[EM] CD & truncation-resistance. Definitions people like.

[C.Benham]

43: A
03: A>B
44: B>C  (sincere is B or B>A)
10: C

C>A  54-46,    A>B  46-44,   B>C 47-10.

Here A is the sincere CW and supported by the largest of the three 
factions of voters, but Winning Votes rewards the buriers by electing B.

Benham and  LV(erw)SME   easily elect  A.    Smith//Approval (equivalent 
here to Max Covered Approval) and Approval Sorted Margins elect C.


On 10/14/2016 1:08 AM, Michael Ossipoff wrote:

> 1. Typically that CWs is a middle CWs, as in your example.

C: (By "CWs" Mike means 'sincere CW').  No, in my example A  could be a 
wing candidate.  Say A is Centre-Left,  B is Centre-Right and  C is
(to use a Kevin Venzke expression) a "Martian" candidate, perhaps Far 
Right.  C should be irrelevant and would be without the B supporters'
burying.

> So the B voters in your example dislike C more than the A voters do.
>
> A C victory will be worse for the B voters than for the A voters.
>
> So the A voters have a more credible threat.
>
C:  No.

> The A voters could say to the B voters:
>
> "Ok, let's get this straight: You're going to bury our candidate, and 
> you think we should show our gratitude by supporting your candidate in 
> 2nd place  ".
>

C: This assumes that the B faction gave notice of their intention to 
bury A (and didn't all just blindly copy their candidates' "how-to-vote 
card" that they saw
for the first time just before they voted.)

Also it assumes that for all (or nearly all) the A voters the B 
faction's voting strategy is the most important issue in the election. 
But in any case in the example
only 6% of the A voters failed to truncate, and that was sufficient to 
allow the B factions' burial to succeed under Winning Votes (and MMPO).

> What happens when there's a CWs is more important than how a natural 
> top cycle is solved.

C: In the 3-candidate (and so 3 factions) scenario, I think we can 
meaningfully distinguish between a "sincere CW" that in order to be the 
actual voted
CW has to rely on rival factions not merely truncating, and one that 
only needs rival factions to not actively bury (order-reverse or vote an 
insincere preference).

I don't much care about the former (weaker) type, and in any case I 
think they are hopeless cause.  Resolving a "natural top cycle" properly 
is more important
than trying to save them (or to "deter" big bad "offensive truncators").

On the other hand the largest-of-three factions definitely shouldn't be 
vulnerable to burial because only 94% of them truncated!

Chris Benham


>
> Hi Chris--
>
> (Replying farther down)
>
> On Oct 11, 2016 10:55 PM, "C.Benham" <cbenham at adam.com.au 
> <mailto:cbenham at adam.com.au>> wrote:
> >
> > On 10/12/2016 12:12 PM, Michael Ossipoff wrote:
> >
> >> Regarding the CD example, Chris suggested scenarios in which one of 
> the other candidates, not A, is the CWs.
> >
> >
> > 33: A>B
> > 32: B (sincere may be B>A)
> > 34: C
> >
> >
> > Mike,
> >
> > I don't recall doing that exactly.   I like compliance with CD.   
> The example I posted recently:
> >
> >> Given that burial vulnerability is unavoidable in Condorcet 
> methods, I think that is more democratic if  (in this respect) larger 
> factions
> >> have the advantage over smaller factions.
> >>
> >> 43: A
> >> 03: A>B
> >> 44: B>C  (sincere is B or B>A)
> >> 10: C
> >>
> >> C>A  54-46,    A>B  46-44,   B>C 47-10.
> >>
> >> Here A is the sincere CW and supported by the largest of the three 
> factions of voters, but Winning Votes rewards the buriers by electing B.
> >>
> >> Benham and  LV(erw)SME   easily elect  A. Smith//Approval elects C.
> >
> >
> > The  "WV strategy" enthusiast might chastise the 3 A>B voters for 
> allowing the B supporters' burial to succeed by not truncating...
>
> (endquote)
>
> Yes. If you believe your favorite is CWs, you can protect hir win by 
> defensive plumping.  ...or at least not ranking someone whose voters 
> might bury.
>
> You wrote:
>
> but if they'd
> > done that then WV would have elected their least-preferred candidate.
>
> (endquote)
>
> Yes, if the B voters bury, then for the A voters, truncation will  
> only worsen their result.
>
> But such non-risk-free punitive defensive strategies are common 
> throughout the animal kingdom, including in human affairs.
>
> 1. Typically that CWs is a middle CWs, as in your example.
>
> So the B voters in your example dislike C more than the A voters do.
>
> A C victory will be worse for the B voters than for the A voters.
>
> So the A voters have a more credible threat.
>
> 2. In such situations, the defender has a more credible threat.
>
> The A voters could say to the B voters:
>
> "Ok, let's get this straight: You're going to bury our candidate, and 
> you think we should show our gratitude by supporting your candidate in 
> 2nd place :^) ".
>
> But, sure, there's at least the hypothetical possibility of the 
> perpetual burial fiasco, if A is in the B voters' bottom set.
>
> But I've told why that fiasco's requirements are a bit mutually 
> contradictory.
>
> Even if A is  in the B voters' bottom-set, the B voters might not 
> bother to  bury (even if it's theoretically optimal), if the chance of 
> success is sufficiently small.
>
> I'm not saying that the majority are always right, but wv is popular.
>
> Benham & Woodall don't reliability have wv strategy.
>
> In Bucklin & Approval, the CWs's voters can protect hir by plumping. 
> Likewise methods with wv strategy.
>
> Voters will do what it takes to protect a perceived CWs, because 
> that's the best they can get.
>
> What happens when there's a CWs is more important than hkw a natural 
> top cycle is solved.
>
> Michael Ossipoff
>
> >
> > The tops-of-the-ballots oriented Benham and  LV(erw)SME handle the 
> scenario by (effectively) laughing off C (and electing A in breach of
> > Minimal Defense), while the more bottoms-of-the-ballots oriented  
> Smith//Approval notes that C is the most "approved" (i.e. voted above
> > bottom) candidate and says to the 44 B>C voters "since you voted for 
> C you can have C".
> >
> >
> >> Chris recently mentioned an incompatibility between CD & Minimal 
> Defense (Eppley's votes-only version of SDSC or WDSC).
> >
> >
> > C: Certainly we can't have all three of  Plurality, CD and Minimal 
> Defense.
> >
> >
> >> When discussing Margins Sorted Approval, I objected that it 
> penalizes truncation instead of electing the CWs
> >
> >
> > C: MSA isn't one of my very favourite Condorcet methods, but I 
> prefer it to Winning Votes.  In the example it elects C.
> >
> > Chris Benham
> >
> >
>

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20161014/f6ffeae5/attachment-0001.htm>