[EM] FBC, center squeeze, and CD

[Michael Ossipoff]

Regarding the statement about burial deterrence,  the majority preferring
the CWs to the buriers' candidate can of course, being a majority, ensure
that some candidate of their choice doesn't have a majority pairwise vote
against hir, because such a majority is impossible if a majority of the
voters decline to be part of it.

So the buriers' candidate has a majority against hir because, by
assumption, those preferring the CWs to hir vote the CWs over hir.  And
there's a candidate whom the buriers like less thaln the CWs who _doesn't_
have a majority pairwise vote against hir.

So the burial is thwarted & penalized.

Michael Ossipoff


On Thu, Nov 10, 2016 at 9:15 AM, Michael Ossipoff <email9648742 at gmail.com>
wrote:

> Well, by the definition of a CWs, the CWs is preferred to each other
> candidate by more people than vice-versa, and that doesn't depend on how
> many dimensions there are.
>
> With n dimensions, of course the dimensions might not all share a common
> median for the distribution, but, for the purpose of wv-like properties, I
> assume that they do, and that there's always a CWs.
>
> But if the voters are uniformly-distributed, or if they're continuously,
> symmetrically distributed about that common median (I assusme that at least
> one of those is so) then, not only is the CWs preferred to each of other
> candidates by more voters than vice-versa, but s/he also has a pairwise
> preference-majority over each of the other candidates.
>
> When I say "the median", I mean the common distribution-median for all of
> the dimensions.
>
> Regarding the line that connects the median to a candidate who is away
> from the median, and regarding the plane that perpendicularly bisects that
> line, a majority of the points in the distribution are on the median side
> of that plane.
>
> I suggest that the n-dimensional generalization of a "wing" is the set of
> candidates on one side of a plane that includes the median.
>
> Of course, because the CWs has a pairwise preference majority over each of
> the other candidates, no candidate can have a preference majority over the
> CWs.
>
> As I was saying, for the purpose of defining wv-like strategy properties,
> I stipulate that only one wing stratgegizes, and the other wing votes
> sincerely.
>
> So, by these assumptions, with wv, or MMPO, or MDDTR, truncation from one
> side can't take the win from the CWs, because the truncators' candidate has
> a voted majority against him (The CWs is voted over hir by a majority), and
> the CWs doesn't have a majority against hir (because no candidate has a
> pairwise preference majority against hir, and no one is burying).
>
> And if some candidate's preferrers bury against the CWs, making a voted
> pairwise majority against hir, and if all the people preferring the CWs to
> the buriers' candidate (those people are a majority, for the reason that I
> stated)
> decline to vote the buriers' candidate over anyone, then the burier's
> candidate can't hava a majoriity over anyone, including the candidate
> they've insincerely ranked over the CWs.
>
> So the wv's, MMPO's & MDDTR's automatic protection against truncation, and
> their deterrence of burial, apply regardless of the dimensionality.
>
> Michael Ossipoff
>
>
>
>
>
> On Wed, Nov 9, 2016 at 10:57 PM, Michael Ossipoff <email9648742 at gmail.com>
> wrote:
>
>> (Replying farther down)
>>
>> On Wed, Nov 9, 2016 at 10:07 PM, C.Benham <cbenham at adam.com.au> wrote:
>>
>>> On 11/10/2016 11:48 AM, Michael Ossipoff wrote:
>>>
>>> But that doesn't change the fact that all of my examples of wv's CWs
>>> "protection" guarantees had the CWs preferred from both sides, and
>>> supported from one wing, the wing opposite the truncating or burying wing.
>>>
>>> That's the "wv-like strategy" that I've been referring to.
>>>
>>> ...even though wv has an additional anti-burial guarantee, or even
>>> though its anti-burial guarantee is stronger and more general.
>>>
>>>
>>> Mike,
>>>
>>> I'm not completely clear on the exact definition of this
>>> property/criterion that you think is worth giving up compliance with
>>> Mono-add-Plump
>>> and Plurality to have.
>>>
>>> Good question. When I previously said what I meant by "wv-like
>> strategy", I assumed that no one is indifferent between the CWs and any
>> other candidate.
>> ...which means that the CWs has _lots_ of support from the preferrers of
>> other candidates.
>>
>> In fact, I assumed, without explicitly saying so, that voters &
>> candidates were on a 1D spectrum, with 2 "wings" (sets of voters separated
>> by the CWs), and that the truncation (innocent or strategic) or burial all
>> came from one wing, so that one wing all unanimously ranked the CWs over
>> the other wing's candidates.
>>
>> So the CWs has a preference majority against everyone, and has a voted
>> pairwise majority against all of the candidates of the strategizing wing.
>>
>> I don't know how well that holds up with more dimensions, with Euclidean
>> or city block distance.
>>
>> Maybe the mathematicians can help with that. Forest?
>>
>> In the meantime, maybe I should just say that "wv-like strategy" is only
>> defined for 1D, with the above-stated assumptions as stipulations.
>>
>>
>>
>>> Yes, in the standard chicken-dilemma example, MDDTR elects A, and that's
>>> a violation of the Plurality Criterion. Try to forgive MDDTR for electing
>>> the most favorite-popular candidate who isn't majority-beaten  :^)
>>>
>>>
>>> I'm afraid I find the justification "most favorite-popular candidate who
>>> isn't majority-beaten" to be quite oblique and arbitrary-sounding.
>>>
>>
>> Majority is a familiar notion. Losing to another candidate by a majority
>> is a reasonable enough grounds for disqualification, if not everyone is.
>>
>> Among the non-disqualified candidates, choosing the most favorite one
>> sounds too natural to be called "arbitrary".
>>
>> And the rule to elect the most favorite candidate who doesn't have
>> someone else ranked over hir by a majority has uniquely many of the best
>> properties. ...practical properties that make voting easier & make
>> sincerity safer.
>>
>>
>>
>>>
>>> "Majority-beaten" can go away if we add a few ballots that just plump
>>> for nobody, so big deal.
>>>
>>
>> Fine. So then I recommend that, in an MDDT election: If your candidate is
>> particularly in danger of majority-disqualification, you should recruit as
>> many voters as possible to plump for no one.
>>
>> ...or wait...Better yet, tell them to rank the candidates you like (and
>> suggest that they should like too) over the ones you don't like.
>>
>> But, whatever you do, get the vote out. Giving an incentive to get
>> everyone to vote--Is that a bad thing? We'd have a big turnout.
>>
>> And then, when one of those people shows up to vote, are they just going
>> to say to to themselves, "He said that it would be in my best interest to
>> come here & plump for no one."? Would that be in their best interest? Or
>> might they realize that, having come to the polling place, it might be even
>> better to preferentially rank the candidates whom they like more.
>>
>> So, by all means, get the vote out.
>>
>> Michael Ossipoff
>>
>>
>>
>>
>>>
>>>
>>
>
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