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

Forest Simmons fsimmons at pcc.edu
Mon Oct 10 15:52:22 PDT 2016

```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

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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