[Election-Methods] "Strong Minimal Defense"//FPP (Whole), a new 3-slot FBC method

[Chris Benham]

Kevin, Forest, interested participants,

My latest favourite   FBC single-winner method:

"1)Voters submit 3-slot ratings ballot, default 'no rating' interpreted 
as bottom-rating.

2) Eliminate any candidate X  who is above-bottom rated on fewer ballots 
than is some
candidate Y on ballots that bottom-rate X.

3) On ballots that top-rate no candidates, promote middle-rated 
candidates to top- rating.

4) Elect the candidate that is (now) top-rated on the greatest number of 
ballots".

For (at least) the time being, I call this  "Strong Minimal 
Defense//FPP(Whole)".

It meets a new criterion I suggest that I tentatively label "Strong 
Minimal Defense" which states:

"If  X has fewer votes (ranking/rating above bottom or equal-bottom) in 
total than Y has on ballots
that have no votes for X, then X can't win".

It implies both Minimal Defense and the Plurality Criterion.

The method meets the  FBC  (and therefore the similar Sincere 
Favourite). If  X wins, changing some
ballots that top-rate X and not Y to top-rating both cannot cause X to 
be eliminated or  for any candidate
to be un-eliminated except Y. The changed ballots cannot diminish the 
absolute post-eliminations FPP(W)
score of X and can boost the final score of only Y.

The method compares favourably with the other 3-slot FBC methods. MDDA, 
MAMPO,  MCA, ER-Bucklin (W)
all fail the  "Independence from Irrelevant Ballots" (IIB) criterion 
which states that if  there is some losing candidate Y
that only appears (voted above bottom or equal-bottom) on some ballots 
that ignore (vote equal-bottom) all other
candidates (and Y is top rated/ranked on fewer ballots than any other 
candidate)  then removing one/some/all of the
Y-plumping ballots must not change the winner

Adding or removing ballots that ignore all the viable candidates can 
change the winner just by changing the size of the
majority threshold. If  the election is contentious and the votes are 
not necessarily counted with the greatest accuracy
and impartiality, it  seems to me to be a great help if election 
monitors/scrutineers/observers can safely pay little attention
to ballots that make no distinction among viable candidates.

SMD//FPP(w)  meets IIB.

I think it meets Majority for Solid Coalitions (aka Mutual Majority) as 
well as any 3-slot method can, meaning that
if more than half the voters rate a subset S of  candidates above all 
others, then a member of  S must win.

In 3-candidate scenarios it generally gives Schulze(winning votes) like 
results.

49: A
24: B
27: C>B

A eliminates C because C is above-bottom rated on a total of 27 ballots, 
while on ballots that bottom-rate (ignore) C
A is above-bottom rated on 49 ballots.  Likewise B eliminates A so B wins.

46: A>B
44: B>C
10: C

C eliminates A, B wins.

46: A
44: B>C
10: C

Now C eliminates A, A eliminates  B.   (Like Schulze the method fails 
Later-no-Harm)


>40 A>B
>35 A=B
>25 B
>  
>
 From the electowiki  ICA page, giving B as the ICA winner(!?).  

In SMD//FPP(w)  no candidate is eliminated, then A scores 75 versus B's 60.

The method meets mono-raise and fails  Clone-Winner.

I invite comments and am open to suggestions for a more popular name, 
perhaps also for the "Strong Minimal Defense"
criterion/set.

Links re.  MDDA,  MAMPO, ICA  for comparison :

http://wiki.electorama.com/wiki/Majority_Defeat_Disqualification_Approval

http://wiki.electorama.com/wiki/Majority_Approval%2C_Minimum_Pairwise_Opposition 


http://wiki.electorama.com/wiki/Improved_Condorcet_Approval

http://nodesiege.tripod.com/elections/#methica


Chris Benham









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