[EM] Preliminary Droop-fit proportionality results

[Kristofer Munsterhjelm]

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?

It's hard to tell because the method is so complex; I don't have any 
other implementations than Schulze's own and my interface with my own 
code. At least Schulze provides some example elections in his papers, so 
I could code up those and check if I get the right results.

More broadly, it would be nice to have test vectors for a number of 
methods, particularly exercising their edge cases... but gathering a 
comprehensive library of them would be a significant undertaking in 
itself, I think.


I agree that Schulze STV seems unreasonably bad here, but the really 
strange part is that they're not "obviously broken" bad. For instance, I 
extended my simulator to find the level of proportionality that best fit 
the method (in the sense of giving the best VSE assuming this level of 
proportionality) for two-seat elections. For STV and Schulze STV, I got 
the following results with two seats, ten candidates:

Name		Prop. quantile	Goodness-of-fit VSE
STV		0.3404		0.7946
Meek/Warren	0.3397		0.7945
Schulze STV	0.393		0.5141

while obviously ill-fitting methods have more extreme values:

Name		Prop. quantile	Goodness-of-fit VSE
LPV0+		0.0004		-0.4447
Bloc Borda	0.5		 0.9331
Plurality loser	0		-0.1641

Here, exact Droop proportionality corresponds to a quantile value of 
1/3; lower than this is more factional, higher is more majoritarian. 
"Plurality loser" elects the candidates with the fewest first preferences.

I'll give more results in another post, but for Schulze STV in 
particular, its best-fit proportionality level doesn't seem too far off 
Droop, and it seems strange that it should be that close by chance.

Further adding to the weirdness is that when I wrote a coalitional 
manipulability simulator for n-1-seat n-candidate elections, Schulze STV 
had a very low manipulability value - which is what you'd expect for a 
method explicitly designed to be resistant to strategy, and not what a 
broken version of it would produce.

So maybe it is broken in some complex way or my proportionality 
simulator in particular is exposing some bug that the other simulators 
don't. I should implement the test elections and see what I get, and 
until then just say "something might be wrong, but if so, whatever is 
causing the error is subtle, not obvious".

-km