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

[Michael Ossipoff]

Forrest--

But, when an anti-defection strategy requires a certain percentage to vote
a certain way, then 1 of 2 things is needed: 1) Probabilistic voting by the
subfaction; or 2) organization of voting by neighborhood or by voters'
names.

That complicates voting, and seems to cancel out the advantage of an easily
explained method definition.

A nice thing about plain MMPO is its simple, brief, naturally-motivated
definition, it's Weak CD, & it's wv strategy & FBC.

Michael Ossipoff e
On Oct 10, 2016 3:52 PM, "Forest Simmons" <fsimmons at pcc.edu> wrote:

> AS Chris Benham and Michael Ossipoff pointed out this Smith//3Score
> doesn't disappoint the defecting faction (B) unless the plumping faction
> (C) is fairly close to half of the electorate. It only works when C is
> plumped on at least 43 percent of the ballots.
>
> To make it work for Mike's example below where C is plumped on only 100
> out of 297 ballots, the middle ranks have to count much les than half of
> the equal top ranks.  About 2 percent of the equal top value would do.
>
> So with sincere ballots the point totals are ...
>
> 99+.02(98) = 100.96 for A,
> 98+ .02(99)= 99.98 for B, and
> 100 for C.  In this case A is both the CW and the points winner.
>
> The B faction's defection simultaneously promotes C to the Smith set and
> reduces A's point total to 99, making C (still with 100 points) the method
> winner.
>
> What makes this example hard is that the C faction is just over one third
> of the electorate, and that the A and B subfactions are very close in size.
>
> For a defection attempt to succeed under these conditions the B faction
> would have to possess very precise information.  If the A faction had the
> same information it would be easy for them to make a defensive move in the
> form of truncating B on a few ballots.
>
> In practice, a point value substantially larger than .02 for the middle
> ranks would be adequate.
>
> What would be a reasonable compromise?
>
> How about 1/4 or 25% ?
>
> In that case the A faction could say to the B faction, "You rank me on two
> ballots and I will rank you on seven."
>
> The resulting equilibrium would be
>
> 92 A
>  7 A>B
> 96 B
>  2 B>A
> 100 C
>
> Candidate A is elected as the CW.
>
> If B defects from this equilibrium proposal ...
>
> 92 A
>  7 A>B
> 98 B
> 100 C
>
> then {A, B, C} forms Smith, and C wins with 100 points, while B gets only
>
> 98+7/4 = 99.75 points.
>
>
> If grade style ballots were in use, the A faction could say I will give
> you two B grades in exchange for two D's.
>
> Two B grade points add up to 1.5 which would bring the B candidate up to
> 99.5, still short of the 100 needed to tie the C candidate.
>
> On the other hand, the two D grades for the A candidate would make her the
> Condorcet Winner.
>
> When the plumping faction forms greater than 39 percent of the electorate,
> then no strategy would be needed other than for the larger subfaction to
> give D grades to the potential defection candidate.
>
> 32 A(4), B(1)
> 31 B(4) (Sincere B>0)
> 39 C(4)
>
> If eight or more of the B faction give A a positive rating, then A wins as
> the only member of the Smith set.
>
> If fewer than eight vote sincerely, then C and B are tied with 156 grade
> points each.
>
> So the method I am now proposing is
>
> Smith//GPA
>
> Elect the member of the Smith set with the largest Grade Point Average.
>
>
>
>
>
>
>
> From: Michael Ossipoff
>> 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>A)
>> 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?
>>
>
>
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