[EM] 3-slot SMD,ER-FPP(w)

[Kevin Venzke]

Hi Chris,

--- En date de : Dim 19.10.08, Chris Benham <cbenhamau at yahoo.com.au> a écrit :
> I have an idea for a new 3-slot voting method:
> 
> *Voters fill out 3-slot ratings ballots, default rating is
> bottom-most
> (indicating least preferred and not approved).
> 
> Interpreting top and middle rating as approval, disqualify
> all candidates
> with an approval score lower than their approval-opposition
> (AO) score.
> (X's  AO score is the approval score of the most
> approved candidate on
> ballots that don't approve X).
> 
> Elect the undisqualified candidate with the highest
> top-ratings score.*

Interesting method, but I'm concerned that rating a candidate in the 
middle can disqualify other candidates, but can't help this candidate 
win, except by preventing him from being disqualified himself. It seems
like a burial risk.

With two major factions supporting A and B, and a third candidate C,
if A faction buries B under C, I believe A will often win. Does B faction
have a defensive strategy that isn't the same as the offensive strategy?
I don't think they do.

Actually, this method isn't that far from MDD,FPP.

> This clearly meets Favourite Betrayal, Participation,
> mono-raise, mono-append,
> 3-slot Majority for Solid Coalitions, "Strong Minimal
> Denfense" (and so Minimal
> Defense and  Woodall's Plurality criterion),
> Independence of  Irrelevant Ballots.

I don't think it satisfies Participation, because your favorite candidate
could be winning, and when your vote is added, you add sufficient
approval to your compromise choice that they are no longer disqualified,
and are able to win instead of your favorite.

> One small technical disadvantage it has compared to
> Majority Choice Approval (MCA)
> and  ER-Bucklin(Whole) and maybe Kevin Venzke's ICA
> method is that it fails
> what I've been calling "Possible Approval
> Winner" (PAW).
> 
> 35: A
> 10: A=B
> 30: B>C
> 25: C
 
> This example is from Kevin Venzke, which he gave to show
> that Schulze (also) elects
> B and so fails this criterion.  It doesn't bother me
> very much. MCA and  Bucklin elect C.

It's an interesting question I think... Having some potential to be the
Approval winner seems like quite a reasonable criterion. It's hard for
me to explain why it can make sense to fail it.

> It seems a bit less vulnerable to Burial strategy than
> Schulze.
> 
> 46: A>B
> 44: B>C  (sincere is B>A)
> 05: C>A
> 05: C>B
> 
> Approval scores:    A51,   B95,   C54 
> Approval Opp.:      A49,   B05,   C46
> Top-ratings scores: A46,   B44,   C10.  
> 
> In this admittedly not very realistic scenario, no
> candidate is disqualified and so A
> wins. Schulze elects the buriers' favourite B.

Well, I would measure burial by starting with a scenario where burial 
*succeeds*, and then see how slightly the scenario can be changed in order 
to make the burial backfire. Even though the burial succeeds here under
Schulze, the strategy seems much more dangerous under Schulze because
the false "C" preference seems to have much more potential to make C win.

Kevin Venzke

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