[EM] Why Clone Independence?

[Colin Champion]

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?

[Yet if the rationale behind IC implicitly assumes a spatial model, the 
rationale behind the consistency criterion implicitly assumes a jury 
model, though both are presented as desirable properties of voting 
systems in general.]

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. 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?

CJC




On 25/01/2023 00:14, Kristofer Munsterhjelm wrote:
> On 1/24/23 22:32, Kristofer Munsterhjelm wrote:
>
>> I would say that it's not so much that clone winner is linked to 
>> compromising and clone loser to burial, as that they're linked to 
>> nomination incentive. For instance, with enough candidates in 
>> impartial culture, Ranked Pairs and Schulze are plenty susceptible to 
>> burial, even though they're cloneproof.
>>
>> (Though perhaps there is a more clear relation in say, a spatial 
>> model. I don't know as I haven't checked.)
>
> A thought occurred to me: it might be that the reverse implication is 
> true: that we can't have vote splitting clone failure without 
> compromising incentive, and we can't have teaming without burial 
> incentive.
>
> This seems intuitively right for Plurality and Borda: suppose for 
> Plurality that A loses after being cloned. Then if everybody decides 
> to rank A1>A2>A3, then that will make A1 win again; this is a 
> compromising strategy for the A-voters. Conversely, in Borda, suppose 
> that after cloning A, A1 wins; then in at least some elections, the 
> B>A voters moving every A clone except A1 to equal last should make A 
> lose again, which is a burial strategy. These countermeasures only 
> work if the A voters or the not-A voters (respectively) hold a large 
> enough share of the votes.
>
> But generalizing it to *every* method would be much harder.
>
> And there's the obvious question: if there are implications for 
> vote-splitting and teaming, then what's the implication for crowding? 
> You'd think nonmonotonicity (due to the chaos), but nope - Kemeny has 
> crowding and is monotone.
>
> -km
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