution=20
or vice versa.
[2] Ideally, the error measure should be designed to generalize to=20
something like the Sainte-Lagu=C3=AB index in the party list case, but I ju=
st=20
chose something easy and broadly reasonable here.
----
Election-Methods mailing list - see https://electorama.com/em for list info
----
Election-Methods mailing list - see https://electorama.com/em for list info
=20
------=_Part_517332_1248802798.1780412070401
Content-Type: text/html; charset=UTF-8
Content-Transfer-Encoding: quoted-printable
<html><head></head><body><div class=3D"ydpcf00fc0dyahoo-style-wrap" style=
=3D"font-family:Helvetica Neue, Helvetica, Arial, sans-serif;font-size:13px=
;"><div></div>
<div dir=3D"ltr" data-setdir=3D"false">Interestingly Kristofer put =
the two methods together suggesting the simulation ran them as if they were=
they same method. I don't really know the difference between all the STV m=
ethods, but QPQ also got a score 0f 0.998 for 9 seats, suggesting it's up t=
here as well. Do we know why Schulze outperformed the others for 5 seats bu=
t not 9?</div><div dir=3D"ltr" data-setdir=3D"false"><br></div><div dir=3D"=
ltr" data-setdir=3D"false">Toby</div><div><br></div>
=20
</div><div id=3D"ydp75ef3b03yahoo_quoted_1145505876" class=3D"ydp75=
ef3b03yahoo_quoted">
<div style=3D"font-family:'Helvetica Neue', Helvetica, Arial, s=
ans-serif;font-size:13px;color:#26282a;">
=20
<div>
On Sunday, 31 May 2026 at 10:34:43 BST, Etjon Basha=
via Election-Methods <[email protected]> wrote:
</div>
<div><br></div>
<div><br></div>
=20
=20
<div><div id=3D"ydp75ef3b03yiv3363098413"><div><div>Thank y=
ou for sharing these Kristofer,<div><br clear=3D"none"></div><div>Always a =
pleasure to see one's biases reinforced by independent sources, with such a=
total Warren/Meek STV victory over Schultze. If only Warren had outdone Me=
ek, this would have been perfect.</div><div><br clear=3D"none"></div><div>B=
est regards,</div><div><br clear=3D"none"></div><div>Etjon</div><div><br cl=
ear=3D"none"></div><div>The only thing th</div></div><br clear=3D"none"><di=
v id=3D"ydp75ef3b03yiv3363098413yqt45435" class=3D"ydp75ef3b03yiv3363098413=
yqt7804498335"><div class=3D"ydp75ef3b03yiv3363098413gmail_quote ydp75ef3b0=
3yiv3363098413gmail_quote_container"><div dir=3D"ltr" class=3D"ydp75ef3b03y=
iv3363098413gmail_attr">On Sun, 31 May 2026, 1:31=E2=80=AFam Kristofer Muns=
terhjelm via Election-Methods, <<a shape=3D"rect" href=3D"mailto:electio=
[email protected]" rel=3D"nofollow" target=3D"_blank">election=
[email protected]</a>> wrote:<br clear=3D"none"></div><block=
quote style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1e=
x;" class=3D"ydp75ef3b03yiv3363098413gmail_quote">So I implemented a quick =
version of a spatial Droop proportionality measure:<br clear=3D"none">
<br clear=3D"none">
The voters are drawn from a standard normal over a 1D opinion space, and <b=
r clear=3D"none">
the candidates are drawn either from the same standard normal or a <br clea=
r=3D"none">
uniform distribution (odd iterations use one, even iterations use the <br c=
lear=3D"none">
other).[1] Each voter ranks the candidates in distance (and rates them <br =
clear=3D"none">
according to negative distance).<br clear=3D"none">
<br clear=3D"none">
The "ideal" kth candidate is the k/(s+1)th quantile of the (drawn) voter <b=
r clear=3D"none">
distribution; the error is then the square root of the sum of squares <br c=
lear=3D"none">
between each ideal kth candidate and the kth candidate actually elected <br=
clear=3D"none">
(in order from leftmost to rightmost).<br clear=3D"none">
<br clear=3D"none">
So, for instance, if it's a two-candidate election and the voters' <br clea=
r=3D"none">
