[EM] new working paper: (edit/second thought)

[Kevin Venzke]

Hi Kristofer,

--- En date de : Sam 19.2.11, Kristofer Munsterhjelm <km-elmet at broadpark.no> a écrit :
> However, if the method passes
> LNHarm, then, to quote Woodall's definition, "adding a later
> preference should not harm any candidate already listed". In
> other words, because later ranks can't harm A, both
> A>B>C>D (the honest ballot) and A>C>D>B
> (the maximally burying ballot) has the same effect on
> whether or not A wins, which is the effect that a bare-A
> vote gives. Since you can't rig the field in favor of A by
> rearranging later ranks, and burial tries to get A to win by
> doing just that, LNHarm secures a method against this kind
> of burial.

It sounds like you're attributing too much to LNHarm. It's quite possible
under a LNHarm method for A>B>C>D to elect B and A>C>D>B to elect A. Here
is a DSC example:

49 B
17 A>C>D
3 A>B>C
17 C>D>A
14 D>A>C

B wins. But change the 3 votes to A>C>D and A wins. (If I made no errors.)
 
> The LNHelp-failure type burial seems to be an
> "untruncating" sort of burial. You have a candidate A and
> you want A to be helped as much as possible by later
> candidates, so you add a bunch of them after the A-bullet
> vote. If the method meets LNHarm but not LNHelp, you don't
> fill later ranks to harm B in particular, but to help A.
> Adding B last is just a precaution so that B won't be helped
> in turn by candidates ranked lower than him.

You should ask though how exactly A is being helped by the new preference.
In MMPO and QR a new preference either does nothing, or directly causes
a (even lower) preference to lose, and that is how you're helping A.

In DSC it is a little less "offensive" in appearance (you may actually
help A directly, not just hurt lower candidates).

> I think JGA only used complete ballots, in which case the
> only type of burial that can happen is the one that LNHarm
> secures against. I'm not sure about this, however.

Without truncation the LNHs usually aren't defined, however.

> If a method meets both LNHelp and LNHarm, then there's no
> point at doing any of what we've called burial. 

Yes, I agree.

> Pushing B to
> the bottom won't make A win, and filling stuff after a
> truncated ballot won't make A win either. Yet that pair
> comes at a great price: one can't have all of LNHelp,
> LNHarm, mutual majority, and monotonicity (see http://www.mcdougall.org.uk/VM/ISSUE6/P4.HTM). Since
> Smith implies mutual majority, any Smith-constrained version
> of a method that meets both LNHs will fail to be monotone.

When you do Smith-constraint you already lose the LNHs though. If you
want both LNHs you are basically stuck with FPP and IRV (and IRV variants
like Craig Carey's IFPP).

Kevin