[EM] Preliminary Droop-fit proportionality results
Toby Pereira
tdp201b at yahoo.co.uk
Tue Jun 2 07:54:30 PDT 2026
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 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 outperformed the others for 5 seats but not 9?
Toby
On Sunday, 31 May 2026 at 10:34:43 BST, Etjon Basha via Election-Methods <election-methods at lists.electorama.com> wrote:
Thank you for sharing these Kristofer,
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 Meek, this would have been perfect.
Best regards,
Etjon
The only thing th
On Sun, 31 May 2026, 1:31 am Kristofer Munsterhjelm via Election-Methods, <election-methods at lists.electorama.com> 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
the candidates are drawn either from the same standard normal or a
uniform distribution (odd iterations use one, even iterations use the
other).[1] Each voter ranks the candidates in distance (and rates them
according to negative distance).
The "ideal" kth candidate is the k/(s+1)th quantile of the (drawn) voter
distribution; the error is then the square root of the sum of squares
between each ideal kth candidate and the kth candidate actually elected
(in order from leftmost to rightmost).
So, for instance, if it's a two-candidate election and the voters'
quantiles are -0.43 and +0.43, and method X elects candidates who are at
-0.27 and +0.34 respectively. Then the error for method X in that
election is the Euclidean distance between (-0.43, 0.43) and (-0.27,
0.34) ~= 0.184.[2]
I then calculated the VSE over this measure with 4096 voters, 10
candidates, and different numbers of seats. Here are some results with
some comments afterwards.
Note that a bad result (low VSE) only gives an indication that the
method doesn't select candidates close to the Droop quantiles, but not
*why*. It doesn't distinguish between that happening because the method
has a different notion of proportionality, or because it has no such
notion and is all over the place.
(I'd like to implement something that determines what that notion of
proportionality is if there is one. But I should read Ryan's post more
thoroughly before I do that.)
2 seats:
Name VSE
Log-penalty voting -1.47
Random ballots 0.29
Isoelastic (r=1) 0.32
Isoelastic (r=10) 0.37
Schulze STV 0.45
SNTV 0.46
QPQ (0.01) 0.47
Psi voting (delta=0) 0.52
Psi voting (Sainte-Laguë) 0.55
Psi voting (d'Hondt) 0.56
QPQ (Sainte-Laguë) 0.59
Isoelastic (r=2) 0.64
(Bloc) Normalized 0-20 Range 0.65
(Bloc) Borda 0.68
PSC-CLE 0.72
QPQ (d'Hondt) 0.79
Meek/Warren STV 0.80
STV 0.80
STV-ME(Schulze) 0.80
Harmonic voting (delta=0.02) 0.80
Harmonic voting (d'Hondt) 0.87
Harmonic voting (Sainte-Laguë) 0.93
5 seats:
Name VSE
Log-penalty voting -1.36
Isoelastic (r=10) -0.30
Schulze STV 0.21
QPQ (0.01) 0.32
Isoelastic (r=1) 0.36
Psi voting (delta=0) 0.39
Random ballots 0.38
Psi voting (Sainte-Laguë) 0.40
Psi voting (d'Hondt) 0.41
(Bloc) Normalized 0-20 Range 0.44
Isoelastic (r=2) 0.44
(Bloc) Borda 0.49
Harmonic voting (delta=0.02) 0.59
SNTV 0.67
Harmonic voting (d'Hondt) 0.76
PSC-CLE 0.81
QPQ (Sainte-Laguë) 0.83
Harmonic voting (Sainte-Laguë) 0.89
STV 0.94
QPQ (d'Hondt) 0.94
Meek/Warren STV 0.94
STV-ME(Schulze) 0.96
9 seats:
Name VSE
Log-penalty voting -0.70
Schulze STV 0.00
Isoelastic (r=10) 0.10
Isoelastic (r=1) 0.19
Random ballots 0.41
SNTV 0.57
Harmonic voting (delta=0.02) 0.57
QPQ (0.01) 0.57
Isoelastic (r=2) 0.71
(Bloc) Normalized 0-20 Range 0.71
(Bloc) Borda 0.81
Psi voting (d'Hondt) 0.82
Psi voting (Sainte-Laguë) 0.82
Psi voting (delta=0) 0.83
Harmonic voting (d'Hondt) 0.90
QPQ (Sainte-Laguë) 0.91
PSC-CLE 0.92
Harmonic voting (Sainte-Laguë) 0.95
STV 0.98
STV-ME(Schulze) 0.98
QPQ (d'Hondt) 0.998
Meek/Warren STV 0.998
("Random ballots" is the method where one repeatedly picks a random
voter and elects their favorite continuing candidate.)
The most surprising part, to me, is the bad fit of Schulze STV and how
little IRV's problems seem to generalize to STV, at least by this
measure. It's also a bit surprising that for most tunable methods,
d'Hondt does better than Sainte-Laguë, but for Harmonic the opposite is
true.
Harmonic seems to do better than Psi, just as it did in the my earlier
simulations.
In retrospect, it's not that surprising that Harmonic is beaten by
ranked methods because it doesn't optimize the same thing (just like
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
that, if passed, leads to good performance here; and STV passes its due
to the way it works, but Schulze STV doesn't because it was designed
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
assumptions about the voter distribution from the candidate distribution
or vice versa.
[2] Ideally, the error measure should be designed to generalize to
something like the Sainte-Laguë index in the party list case, but I just
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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20260602/0a6ac2d0/attachment.htm>
More information about the Election-Methods
mailing list