[EM] Smith//3Score (was MAM vs Schulze)

[Michael Ossipoff]

On Oct 10, 2016 8:36 PM, "C.Benham" <cbenham at adam.com.au> wrote:
>>
>> 99: A>B
>> 98: B (sincere is B>C)
>> 100: C
>
>
> Mike,
>
> Don't you mean "(sincere is B>A)" ?
>
> Chris

Yes. Sorry about the typo.

Michael Ossipoff
>
>
>
> On 10/11/2016 3:08 AM, Michael Ossipoff wrote:
>>
>> Yes, the method still allows chicken dilemma defection to succeed.
>>
>> I tried an example in which the B faction is about as large as possible
in comparison to the C faction.
>>
>> 99: A>B
>> 98: B (sincere is B>C)
>> 100: C
>>
>> This results in a cycle, so everyone is in the Smith-set.
>>
>> B has more Borda points than anyone else.
>>
>> It looks as if it isn't possible to have CD in a strategically good,
reliable, uncriticizable.  rank method.
>>
>> ICT isn't good as a ranking method. Only as a 3-slot method in which the
middle rating is used only in Chicken-Dilemma situations.
>>
>> In ICT, a candidate you rank middle doesn't get much protection from you.
>>
>> But, in a chicken dilemma situation you don't expect B to be a CWs
anyway.
>>
>> 3-Slot ICT is still my favorite, to be used as an Approval version
rather than a ranking method, with the middle rating only for chicken
dilemma.
>>
>> Plain MMPO meets Weak CD, FBC, LNHa, and has wv-like strategy.
>>
>> Though it fails CD's strong original version, if the defection is a
burial--The method's wv burial defensive advice would warn the A voters to
not rank B, if A is likely to be CWs.
>>
>> That's a unique, impressive & amazing set of advantages.
>>
>> But there are some strongly-felt criticisms to it. I've answered them,
and it seems to me that only one of them is a genuine problem:
>>
>> ...the possibility of the perpetual burial fiasco.
>>
>> But I've told here why there's something a bit mutually contradictory
about that fiasco's requirements.
>>
>> So I suggest that it doesn't rule out MMPO or MAM, though it makes them
just a little questionable & unreliable.
>>
>> ...but still worth a try because of big advantages.
>>
>> I'd hoped that Bucklin with conditional votes would be a good CD
method.  But it's not as good as I'd hoped, because the conditional votes
option can be strategically taken advantage of, resulting in another
chicken dilemma, differently-caused.
>>
>> I don't know if that rules out the conditional option, but it supports
the conclusion that a CD rank method always costs.
>>
>> Michael Ossipoff
>>
>>
>> On Oct 9, 2016 3:19 PM, "Forest Simmons" <fsimmons at pcc.edu> wrote:
>>>
>>>
>>>
>>> (Continued below)
>>>
>>>>
>>>> Now, how do we adapt this to general rankings? We assume that equal top
>>>> rankings and equal bottom or multiple truncations are allowed.
>>>>
>>>> For each ballot on which a candidate is ranked above bottom but below
top
>>>> that candidate receives one point.  For each ballot on which the
candidate
>>>> is ranked top or equal top that candidate receives two points.
>>>>
>>>> The Smith candidate with the greatest number of points wins.
>>>>
>>>> [End of definition]
>>>>
>>>> Note that the method does satisfy CD unlike Smith//ImplicitApproval.
>>>> Jameson's idea of three slot scores makes it work.
>>>>
>>>> How does it do on burial?
>>>
>>>
>>> Note that for three candidates and complete rankings the method is just
Smith//Borda.  But Smith//Borda is extremely clone dependent.  The three
category (top, middle, bottom) point system is key to making the method
clone proof.
>>>
>>> For public proposal it is important to have a non-cryptic definition of
Smith.
>>>
>>> The smallest set each of whose members pairwise beats every candidate
outside the set is succinct, but probably (by itself) too cryptic for the
non-technical reader.
>>>
>>> I think the idea of a beat-path is very intuitive.  I remember that ten
or fifteen years ago Michael said that he had success explaining Schulze to
various people on the street from the beat-path perspective.
>>>
>>> If A beats B beats C beats D, then that chain of defeats is called a
beat-path from A to D.
>>>
>>> The human brain is adept at generalizing this kind of definition to a
path with more or fewer steps..
>>>
>>> For the purpose of defining the Smith set we don't even need to talk
about the strength of a beat-path.
>>>
>>>   Candidate X is a member of Smith iff for each candidate Y (other than
X itself), there is a beat-path from X to Y.
>>>
>>> In typical public elections we expect Smith to be a cycle of three.  In
that case Smith//3Score is the same as Max Covering 3Score.  In general the
latter is preferable because no matter how large Smith may be it continues
to elect an uncovered candidate.
>>>
>>> For public consumption it is mainly a question of ease of
understanding.
>>>
>>> Which is easier to understand a sequence of successive pairwise defeats
or a covering relation.
>>>
>>> Another way to elect the same candidate when the top cycle has only
three members is to list the candidates by their point totals (highest
total at the top of the list) and starting with the bottom candidate move
up the list replacing pairwise losers with winners.
>>>
>>> In other words the winner will be the highest listed candidate that
beats both the champion from below and every (if any) candidate above it in
the list.
>>>
>>> I would be perfectly happy with any of these proposals, though there is
an obvious soft spot in my heart for the covering version.
>>>
>>> Another reason I like the covering version is that various
strengthenings of the covering relation can be put to good use to refine
this method.  More on that in another post.
>>>
>>> Forest
>>>
>>>
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info
>>>
>>
>>
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