quantiles are -0.43 and +0.43, and method X elects candidates who are at <b=
r clear=3D"none">
-0.27 and +0.34 respectively. Then the error for method X in that <br clear=
=3D"none">
election is the Euclidean distance between (-0.43, 0.43) and (-0.27, <br cl=
ear=3D"none">
0.34) ~=3D 0.184.[2]<br clear=3D"none">
<br clear=3D"none">
I then calculated the VSE over this measure with 4096 voters, 10 <br clear=
=3D"none">
candidates, and different numbers of seats. Here are some results with <br =
clear=3D"none">
some comments afterwards.<br clear=3D"none">
<br clear=3D"none">
Note that a bad result (low VSE) only gives an indication that the <br clea=
r=3D"none">
method doesn't select candidates close to the Droop quantiles, but not <br =
clear=3D"none">
*why*. It doesn't distinguish between that happening because the method <br=
clear=3D"none">
has a different notion of proportionality, or because it has no such <br cl=
ear=3D"none">
notion and is all over the place.<br clear=3D"none">
<br clear=3D"none">
(I'd like to implement something that determines what that notion of <br cl=
ear=3D"none">
proportionality is if there is one. But I should read Ryan's post more <br =
clear=3D"none">
thoroughly before I do that.)<br clear=3D"none">
<br clear=3D"none">
2 seats:<br clear=3D"none">
Name &=
nbsp; VSE<br clear=3D"none">
Log-penalty voting -1.47<br=
clear=3D"none">
Random ballots  =
; 0.29<br clear=3D"none">
Isoelastic (r=3D1) &=
nbsp;0.32<br clear=3D"none">
Isoelastic (r=3D10) =
0.37<br clear=3D"none">
Schulze STV &=
nbsp; 0.45<br clear=3D"none">
SNTV &=
nbsp; 0.46<br clear=3D"none">
QPQ (0.01) &n=
bsp; 0.47<br clear=3D"none">
Psi voting (delta=3D0) 0.52<=
br clear=3D"none">
Psi voting (Sainte-Lagu=C3=AB) 0.55<br clear=3D"=
none">
Psi voting (d'Hondt) 0.56<br=
clear=3D"none">
QPQ (Sainte-Lagu=C3=AB) &nb=
sp;0.59<br clear=3D"none">
Isoelastic (r=3D2) &=
nbsp;0.64<br clear=3D"none">
(Bloc) Normalized 0-20 Range 0.65<br clear=3D"none">
(Bloc) Borda =
0.68<br clear=3D"none">
PSC-CLE  =
; 0.72<br clear=3D"none">
QPQ (d'Hondt) =
0.79<br clear=3D"none">
Meek/Warren STV &nbs=
p; 0.80<br clear=3D"none">
STV &n=
bsp; 0.80<br clear=3D"none">
STV-ME(Schulze) &nbs=
p; 0.80<br clear=3D"none">
Harmonic voting (delta=3D0.02) 0.80<br clear=3D"none">
Harmonic voting (d'Hondt) 0.87<br clear=3D"none"=
>
Harmonic voting (Sainte-Lagu=C3=AB) 0.93<br clear=3D"none">
<br clear=3D"none">
5 seats:<br clear=3D"none">
Name &=
nbsp; VSE<br clear=3D"none">
Log-penalty voting -1.36<br=
clear=3D"none">
Isoelastic (r=3D10) -=
0.30<br clear=3D"none">
Schulze STV &=
nbsp; 0.21<br clear=3D"none">
QPQ (0.01) &n=
bsp; 0.32<br clear=3D"none">
Isoelastic (r=3D1) &=
nbsp;0.36<br clear=3D"none">
Psi voting (delta=3D0) 0.39<=
br clear=3D"none">
Random ballots  =
; 0.38<br clear=3D"none">
Psi voting (Sainte-Lagu=C3=AB) 0.40<br clear=3D"=
none">
Psi voting (d'Hondt) 0.41<br=
clear=3D"none">
(Bloc) Normalized 0-20 Range 0.44<br clear=3D"none">
Isoelastic (r=3D2) &=
nbsp;0.44<br clear=3D"none">
(Bloc) Borda =
0.49<br clear=3D"none">
Harmonic voting (delta=3D0.02) 0.59<br clear=3D"none">
SNTV &=
nbsp; 0.67<br clear=3D"none">
Harmonic voting (d'Hondt) 0.76<br clear=3D"none"=
>
PSC-CLE  =
; 0.81<br clear=3D"none">
QPQ (Sainte-Lagu=C3=AB) &nb=
sp;0.83<br clear=3D"none">
Harmonic voting (Sainte-Lagu=C3=AB) 0.89<br clear=3D"none">
STV &n=
bsp; 0.94<br clear=3D"none">
QPQ (d'Hondt) =
0.94<br clear=3D"none">
Meek/Warren STV &nbs=
p; 0.94<br clear=3D"none">
STV-ME(Schulze) &nbs=
p; 0.96<br clear=3D"none">
<br clear=3D"none">
9 seats:<br clear=3D"none">
Name &=
nbsp; VSE<br clear=3D"none">
Log-penalty voting -0.70<br=
clear=3D"none">
Schulze STV &=
nbsp; 0.00<br clear=3D"none">
Isoelastic (r=3D10) =
0.10<br clear=3D"none">
Isoelastic (r=3D1) &=
nbsp;0.19<br clear=3D"none">
