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

Mon Oct 10 18:01:53 PDT 2016

```Forest,

Why do you want to give any points at all for middle ratings?

What is wrong with  simply 3-slot  Smith//Top Ratings?

Or 3-slot TTR, Top Ratings (aka ICT)?

Chris Benham

On 10/11/2016 9:22 AM, Forest Simmons 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
>
> 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
>     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
>     <mailto: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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