[EM] A possible low-strategy PR concept when picking n-1 winners from n candidates

[Kristofer Munsterhjelm]

On 2026-05-02 01:31, Gustav Thorzen via Election-Methods wrote:
> On Fri, 1 May 2026 23:38:43 +0200
> Kristofer Munsterhjelm via Election-Methods <election-methods at lists.electorama.com> wrote:
> 
>> When picking a winner from two candidates, majority rule is
>> strategyproof. I was playing with ways to generalize this to multiwinner
>> to find at least *some* domain where a method can be both Droop
>> proportional and strategy-proof, and found this for elections with n
>> candidates and (n-1) seats:
> 
> Unless I misunderstood what is ment here,
> it seems like you claim to have found a counterexample
> to Duggan-Schwartz impossibility theorem (reducing to Gibbard-Satterthwaite when single winner)
> https://en.wikipedia.org/wiki/Duggan-Schwartz_theorem (wikipedia summary only)
> and there is also a corresponding generalization to Gibbards theorem without
> the rankorder ballots requirement (though I don't know any common name for that one).

I might have been a bit unclear. By "some domain", I mean a subset of 
elections where a method can pick an outcome (here, a set of winners) so 
that there's no incentive for the voters to lie about their preferences 
if that election corresponds to their honest preferences.

Single-winner methods that pass the majority criterion are strategyproof 
when a majority honestly prefers a certain candidate to everybody else. 
If they vote honestly, then their preferred candidate will be the 
majority winner. The majority voters have no incentive to alter their 
ballots because the only thing that can accomplish is to make someone 
they like less win; and the minority voters are ignored entirely, so 
they have no incentive to lie either.

More broadly, methods that elect from the resistant set are 
strategyproof when the honest election has a "super Condorcet winner" - 
a candidate who disqualifies everybody else. This explains a significant 
part of IRV's resistance to coalitional manipulation.

Gibbard shows that we can't have perfection - we can't have a method 
that's always strategyproof. But some methods may still be better than 
others.

So what I was asking is if there's some domain where some PR methods are 
strategyproof. If we could find such a domain, and it's large enough, it 
might explain, for instance, why Schulze STV has such low coalitional 
manipulability rates under impartial culture, but not under spatial models.

Or it could be useful for mechanism design.

For instance, a number of single-winner voting methods are all 
manipulable with probability one under the impartial culture as the 
number of voters approaches infinity. The Schulze method is one of 
these, but its multiwinner generalization, Schulze STV, is strangely 
robust to coalitional manipulation when picking (n-1) from n winners 
under impartial culture.

On the other hand, single-winner IRV is resistant to strategy (IC 
manipulability does not converge to unity), but its multiwinner 
generalization, STV, is considerably more vulnerable to vote management 
than Schulze STV, and so fares worse.

Perhaps exploring strategyproof domains for both single- and n-1-seat 
elections could give some idea of how to get the best of both worlds?

-km