[EM] FBC, center squeeze, and CD

[Michael Ossipoff]

I guess that MAM & Beatpath _do_ have the anti-burial counterstrategy of
refusal to rank a likely buriers' candidate over anyone.

In MAM & Beatpath, the buriers' candidate has to beat someone who beats the
CWS, becauses the CWs beats the burier's candidate, and they can't prevent
that.

A majority prefer the CWs to the buriers' candidate, and, being a majority,
they have the power to ensure that the buriers' candidate doesn't beat
anyone--just by refusing to rank hir over anyone.

That _does_ work in MAM & Beatpath, but it doesn't work in MDDTR, because,
in MDDTR, all that's necessary is for successful burial is that _someone_
majoriity-beat the candidate who majoriity-beats the CWs.

(..along with the requirement that the buriers' candidate be the most
top-voted,requiring that s/he occupies a relatively empty region of
issue-space.)

So it;s definitely not correct to say that MDDTR has wv-like strategy,
because, though MDDTR is truncation-proof, it doesn't share the
strategic-truncation anti-burial counterstrategy of MAM & Beatpath.

So then the question is:

Is there a method that meets FBC & CD, and really has wv-like strategy?

Michael Ossipoff



On Fri, Nov 11, 2016 at 12:26 PM, Michael Ossipoff <email9648742 at gmail.com>
wrote:

> 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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