Re: Preliminary Droop-fit proportionality results
Toby Pereira via Election-Methods <[email protected]> Sat, 30 May 2026 16:07:08 +0000 (UTC)
| Newsgroups | gmane.politics.election-methods |
|---|---|
| Message-ID | <[email protected]> |
--===============6023393890621022738==
Content-Type: multipart/alternative;
boundary="----=_Part_10792089_352675288.1780157228783"
------=_Part_10792089_352675288.1780157228783
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: quoted-printable
Some interesting results. I'm not really that knowledgeable on how the dif=
ferent STV methods all philosophically differ from each other, but it is in=
teresting how Schulze STV doesn't not perform that brilliantly here. So it =
seems that QPQ and Meek/Warren are better when it comes to "optimal" PR (fo=
r some definition of optimal anyway) rather than strategy-resistance.
I'm not at all surprised that Harmonic voting does better than Psi. I alway=
s felt Psi was "wrong" and in need of repair. Harmonic voting does that rep=
air. Thiele-based methods can still go wrong in some cases if you don't hav=
e unlimited clones, but I don't think the way your opinion space has been d=
efined would show this - which isn't a criticism by the way.
For a cardinal-based definition of PR, I think it's unlikely you could do m=
uch better than Harmonic voting with this sort of simulation. The COWPEA / =
COWPEA Lottery method doesn't have a known sensible deterministic counterpa=
rt, and that's the only other cardinal PR philosophy that I consider to be =
robustly good (in a theoretical, as opposed to practical, way). One way to =
test the two philosophies against each other would be to use the lottery fo=
rm of both in a simulation with many elected candidates and compare the dif=
ferences.
Toby
On Saturday, 30 May 2026 at 16:32:05 BST, Kristofer Munsterhjelm via El=
ection-Methods <[email protected]> wrote: =20
=20
So I implemented a quick version of a spatial Droop proportionality measur=
e:
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 VSE
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 0.29
Isoelastic (r=3D1)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 0=
.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 0.46
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 0.47
Psi voting (delta=3D0)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 0.52
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 0.56
QPQ (Sainte-Lagu=C3=AB)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 0.5=
9
Isoelastic (r=3D2)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 0=
.64
(Bloc) Normalized 0-20 Range=C2=A0 =C2=A0 0.65
(Bloc) Borda=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 0.68
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 0.80
Harmonic voting (d'Hondt)=C2=A0 =C2=A0 =C2=A0 =C2=A0 0.87
Harmonic voting (Sainte-Lagu=C3=AB)=C2=A0 0.93
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 VSE
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 -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 0.32
Isoelastic (r=3D1)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 0=
.36
Psi voting (delta=3D0)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 0.39
Random ballots=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 0.38
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 0.41
(Bloc) Normalized 0-20 Range=C2=A0 =C2=A0 0.44
Isoelastic (r=3D2)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 0=
.44
(Bloc) Borda=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 0.49
Harmonic voting (delta=3D0.02)=C2=A0 =C2=A0 0.59
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 0.67
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 0.8=
3
Harmonic voting (Sainte-Lagu=C3=AB)=C2=A0 0.89
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 VSE
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 0=
.19
Random ballots=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 0.41
