[EM] Re: MMPO, Majority, Condorcet failures (Raynaud versions)

[Chris Benham]

  Gervase,
On  Tues.Dec.21 you wrote:

>Monotonicity to me seems to be a very fundamental requirement for ranked 
>election methods.  If I had to choose between Clone Independence and 
>Monotonicity, but not both, then I think I would go for Monotonicity.
>
Why?  I  live in  Australia, where  IRV's  failure of   Mono-raise 
 (lack of  Monotonicity)  goes virtually completely
unnoticed, much less worried about.  Failure of  Clone Independence  on 
the other hand, tends to have obvious
pernicious effects  which begin with the nominations. (There is either a 
split-vote problem, or a Rich Party problem).

Mono-raise has fallen off my list of  "fundamental requirements",  and 
 I now rate it as merely highly desirable.
It is somewhat hard to meet, and the best methods  that meet it  seem to 
be much more vulnerable to  Burying than the
best methods that don't  (as evidenced by a lot of good examples from 
James Green-Armytage).

Your remark was prompted by my  opinion that  Raynaud is  better  than 
MinMax Pairwise Oppostion (MMPO).
MMPO  meets  Mono-raise and  Later-no-harm. Raynaud loses those but 
gains  (Mutual) Majority, Condorcet, and
Clone Independence.  Given that it seems to give similar results in the 
3-candidate, lots of truncating, scenarios that
Kevin Venzke was concerned about, surely that is a great trade!

It seems to me that  three versions of  Raynaud are possible ( one that 
meets Symmetric Completion and two that don't).
The obvious one that does is  Raynaud (Margins).  The other two  could 
be called  Raynaud (Pairwise Opposition),
which eliminates the candidate which loses the pairwise comparison in 
which the winner  has the highest gross score
(explicit winning votes);  and  Raynaud (Gross Loser), which eliminates 
the candidate with the lowest gross score in any
pairwise comparison.

In this example of  Kevin Venzke's:

49: A
24: B
27: C>B

A>C  49-27 (m 22)
C>B  27-24  (m 3)
B>A  51-49  (m 2)

The three versions each give a different winner.  PO eliminates A and 
elects C, failing Plurality.
GL eliminates  B and elects C, failing  Minimal Defense.  Margins 
eliminates C  and elects B.

Douglas Woodall gives this demonstration that Raynaud fails Mono-raise:

7 abc
7 bca
6 cab

"There are no trucated ballots, so the three methods are identical.  I think
c has the most decisive defeat here, by b, and so c is eliminated and a
is elected.  But if you replace two of the bca ballots by abc, then b has
the most decisive defeat, by a, and so b is eliminated and c is elected."


Chris Benham









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