[EM] Why Clone Independence?
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
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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