[EM] FBC, center squeeze, and CD

Fri Nov 11 09:26:17 PST 2016

I said that a candidate's beat region, in 2D issue-space, with Euclidean
distance, is the circle that just fits between hir and the voter-median
point.

Actually it's the circle that's the locus of points as far from the
voter-median point as the candidate is.

So it's 4 times bigger, but that doesn't change the conclusions, except
that  it makes it that much easier to find a candidate who is
majority-beaten by someone other than the CWs, making it even more unlikely
for any burial-deterrence to be possible.

--------------------------------------------------------------

But I should say that--while MDDTR has full truncation-resistance, just as
I always said that wv has, but doesn't qualify as a good rank method
because of its burial-vulnerability--ICT doesn't have protection against
truncation _or_ burial.

I haven't been advocating ICT as a rank method. I've been advocating it as
a version of Approval, with a middle rating that can be used for
defection-deterrence in the chicken-dilemma example.

MDDTR would be even better for that than ICT would, because, with MDDTR,
when you demote a candidate to middle-rating, s/he still has full
truncation-resistance.

So, though, as a defection deterring Approval-version, 3-Slot ICT is good,
3-slot MDDTR is better.

Michael Ossipoff

On Fri, Nov 11, 2016 at 2:17 AM, Michael Ossipoff <email9648742 at gmail.com>
wrote:

> 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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