[EM] A set of clone independence criteria more applicable to multiwinner

[Kristofer Munsterhjelm]

On 2025-10-08 20:07, Markus Schulze via Election-Methods wrote:
> Dear Kristofer,
> 
> in section 9.2 of my paper "The Schulze Method of Voting",
> I define independence of clones for proportional ranking
> methods and I explain, why the Schulze proportional ranking
> method satisfies this criterion:
> 
> https://arxiv.org/pdf/1804.02973.pdf
> 
> Suppose candidate D had the Z-th place in the proportional
> ranking. Suppose candidate D is replaced by a set of clones
> D(1), ..., D(n). Then the highest ranked clone D(1) must
> get the Z-th place of the proportional ranking and there
> must be no change in the places 1, ..., (Z-1) of the
> proportional ranking.
> 
> Example: Suppose the original proportional ranking was
> A, B, C, D, E, F, G, ...
> Then the new proportional ranking could be
> A, B, C, D(1), G, F, E, D(2), ...
> 
> One might argue that the order of the candidates between D(1)
> and D(2) shouldn't change either since D(2) is the first candidate
> who disrupts the original proportional ranking. However, I
> believe that already the sheer existence of potential winning
> sets with two candidates from the set of clones can change
> the order of the candidates between D(1) and D(2).

I'm having some difficulty seeing how that could be considered a good 
thing, at least for general multiwinner methods. Suppose we're electing 
five candidates, and before cloning the outcome is

{A, B, C, D, E}.

Then suppose D is cloned. It would seem to be just an IIA failure to 
then have the outcome change to

{A, B, C, D1, G}.

Now we pretty much have to live with IIA failures as a class. But 
single-winner clone independence says that we don't need to have IIA 
failures when the irrelevant alternatives are clones.

(Something like "outcome is {A,B,C} then we clone A and get {A1, A2, B}" 
is not an IIA failure since A2 is not an irrelevant alternative, I think.)

Do you have an example where it makes sense for the elected candidates 
to change in this way?

It might be more reasonable for proportional orderings (though I don't 
see why either), but proportional orderings are more constrained than 
general multiwinner methods (e.g. the LCR example). I'd still be 
interested in a proportional ordering example where this kind of change 
makes sense, though.

-km