[EM] Why Clone Independence?

[Kristofer Munsterhjelm]

I seem to have forgotten to reply to this post. Well, here goes :-)

On 25.01.2023 11:36, Colin Champion wrote:
> A couple of observations/questions.
> 
> Firstly it isn't clear to me that IC makes a lot of sense except under a 
> spatial model. The definition of clones is two candidates who are 
> consecutive in all ballots, but the concept is only practically useful 
> if this corresponds to some property inherent in the candidates. Under a 
> spatial model, two coincident candidates will be consecutive in all 
> ballots. (The converse isn't clear.) The presence of clones might then 
> arise through cultural factors or strategic nomination.
> 
> Under a jury model, if A is unmistakably better than B and C, and B and 
> C are unmistakably better than D, then B and C will be consecutive in 
> all ballots. But suppose that B and C are always consecutive while 
> sometimes coming above and sometimes below both A and D. Shouldn't we 
> assume that the consecutiveness is a coincidence and decline to draw any 
> conclusions from it?

Suppose the true order is A>B>C>D. Then if you get both A>B>C>D and 
D>C>B>A, then it seems you're not in a Kemeny type jury model, at least, 
because a judge has to be very unlucky to get all of his X>Y preferences 
reversed. So in such a situation, I'd say that's more evidence that 
you're not in a jury model, in which case clone independence neither 
helps nor hurts you.

Though my inuition might be wrong; I'm not entirely sure about the 
relative likelihoods here.

> Secondly, Kristofer justifies the IC criterion as a convenient tool for 
> designing methods which are free from nomination incentive, saying that 
> trying to do so directly is "incredibly messy". However presumably one 
> can *measure* the susceptibility of a method to the nomination incentive 
> (especially if a spatial model is assumed), so this line of thought 
> doesn't justify accepting or rejecting a method on account of its 
> satisfying IC.

Yes, it's more about design than about testing. Testing for nomination 
incentive is harder than testing for clone independence, but perfectly 
doable. (That's what JGA did.)

But I don't know of any theory of how to design a method to specifically 
resist nomination incentive, or any model of incentive that could easily 
guide method design. On the other hand, clone independence is at least a 
simple criterion, so it's easier to figure out in one's head if this or 
that passes or fails.

I agree that this provides no justification to optimize for clone 
independence (something correlated with what we want) rather than lack 
of nomination incentive (what we actually want).

The most intuitive jusitification would probably be something like 
"don't give the opposition anything to use against us". If clone 
independence doesn't itself hinder anything desirable, then picking it 
up would prevent say, FairVote from saying "but you know, IRV is clone 
independent and your method isn't"; even if the proposed method has much 
lower nomination incentive than IRV, it would be preferable to not have 
to deal with the potential for confusion.

All of that hinges on clone independence being "cheap", though.

> Presumably there are other nomination strategies besides 
> nominating (or denominating) clones. JGA has shown that minimax isn't 
> particularly vulnerable to nomination incentives - is it obvious that 
> clone-independent methods are particularly resistant? Or is it possible 
> that clone dependence is simply a form of error which has been 
> identified and taxonomised, but which is not intrinsically more 
> important than any other form or error?

 From what I know, IRV has serious nomination incentive while being 
clone independent, while all the cloneproof Condorcet methods also have 
low nomination incentive (like most serious non-cloneproof Condorcet 
methods). I would *suspect* that DAC and DSC, while being theoretically 
cloneproof, also have nomination incentive, but I don't have proof of this.

So it's definitely possible that the correlation isn't particularly 
strong: that it's the Condorcet rather than the clone independence that 
reduces nomination incentive. In that case, I would guess it goes 
something like... spatial models rarely have huge Condorcet cycles, and 
when the Smith set is small, you get free IIA against anything outside 
it (strategy notwithstanding); so it doesn't particularly matter if 
outside-of-Smith candidates' parties nominate a few or a lot. If that's 
right, then robust clone independence (the thing that's actually 
correlated with nomination incentive) would mostly matter in cases with 
heavily multidimensional politics and large Smith sets.

That's also just a guess, though.

-km