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 0.57
Harmonic voting (delta=3D0.02)=C2=A0 =C2=A0 0.57
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 0.57
Isoelastic (r=3D2)=C2=A0=C2=A0=C2=A0 =C2=A0=C2=A0=C2=A0 0.71
(Bloc) Normalized 0-20 Range=C2=A0 =C2=A0 0.71
(Bloc) Borda=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 0.81
Psi voting (d'Hondt)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 0.82
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 0.83
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 0.9=
1
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 0.95
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
=20
------=_Part_10792089_352675288.1780157228783
Content-Type: text/html; charset=UTF-8
Content-Transfer-Encoding: quoted-printable
<html><head></head><body><div class=3D"ydp18e5a207yahoo-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">Some interesting results. I'=
m not really that knowledgeable on how the different STV methods all philos=
ophically differ from each other, but it is interesting how Schulze STV doe=
sn't not perform that brilliantly here. So it seems that QPQ and Meek/Warre=
n are better when it comes to "optimal" PR (for some definition of optimal =
anyway) rather than strategy-resistance.</div><div dir=3D"ltr" data-setdir=
=3D"false"><br></div><div dir=3D"ltr" data-setdir=3D"false">I'm not at all =
surprised that Harmonic voting does better than Psi. I always felt Psi was =
"wrong" and in need of repair. Harmonic voting does that repair. Thiele-bas=
ed methods can still go wrong in some cases if you don't have unlimited clo=
nes, but I don't think the way your opinion space has been defined would sh=
ow this - which isn't a criticism by the way.</div><div dir=3D"ltr" data-se=
tdir=3D"false"><br></div><div dir=3D"ltr" data-setdir=3D"false">For a cardi=
nal-based definition of PR, I think it's unlikely you could do much better =
than Harmonic voting with this sort of simulation. The COWPEA / COWPEA Lott=
ery method doesn't have a known sensible deterministic counterpart, and tha=
t's the only other cardinal PR philosophy that I consider to be robustly go=
od (in a theoretical, as opposed to practical, way). One way to test the tw=
o philosophies against each other would be to use the lottery form of both =
in a simulation with many elected candidates and compare the differences.</=
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"ydpc417abe1yahoo_quoted_1013653349" class=3D"ydpc4=
17abe1yahoo_quoted">
<div style=3D"font-family:'Helvetica Neue', Helvetica, Arial, s=
ans-serif;font-size:13px;color:#26282a;">
=20
<div>
On Saturday, 30 May 2026 at 16:32:05 BST, Kristofer=
Munsterhjelm via Election-Methods <[email protected]=
m> wrote:
</div>
<div><br></div>
<div><br></div>
=20
=20
<div><div dir=3D"ltr">So I implemented a quick version of a=
spatial Droop proportionality measure:<br></div><div dir=3D"ltr"><br></div=
><div dir=3D"ltr">The voters are drawn from a standard normal over a 1D opi=
nion space, and <br></div><div dir=3D"ltr">the candidates are drawn either =
from the same standard normal or a <br></div><div dir=3D"ltr">uniform distr=
ibution (odd iterations use one, even iterations use the <br></div><div dir=
=3D"ltr">other).[1] Each voter ranks the candidates in distance (and rates =
them <br></div><div dir=3D"ltr">according to negative distance).<br></div><=
div dir=3D"ltr"><br></div><div dir=3D"ltr">The "ideal" kth candidate is the=
k/(s+1)th quantile of the (drawn) voter <br></div><div dir=3D"ltr">distrib=
ution; the error is then the square root of the sum of squares <br></div><d=
iv dir=3D"ltr">between each ideal kth candidate and the kth candidate actua=
lly elected <br></div><div dir=3D"ltr">(in order from leftmost to rightmost=
).<br></div><div dir=3D"ltr"><br></div><div dir=3D"ltr">So, for instance, i=
f it's a two-candidate election and the voters' <br></div><div dir=3D"ltr">=
