[EM] FBC, center squeeze, and CD

Thu Nov 10 23:17:25 PST 2016

Uh-oh...

When I first proposed wv, and when I've evaluated pairwise-count methods'
properties for protection from truncation, I always looked only at
3-candidate examples.  By that, wv, MMPO, & MDDTR looked pretty good in
that regard.
wv-like strategy.

Well, they still meet SFC, and are fully resistant to truncation. That's
the good news...

But, when looked at in 2D issue-space (with Euclidean distances), and a
voter-distribution that is uniform or the same in every direction from the
all-dimensions median...MDDTR is completely vulnerable and un-defendable
from burial.

I haven't looked at 1D. I looked at 2D. Maybe, in 1D, it will turn out to
not have that problem. But if the method has a problem in one
dimensionality, I guess one would expect it in all dimensionalities.

Maybe the problem doesn't happen with city-block distance, but I guess the
likely presumption is that it does.

SFC is a very good thing, and its premises are well-met, by the assumptions
I used. But the burial vulnerability spoils MDDTR, at least in 2D.

I have no idea whether wv, which I began proposing in the late '80s, has
the same thoroughgoing vulnerability to burial. I no longer propose
wv--except that I like MAM for CIVS polls, where the burial problem isn't a
problem, because there evidently is no offensive strategy used at CIVS.

In 2D, with the voter-distribution assumptions I described, the CWs has a
preference majority over everyone, and, with sincere voting majority
pair-beats everyone.

Of course burial could make someone beat hir. The closer to the
voter-median point a candidate is, the fewer burriers are needed to make
that candidate majority-beat the CWs.

In MDDTR, if you can make someone majority-beat the CWs, then everyone is
majority-beaten, and so no one is disqualified. Then, if your candidate is
the most favorite, & your burial is successful.

...unless the candidate you're burying the CWs with isn't majority-beaten
by someone else, other than the CWs..

By the assumptions that I described, a candidate  has a "beat-region", such
that a candidate in that region of issue-space will majority-beat hir.

The closer the candidate is to the voter-median point, the smaller hir
beat-region is.

It consists of the circle that just fits between the candidate and the
median.

I guess maybe in 3-space it would be a sphere.

If you want to bury the CWs in MDDTR, just bury hir under a candidate who
has 1 or more candidates in hir beat-region.

There's no way to defend against that if your wing has a number of such
candidates and you don't know which one will be used for the burial of the
CWs.

Of course maybe you just havve 0 or 1 such candidate, and then there isn't
a problem. But, in general there is. At least in 2D.

It seems likely that wv has the same problem, because the burial deterrence
depends on a threat to keep the candidate used in the burial from being
beaten. That's easy in the 3-candidate example: Just don't rank the
buriers' candidate. It's nothing like that in 2D issue-space with
continuously-distributed voters.

There's an enouraging fact: The larger beat-regions belong to candidates
farther from the voter-median point, where it takes more buriers to make
the candidate majority-beat the CWs. But the distance only varies with the
square-root of the size of the beat-region.

But these mitigations that I've mentioned don't seem enough to justify a
pairwise-count method.

I guess Bucklin is the only rank method that can be recommended..

Michael Ossipoff

On Thu, Nov 10, 2016 at 11:26 AM, Michael Ossipoff <email9648742 at gmail.com>
wrote:

> 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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