[EM] Schulze STV bugs and updated results (was: Re: Preliminary Droop-fit proportionality results)

[Etjon Basha]

Boo!

On Thu, 18 June 2026, 12:28 am Kristofer Munsterhjelm, <
km-elmet at munsterhjelm.no> wrote:

> On 2026-06-02 23:11, Toby Pereira wrote:
> > I see yes, thanks. In that case, Schulze STV seems to do pretty
> > terribly, not just a bit worse than other STV methods. And looking at
> > your whole list, considerably worse than things like (Bloc) Borda! It's
> > definitely not broken in your simulation?
>
> I added some tests to Schulze STV and found an election where quadelect
> would return the wrong outcome.
>
> The bug appears to have been caused by undefined behavior in Schulze's
> own code, where a line does something that has no clear order of
> execution, and different compilers resolve the ambiguity differently. I
> tested Schulze's prog01 compiled with a modern gcc and got the same bug.
>
> After fixing the bug, I tested the example elections referenced in
> "Implementing the Schulze STV Method"[1], table 2, and the Schulze STV
> code used by my simulator now gives the correct outcome - i.e. the ones
> listed in the paper - for all of them.
>
> I then ran my multiwinner simulations and got much better results.
> Sorry, Etjon :-)
>
> Droop spatial proportionality:
>
> Two seats, 10 candidates, 14400 elections:
>
> Name           Droop goodness-of-fit VSE
> Meek/Warren    0.7932
> Harmonic (S-L) 0.9254
> Schulze STV    0.9997
>
> Three seats:
>
> Warren         0.8712
> Meek           0.8713
> Harmonic (S-L) 0.8925
> Schulze STV    0.9992
>
> Four seats:
>
> Harmonic (S-L) 0.8880
> Warren         0.9184
> Meek           0.9185
> Schulze STV    0.9954
>
> Five seats:
>
> Harmonic (S-L) 0.8809
> Warren         0.9426
> Meek           0.9428
> Schulze STV    0.9874
>
> Six seats:
>
> Harmonic (S-L) 0.8779
> Meek           0.9598
> Warren         0.9598
> Schulze STV    0.9758
>
> Nine seats:
>
> Harmonic (S-L) 0.9450
> Schulze STV    0.9497
> Meek           0.9979
> Warren         0.9980
>
>
> The quantile fits for two out of ten are (288k elections):
>
> Name           Prop. quantile    Goodness-of-fit VSE
> Schulze STV    0.3377            0.9961
> Harmonic (S-L) 0.3498            0.9223
> Meek/Warren    0.3344            0.8090
>
> and for the 2-of-4 CFC-Kemeny comparison (5760 elections):
>
> Name           Prop. quantile    Goodness-of-fit VSE
> Harmonic (S-L) 0.3317            0.9414
> Meek/Warren    0.3321            0.9602
> Schulze STV    0.3345            0.9989
> CFC-Kemeny     0.2493            0.9998
>
> as well as 2-of-5 (7200 elections):
>
> Name           Prop. quantile    Goodness-of-fit VSE
> Meek/Warren    0.3346            0.9208
> Harmonic (S-L) 0.3383            0.9294
> CFC-Kemeny     0.2441            0.9967
> Schulze STV    0.3371            0.9967
>
> So Schulze STV seems to be pretty good, but its margin over other
> methods shrinks as seats/candidates ratio increases, to the point where
> Meek and Warren beats it with nine seats.
>
> Perhaps this has something to do with how Schulze STV's main calculation
> is on sets that differ by one candidate, that it then uses widest path
> to extrapolate; if there are more winners, such paths may have more
> steps. But I don't know for sure.
>
> I also found a few crash-inducing memory access bugs in Schulze's
> implementation, but the code is difficult enough to understand that I'm
> unsure how to fix them. I'll probably give more details in another post.
>
> -km
>
> [1]
>
> https://sites.math.duke.edu/~bray/Courses/49s/Additional%20Reading/Schulze/Schulze3/schulze3.pdf
>
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