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0% IC manipulability in (n-1)-out-of-n elections: bug or just that good?

KM
Kristofer Munsterhjelm
Fri, Aug 22, 2025 11:01 AM

I thought I'd give some results from my testing of multiwinner methods
when asked to fill n-1 seats with n candidates running. I should still
do so, but I got some strange results that seem almost too good to be true.

Schulze STV has manipulability zero under impartial culture, which means
it's almost everywhere strategyproof under that model if you have enough
voters.

This seems obviously wrong, like it should be a bug; but I haven't had
much luck finding what that bug is. So if anybody could try to
independently verify it or prove it wrong, that would be much appreciated!

Concretely, my Monte-Carlo solver found the following manipulability values:

99 voters, 3 cands, 2 seats, impartial culture: 0/15000 (0%)
99 voters, 3 cands, 2 s., Gaussian spatial 4D, sigma=1: 2558/15000 (17%)
99 voters, 4 cands, 3 s., impartial culture: 0/15000 (0%)
99 voters, 4 cands, 3 s., Gaussian spatial 4D, sigma=1: 4398/15000 (29%)

As a comparison, Meek STV has the following values:

99/3/2, impartial culture:          7042/15000 (47%)
99/3/2, Gaussian spatial, 4D, s=1:  6468/15000 (43%)

99/4/3, impartial culture:        11904/15000 (79%)
99/4/3, Gaussian spatial, 4D, s=1: 10969/15000 (73%)

It's hard to think of a bug that only hits IC unless the bug is in the
IC generator itself. But 0% manipulability is very strange, even for a
DSV-like method - which, as far as I understand, Schulze STV is, due to
calculating the strength of vote managements.

-km

I thought I'd give some results from my testing of multiwinner methods when asked to fill n-1 seats with n candidates running. I should still do so, but I got some strange results that seem almost too good to be true. Schulze STV has manipulability zero under impartial culture, which means it's almost everywhere strategyproof under that model if you have enough voters. This seems obviously wrong, like it should be a bug; but I haven't had much luck finding *what* that bug is. So if anybody could try to independently verify it or prove it wrong, that would be much appreciated! Concretely, my Monte-Carlo solver found the following manipulability values: 99 voters, 3 cands, 2 seats, impartial culture: 0/15000 (0%) 99 voters, 3 cands, 2 s., Gaussian spatial 4D, sigma=1: 2558/15000 (17%) 99 voters, 4 cands, 3 s., impartial culture: 0/15000 (0%) 99 voters, 4 cands, 3 s., Gaussian spatial 4D, sigma=1: 4398/15000 (29%) As a comparison, Meek STV has the following values: 99/3/2, impartial culture: 7042/15000 (47%) 99/3/2, Gaussian spatial, 4D, s=1: 6468/15000 (43%) 99/4/3, impartial culture: 11904/15000 (79%) 99/4/3, Gaussian spatial, 4D, s=1: 10969/15000 (73%) It's hard to think of a bug that only hits IC unless the bug is in the IC generator itself. But 0% manipulability is very strange, even for a DSV-like method - which, as far as I understand, Schulze STV is, due to calculating the strength of vote managements. -km