[EM] MinMax Losing Votes (equal-ranking whole) Margins

[C.Benham]

My enthusiasm for this method has increased, so I thought I'd add a few 
more examples.

46 A>B
44 B>C (sincere is B or B>A)
05 C>A
05 C>B

This is similar to an earlier example, but here the supporters of the 
candidate being targeted by the buriers (A)
are all voting B above C instead of truncating.  It still elects A.

A>B 51-49,  B>C  90-10,  C>A 54-46.   MinMax (Losing Votes) scores: 
B49,  A46,  C10.

The directions of the defeats and the MMLV scores are all unchanged, so 
neither is the winner.

(Winning Votes and Margins both elect the buriers' candidate B. The 
scenario was brought up a few years ago by
James Green-Armytage as a prime example where such Condorcet methods are 
more vulnerable to strategy than
IRV.)

46 A>C
10 B>A
10 B>C
34 C=B

B>A>C>B.

(Interpreting "strictly ranked below no other candidate" as Top Rating)

Top Ratings: B54 > A46 > C34.

I hope we can agree that if any candidates are top-rated on more than 
half the ballots then one of them should win.
Not doing so would be a failure of Forest's  Stable Approval Potential 
Criterion.  Electing A here would be a failure of
Steve Eppley's Non-Drastic Defense criterion, that says that if on more 
than half the ballots X is voted both above Y
and below no other candidate (i.e. no lower than equal-top) then Y must 
not win.

The point is that MinMax Losing Votes Margins  (where ballots that vote 
any X and Y equal and above bottom either
have no effect on the X -Y pairwise tallies, just like ballots that 
truncate them both, or contribute a half-vote to each)
elects A (just like ordinary Margins).

But the MinMax LosingVotes (equal-ranking whole) Margins method I'm 
proposing easily elects B.

C>B 80-54 (with the 34 C=B ballots giving a whole vote to both 
sides),    B>A 54-46,     A>C 56-44.

MMLV(erw) scores:  B54 > A46 > C44.     Margins Sort gives the order B>A>C.

C>B (44-54 = -10)     B>A (54-46 = 8)      A>C  (46-44 = 8)    B's 
pairwise defeat is the weakest (lowest defeat score) and so B wins.

35 A
10 A=B
30 B>C
25 C

A>B>C>A.     MMLV(erw) scores:  A45 > B40 > C25 Margins Sort elects A.

C>A -20,    A>B 5,   B>C 15.     A has by far the weakest defeat and so 
wins.

I don't like that both Winning Votes and ordinary Margins both elect B, 
who is pairwise beaten and positionally dominated
by A (i.e. A is both more approved and more top-rated) and is also the 
least approved candidate.

34 A>B
17 C>A
16 B>C
31 B
02 B>C  (sincere is B or B>A)

A is the sincere Condorcet winner (and a sincere Mutual Dominant Third 
winner).

A>B>C>A.    MMLV(erw)  scores:  B49 > A34 > C17. The margin between 
adjacent candidates B and A (15)  is smaller than
that between A and C (17), and A pairwise beats B, so Margins Sort first 
flips that order to give A>B>C with no candidate pairwise
beating the next highest in the order, and so elects the candidate 
highest in this final order, A.

C>A -17,   A>B -15,   B>C +32.      A has the weakest defeat and so wins.

It looks to me  like MMLV(erw)M  meets  Unburiable Mutual Dominant Third!

(If that is the case, then I was too pessimistic in answering a question 
from Kristofer about the mutual compatibility of UMDT,
Condorcet and Mono-raise.)

25 A>B
26 B>C
23 C>A
26 C

C>A>B>C.   (Approvals: C75 > B51 > A48.   Top Ratings: C49 > B26 > 
A25)    MMLV(erw) scores: C49 > B26 > A25.  Margins Sort settles on C>A>B.

B>C -23,    C>A +24,  A>B -1.  C's defeat is by far the weakest.

I like that MMLV(erw)M  elects the prettyist and strongest-looking 
candidate, C.   Benham/Woodall  (like IRV) and Winning Votes all elect B.

Thanks for taking an interest.

Chris  Benham













On 4/26/2014 4:10 AM, C.Benham wrote:
> This is my new idea for a Condorcet method that meets Mono-raise and 
> Chicken Dilemma and is relatively resistant
> to Burial strategy.
>
> *Voters rank from the top however many candidates they wish Truncation 
> and equal-ranking is allowed.
>
> A pairwise matrix is created, giving normal gross scores except that 
> ballots that explicitly equal rank (not truncate) any two
> candidates X and Y give a whole vote to each in that pairwise contest.
>
> Using this information, give each alternative a score that equals the 
> smallest number of votes it received in a pairwise loss.
>
> Henceforth we are only concerned with the direction of the pairwise 
> defeats and these individual candidate scores.
>
> Use the Schulze algorithm, weighing each pairwise "defeat" by the 
> absolute margin of difference between the two candidates'
> scores.  (Or use Ranked Pairs or River in the same way if you prefer).
>
> Or use the candidate scores for the Margins Sort algorithm.*
>
> This method uses the same type of pairwise matrix as a  Schulze 
> (Losing Votes) variant I suggested earlier. I think this is much
> better.
>
> 46 A
> 44 B>C (sincere is B or B>A)
> 05 C>A
> 05 C>B
>
> A>B 51-49,  B>C  44-10,  C>A 54-46.   MinMax (Losing Votes) scores: 
> B49,  A46,  C10.
>
> The method I suggested earlier elects the buriers' candidate B, but my 
> new method elects A (the "sincere CW").
>
> The Margins Sort version begins with the MM(LV) order B>A>C, then 
> notices that the two adjacent candidates with the two most
> similar scores are B and A and that A pairwise beats B, so flips that 
> order and then considers A>B>C and then sees that there for each
> pair of adjacent candidates, the one higher in the order pairwise 
> beats the one lower in the order and so is content and elects the now
> highest-ordered candidate.
>
> The other versions look at the pairwise results weighted thus:  A > B 
> (46-49 = -3)   B>C (49-10 = 39)   C>A (10-46 = -36).
>
> A's pairwise defeat score (negative 36) is by far the lowest so A wins.
>
> Chris Benham
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