quantiles are -0.43 and +0.43, and method X elects candidates who are at <b=
r></div><div dir=3D"ltr">-0.27 and +0.34 respectively. Then the error for m=
ethod X in that <br></div><div dir=3D"ltr">election is the Euclidean distan=
ce between (-0.43, 0.43) and (-0.27, <br></div><div dir=3D"ltr">0.34) ~=3D =
0.184.[2]<br></div><div dir=3D"ltr"><br></div><div dir=3D"ltr">I then calcu=
lated the VSE over this measure with 4096 voters, 10 <br></div><div dir=3D"=
ltr">candidates, and different numbers of seats. Here are some results with=
<br></div><div dir=3D"ltr">some comments afterwards.<br></div><div dir=3D"=
ltr"><br></div><div dir=3D"ltr">Note that a bad result (low VSE) only gives=
an indication that the <br></div><div dir=3D"ltr">method doesn't select ca=
ndidates close to the Droop quantiles, but not <br></div><div dir=3D"ltr">*=
why*. It doesn't distinguish between that happening because the method <br>=
</div><div dir=3D"ltr">has a different notion of proportionality, or becaus=
e it has no such <br></div><div dir=3D"ltr">notion and is all over the plac=
e.<br></div><div dir=3D"ltr"><br></div><div dir=3D"ltr">(I'd like to implem=
ent something that determines what that notion of <br></div><div dir=3D"ltr=
">proportionality is if there is one. But I should read Ryan's post more <b=
r></div><div dir=3D"ltr">thoroughly before I do that.)<br></div><div dir=3D=
"ltr"><br></div><div dir=3D"ltr">2 seats:<br></div><div dir=3D"ltr">Name&nb=
sp; &=
nbsp; VSE<br></div><div dir=3D"ltr">Log-penalty voting =
-1.47<br></div><div dir=3D"ltr">=
Random ballots  =
; 0.29<br></div><div dir=3D"ltr">Isoelastic (r=3D1) &n=
bsp; 0.32<br></div><div dir=3D"ltr">Isoelastic=
(r=3D10) 0.37<br></=
div><div dir=3D"ltr">Schulze STV &=
nbsp; 0.45<br></div><div dir=3D"ltr">SNTV =
&nbs=
p; 0.46<br></div><div dir=3D"ltr">QPQ (0.01) &n=
bsp; 0.47<br></div=
><div dir=3D"ltr">Psi voting (delta=3D0) =
0.52<br></div><div dir=3D"ltr">Psi voting (Sainte-Lagu=C3=AB) =
0.55<br></div><div dir=3D"ltr">Psi voting (d'Hondt)&n=
bsp; 0.56<br></div><div dir=3D"ltr">QPQ=
(Sainte-Lagu=C3=AB) 0.59<=
br></div><div dir=3D"ltr">Isoelastic (r=3D2) &nb=
sp; 0.64<br></div><div dir=3D"ltr">(Bloc) Normalized =
0-20 Range 0.65<br></div><div dir=3D"ltr">(Bloc) Borda =
0.68<br></d=
iv><div dir=3D"ltr">PSC-CLE =
0.72<br></div><div dir=3D"ltr">Q=
PQ (d'Hondt) =
0.79<br></div><div dir=3D"ltr">Meek/Warren STV &=
nbsp; 0.80<br></div><div dir=3D"ltr">STV=
 =
; 0.80<br></div><div dir=3D"ltr">STV-ME(Schulze=
) 0.80<br></d=
iv><div dir=3D"ltr">Harmonic voting (delta=3D0.02) 0.80<br></=
div><div dir=3D"ltr">Harmonic voting (d'Hondt) 0=
.87<br></div><div dir=3D"ltr">Harmonic voting (Sainte-Lagu=C3=AB) 0.=
93<br></div><div dir=3D"ltr"><br></div><div dir=3D"ltr">5 seats:<br></div><=
div dir=3D"ltr">Name =
VSE<br></div><div dir=3D"ltr">L=
og-penalty voting -1.36<br>=
</div><div dir=3D"ltr">Isoelastic (r=3D10)  =
; -0.30<br></div><div dir=3D"ltr">Schulze STV &=
nbsp; 0.21<br></div=
><div dir=3D"ltr">QPQ (0.01)  =
; 0.32<br></div><div dir=3D"ltr">Isoelastic (r=
=3D1) 0.36<br></div=
><div dir=3D"ltr">Psi voting (delta=3D0) =
0.39<br></div><div dir=3D"ltr">Random ballots &=
nbsp; 0.38<br></div><div dir=3D"ltr">Ps=
i voting (Sainte-Lagu=C3=AB) 0.40<br></div><div =
dir=3D"ltr">Psi voting (d'Hondt) =
0.41<br></div><div dir=3D"ltr">(Bloc) Normalized 0-20 Range 0=
.44<br></div><div dir=3D"ltr">Isoelastic (r=3D2) =
0.44<br></div><div dir=3D"ltr">(Bloc) Borda&n=
bsp; 0.49<b=
r></div><div dir=3D"ltr">Harmonic voting (delta=3D0.02) 0.59<=
br></div><div dir=3D"ltr">SNTV &nb=
sp; 0.67<br></div><div di=
r=3D"ltr">Harmonic voting (d'Hondt) 0.76<br></di=
v><div dir=3D"ltr">PSC-CLE =
0.81<br></div><div dir=3D"ltr">QP=
Q (Sainte-Lagu=C3=AB) 0.83=
<br></div><div dir=3D"ltr">Harmonic voting (Sainte-Lagu=C3=AB) 0.89<=
br></div><div dir=3D"ltr">STV &nbs=
p; 0.94<br></div><d=
iv dir=3D"ltr">QPQ (d'Hondt)  =
; 0.94<br></div><div dir=3D"ltr">Meek/Warren STV =
0.94<br></div><div=
dir=3D"ltr">STV-ME(Schulze)  =
