[EM] MMPO tiebreakers that don't violate FBC.

[fsimmons at pcc.edu]

Mike,

I like MMPO2 because (unlike MMPO1) it takes into account opposition from
supporters of eliminated candidates, so is more broad based, and it is easily
seen to satisfy the FBC. Also it allows more brad based support than MMPO3 where
only the support by top raters is considered in the tie breaking process.

Forest

Mike Ossipoff wrote ...

>First of all, no one has found an example in which my most recent MMPO tiebreaker
fails FBC.
 
"Solve MMPO's ties by MMPO".
 
I'll call that tiebreaker 1.
 
>Tiebreaker 2:
 
Whenever there's a tie, the winner is the candidate whose next largest pairwise
opposition is the
least. ("next largest" after the pairwise opposition with which s/he is tied
with other
candidates)
 
>Tiebreaker 3:
 
If there is a tie, the winner is the candidate with the most top-ratings.
 
MMPO with tiebreaker 1 is MMPO1
 
MMPO with tiebreaker 2 is MMPO2
 
MMPO with tiebreaker 3 is MMPO3.
 
 
MMPO2 and MMPO3 meet FBC.
 
No one has found an example in which MMPO1 fails FBC.
 
MDDTR meets FBC, CD, and Later-No-Harm (LNHa); and fails Mono-Add-Plump.
 
MMPO2 and MMPO3 meet FBC, CD & LNHa, and Mono-Add-Plump; and "fails" in Kevin's 
MMPO bad-example:
 
9999: A
1:    A=C
1:    B=C
9999: B
 
In this example, MMPO elects C. 
 
MCA, MTA, MDDTR, MDDA, ABucklin and MDD,ABucklin return a tie between A & B.
 
How bad is this result of MMPO's?
 
Notice that nearly all of the A voters are indifferent between B and C. 
And the one A voter who isn't indifferent prefers C to B.
 
Likewise nearly all of the B voters are indifferent between A and C.
And the one B voter who isn't indiffefrent prefers C to A.
 
So how bad can c be? How bad can MMPO's result be?
 
So, the choice between MMPO and MDDTR is a choice between failing
Mono-Add-Plump, vs 
"failing" in kevin's MMPO bad-example. Only polling will tell which "failure" is
more likely to appear bad to potential petition-signers and enaction-voters.
 
When we regard the pairwise comparison between C and A, and the pairwise comparison
between C and B, in isolation, it's easy to forget that we aren't actually
holding those
two pairwise elections. We're used to looking at pairwise contests, because
we're used to
pairwise-count methods. But no one is saying that the one voter who votes C over
A is
more important than the greater number who vote A over c. I suggest that the 
strong pairwise defeats against C look more important than they are, because we're
used to looking at pairwise count methods, with the result that we actually start
believing that there was a a 2-candidate election between A and C, and one
between B and C.
 
As I said, MDDTR and MMPO might be "controversial", because of failure of
Mono-Add-Plump,
or "failure" in Kevin's MMPO bad-example. So, I don't consider them to be the
easiest or
best public proposals. It would be necessary to talk to some people before being
sure 
that they'd be winnable proposals.
 
A 3-slot version of SFC should be written, to tell of the SFC-like guarantee
offered by
MDDTR. (Strictly speaking, SFC can only be passed by full ranking methods.)
 
By the way, when people object to "random-fill incentive" for MDDTR, maybe they're
forgetting that MDDTR is a 3-slot method.
 
And, if MMPO were proposed as a 3-slot method, that would avoid the "random-fill
incentive"
criticism of it too.
 
 
Mike Ossipoff
  		 	   		  

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