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

[Chris Benham]

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.*

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.

This  "3-slot Strong Minimal Defense, Equal-Ranking First-Preference Plurality 
(Whole)" method is my new clear favourite 3-slot single-winner method.

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

Approval scores:  A45,   B40,  C55
Approval Opp.:    A55,  B35,   C45
Top-ratings score: A45,  B40,   C25.  

C's approval opposition to A is 55, higher than A's approval score of 45, so A is
disqualified.  The undisqualified candidate with the highest top-ratings score is B,
so B wins.  But if we pretend that on each ballot there is an invisible approval
threshold that makes some distinction among the candidates but not among those
with the same rank, then B cannot have an approval score as high a A's.

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 is more Condorcetish and has a less severe later-harm problem than MCA, Bucklin,
or  Cardinal Ratings (aka Range, Average Rating, etc.)

40: A>B
35: B
25: C

Approval scores:    A40,   B75,   C25 
Approval Opp.:      A35,   B25,   C75
Top-ratings scores: A40,   B35,   C25 

They elect B, but SMD,FPP(w) elects the Condorcet winner A.

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.


Chris  Benham

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