; 0.96<br></div><div dir=3D"ltr"><br></div><div dir=3D"ltr">9=
seats:<br></div><div dir=3D"ltr">Name &n=
bsp; VSE<br></div>=
<div dir=3D"ltr">Log-penalty voting  =
; -0.70<br></div><div dir=3D"ltr">Schulze STV &n=
bsp; 0.00<br></div><div di=
r=3D"ltr">Isoelastic (r=3D10) &nbs=
p; 0.10<br></div><div dir=3D"ltr">Isoelastic (r=3D1) &n=
bsp; 0.19<br></div><div dir=3D"ltr">Ran=
dom ballots =
0.41<br></div><div dir=3D"ltr">SNTV  =
; 0.57<br></div><d=
iv dir=3D"ltr">Harmonic voting (delta=3D0.02) 0.57<br></div><=
div dir=3D"ltr">QPQ (0.01) =
0.57<br></div><div dir=3D"ltr">Isoelastic (r=
=3D2) 0.71<br></div><div dir=3D"ltr">=
(Bloc) Normalized 0-20 Range 0.71<br></div><div dir=3D"ltr">(=
Bloc) Borda &=
nbsp; 0.81<br></div><div dir=3D"ltr">Psi voting (d'Hondt) &nb=
sp; 0.82<br></div><div dir=3D"ltr">Psi voting (Sainte=
-Lagu=C3=AB) 0.82<br></div><div dir=3D"ltr">Psi =
voting (delta=3D0) 0.83<br></div>=
<div dir=3D"ltr">Harmonic voting (d'Hondt) 0.90<=
br></div><div dir=3D"ltr">QPQ (Sainte-Lagu=C3=AB)  =
; 0.91<br></div><div dir=3D"ltr">PSC-CLE =
&nbs=
p; 0.92<br></div><div dir=3D"ltr">Harmonic voting (Sainte-Lagu=C3=AB) =
0.95<br></div><div dir=3D"ltr">STV &nbs=
p; 0.98<br><=
/div><div dir=3D"ltr">STV-ME(Schulze) &nb=
sp; 0.98<br></div><div dir=3D"ltr">QPQ (d'Hondt) =
0.998<br></=
div><div dir=3D"ltr">Meek/Warren STV &nbs=
p; 0.998<br></div><div dir=3D"ltr"><br></div><div dir=
=3D"ltr">("Random ballots" is the method where one repeatedly picks a rando=
m <br></div><div dir=3D"ltr">voter and elects their favorite continuing can=
didate.)<br></div><div dir=3D"ltr"><br></div><div dir=3D"ltr">The most surp=
rising part, to me, is the bad fit of Schulze STV and how <br></div><div di=
r=3D"ltr">little IRV's problems seem to generalize to STV, at least by this=
<br></div><div dir=3D"ltr">measure. It's also a bit surprising that for mo=
st tunable methods, <br></div><div dir=3D"ltr">d'Hondt does better than Sai=
nte-Lagu=C3=AB, but for Harmonic the opposite is <br></div><div dir=3D"ltr"=
>true.<br></div><div dir=3D"ltr"><br></div><div dir=3D"ltr">Harmonic seems =
to do better than Psi, just as it did in the my earlier <br></div><div dir=
=3D"ltr">simulations.<br></div><div dir=3D"ltr"><br></div><div dir=3D"ltr">=
In retrospect, it's not that surprising that Harmonic is beaten by <br></di=
v><div dir=3D"ltr">ranked methods because it doesn't optimize the same thin=
g (just like <br></div><div dir=3D"ltr">single-winner Range has a different=
objective than majority rule).<br></div><div dir=3D"ltr"><br></div><div di=
r=3D"ltr">If I were to guess, I'd imagine that there is some kind of proper=
ty <br></div><div dir=3D"ltr">that, if passed, leads to good performance he=
re; and STV passes its due <br></div><div dir=3D"ltr">to the way it works, =
but Schulze STV doesn't because it was designed <br></div><div dir=3D"ltr">=
primarily to be strategy-resistant. But that's just a guess.<br></div><div =
dir=3D"ltr"><br></div><div dir=3D"ltr">-km<br></div><div dir=3D"ltr"><br></=
div><div dir=3D"ltr">[1] My point with doing this was to penalize methods t=
hat just make <br></div><div dir=3D"ltr">assumptions about the voter distri=
bution from the candidate distribution <br></div><div dir=3D"ltr">or vice v=
ersa.<br></div><div dir=3D"ltr"><br></div><div dir=3D"ltr">[2] Ideally, the=
error measure should be designed to generalize to <br></div><div dir=3D"lt=
r">something like the Sainte-Lagu=C3=AB index in the party list case, but I=
just <br></div><div dir=3D"ltr">chose something easy and broadly reasonabl=
e here.<br></div><div dir=3D"ltr">----<br></div><div dir=3D"ltr">Election-M=
ethods mailing list - see <a href=3D"https://electorama.com/em" rel=3D"nofo=
llow" target=3D"_blank">https://electorama.com/em</a> for list info<br></di=
v></div>
</div>
</div></body></html>
------=_Part_10792089_352675288.1780157228783--
--===============6023393890621022738==
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
--===============6023393890621022738==--