[EM] Smith//3Score (was MAM vs Schulze)
C.Benham
cbenham at adam.com.au
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
> 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
> <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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