Random ballots  =
; 0.41<br clear=3D"none">
SNTV &=
nbsp; 0.57<br clear=3D"none">
Harmonic voting (delta=3D0.02) 0.57<br clear=3D"none">
QPQ (0.01) &n=
bsp; 0.57<br clear=3D"none">
Isoelastic (r=3D2) &=
nbsp;0.71<br clear=3D"none">
(Bloc) Normalized 0-20 Range 0.71<br clear=3D"none">
(Bloc) Borda =
0.81<br clear=3D"none">
Psi voting (d'Hondt) 0.82<br=
clear=3D"none">
Psi voting (Sainte-Lagu=C3=AB) 0.82<br clear=3D"=
none">
Psi voting (delta=3D0) 0.83<=
br clear=3D"none">
Harmonic voting (d'Hondt) 0.90<br clear=3D"none"=
>
QPQ (Sainte-Lagu=C3=AB) &nb=
sp;0.91<br clear=3D"none">
PSC-CLE  =
; 0.92<br clear=3D"none">
Harmonic voting (Sainte-Lagu=C3=AB) 0.95<br clear=3D"none">
STV &n=
bsp; 0.98<br clear=3D"none">
STV-ME(Schulze) &nbs=
p; 0.98<br clear=3D"none">
QPQ (d'Hondt) =
0.998<br clear=3D"none">
Meek/Warren STV &nbs=
p; 0.998<br clear=3D"none">
<br clear=3D"none">
("Random ballots" is the method where one repeatedly picks a random <br cle=
ar=3D"none">
voter and elects their favorite continuing candidate.)<br clear=3D"none">
<br clear=3D"none">
The most surprising part, to me, is the bad fit of Schulze STV and how <br =
clear=3D"none">
little IRV's problems seem to generalize to STV, at least by this <br clear=
=3D"none">
measure. It's also a bit surprising that for most tunable methods, <br clea=
r=3D"none">
d'Hondt does better than Sainte-Lagu=C3=AB, but for Harmonic the opposite i=
s <br clear=3D"none">
true.<br clear=3D"none">
<br clear=3D"none">
Harmonic seems to do better than Psi, just as it did in the my earlier <br =
clear=3D"none">
simulations.<br clear=3D"none">
<br clear=3D"none">
In retrospect, it's not that surprising that Harmonic is beaten by <br clea=
r=3D"none">
ranked methods because it doesn't optimize the same thing (just like <br cl=
ear=3D"none">
single-winner Range has a different objective than majority rule).<br clear=
=3D"none">
<br clear=3D"none">
If I were to guess, I'd imagine that there is some kind of property <br cle=
ar=3D"none">
that, if passed, leads to good performance here; and STV passes its due <br=
clear=3D"none">
to the way it works, but Schulze STV doesn't because it was designed <br cl=
ear=3D"none">
primarily to be strategy-resistant. But that's just a guess.<br clear=3D"no=
ne">
<br clear=3D"none">
-km<br clear=3D"none">
<br clear=3D"none">
[1] My point with doing this was to penalize methods that just make <br cle=
ar=3D"none">
assumptions about the voter distribution from the candidate distribution <b=
r clear=3D"none">
or vice versa.<br clear=3D"none">
<br clear=3D"none">
[2] Ideally, the error measure should be designed to generalize to <br clea=
r=3D"none">
something like the Sainte-Lagu=C3=AB index in the party list case, but I ju=
st <br clear=3D"none">
chose something easy and broadly reasonable here.<br clear=3D"none">
----<br clear=3D"none">
Election-Methods mailing list - see <a shape=3D"rect" href=3D"https://elect=
orama.com/em" rel=3D"nofollow" target=3D"_blank">https://electorama.com/em<=
/a> for list info<br clear=3D"none">
</blockquote></div></div>
</div></div><div class=3D"ydp75ef3b03yqt7804498335" id=3D"ydp75ef3b03yqt467=
02">----<br clear=3D"none">Election-Methods mailing list - see <a shape=3D"=
rect" href=3D"https://electorama.com/em" rel=3D"nofollow" target=3D"_blank"=
>https://electorama.com/em</a> for list info<br clear=3D"none"></div></div>
</div>
</div></body></html>
------=_Part_517332_1248802798.1780412070401--
--===============1183282871216801904==
Content-Type: text/plain; charset="us-ascii"
MIME-Version: 1.0
Content-Transfer-Encoding: 7bit
Content-Disposition: inline
----
Election-Methods mailing list - see https://electorama.com/em for list info
--===============1183282871216801904==--