[EM] Why Clone Independence?

Kristofer Munsterhjelm km_elmet at t-online.de
Tue Jan 24 16:14:14 PST 2023

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.


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