[EM] Preliminary Droop-fit proportionality results
Etjon Basha
etjonbasha at gmail.com
Sun May 31 02:33:51 PDT 2026
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.
> ----
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>
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