[EM] Re: Condorcet completed by SC reverse rankings IRV elimination

[Chris Benham]

On Sat. Jan.17,2004  I  posted  this:

I propose and reccomend this single-winner  Condorcet  compliant method:
Plain ranked-ballots, equal preferences and truncation ok.
1: Eliminate all candidates who are not members of the Schwartz set.
2: If  more than one candidate remains, then based on the symetrically 
completed (SC) and reversed rankings,
eliminate the candidate picked by the Alternative Vote (aka IRV).
Repeat steps 1 and 2 until only one candidate (the winner) remains.

I included the statement:
Unlike  WV, this method  meets  Symetric Completion, and  I  believe 
that that allows it to meet my
Decisiveness Fairness Standard.

Since then I have been asked why I like  the Symetric Completion 
Criterion.  Kevin Venzke explained (Thurs.Jan.22,04)
"According to the mentality of Symmetric Completion (criterion), two 
voters voting A=B>C>D should have exactly the
same effect as one of the two voting A>B>C>D and the other voting 
B>A>C>D.....
My interpretation is that a faction shouldn't spoil the election for 
themselves because they opt to express strict preferences
among their favorites, instead of using approval strategy."
I referred to my "Decisiveness Fairness Standard" on  Wed.Jan.21,04:
If the method allows equal early preferences, then it is unfair (and in 
my opinion absurd and very bad) that a faction of voters that all vote a 
set of candidates above all other candidates should be advantaged or 
disadvantaged (at least on average) by voting equal preferences.

An argumentative Mike Ossipoff  claims that he doesn't  understand this 
plain English, so I will explain.
An  "early" preference is a non-last preference (or ranking). A "faction 
of voters" is a set of voters that vote a set of candidates above the 
other candidates. The faction is "advantaged"  if  the probability of 
 the winner coming from the set of candidates they support is increased, 
and  "disadvantaged"  if  it is decreased.
Or  to say  (very nearly) the same thing in another way, if candidates 
 A and B are a clone set, the probabilty that the winner will come from 
this set should be completely unaffected by how the clones are voted in 
relation to each other.
I  like  Symetric Completion  because I  believe  that  a method that 
meets it is at least trying to meet this standard, and I  don't see how
methods that flout it can. Winning Votes flouts SCC and  certainly fails 
DFS.
WV  seems to be based on the assumption that there were separate 
elections, each held on different days with different ballot papers
and with different numbers of voters being able to make it, for each of 
the pairwise comparisons. But as there was only one election,
with all  the same voters being asked to rank the same candidates, I 
don't accept that  there are  "non-majority"  pairwise results (which 
for some reason some people like to call  "defeats")  versus glorious 
super-legitimate "Majority" pairwise results. There are only implicit
majorities versus explicit majorities, and I see  no reason in principle 
to distinguish between them.
The only arguement  IMO of  any merit in favour of   putting up with the 
evil/absurdity  of flouting  SCC/DFS, has been that that is neccessary 
to avoid the strategy problems of  Margins.
But it now seems that my new method does a  better job of resisting 
 strategy than does WV.

Mike  Ossipoff  seems skeptical   (Mon.Jan.26,04):
"Chris, you've found several examples in which SCRRIRVE resists 
offensive order-reversal better than wv does. But with wv,
defensive truncation or defensive equal-ranking can reliably make it 
impossible for offensive order-reversal to succeed. Is that
true of SCRRIRVE?"
Yes,  I  think that can be safely inferred from IRV's  known  quality of 
being  Burying-proof.

MO: "It's for you to show."
 
My  limits are different  from those of  MO  and others on this list. 
That is why we are engaged in this friendly collaboration (in which I 
provide thoughtful creative input  and  MO  helps by telling me I have 
to do everything else).

MO: "In wv, truncation can't steal an election from a CW under 
conditions that
I've described. Is that true of SCRRIRVE?"

This is a better question than I first thought. (CC)SCRRIRVE  seems  to 
do such  a good job of  resisting Burying, and srategic truncation
(especially in a method that meets SCC)  I thought is  just being a 
milder version of the same thing.
The short answer is no. Here is  an example from James Green-Armytage 
(Fri.Jan.16,04). It is the only example I have yet found in which
WV  resists strategy better  than (CC)SCRRIRVE.
http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-January/011681.html
Sincere preferences:
28:A>B>C
27:B>A>C
23:C>A>B
22:C>B>A
100 ballots.  A is the CW.

If  the B voters  Bury A and the other voters vote sincerely, then  B 
wins with both methods.
If  the B voters Bury A  and  the A voters truncate, then C wins with 
both methods.

B voters strategically (offensively) truncate and all the other voters 
vote sincerely:
28:A>B>C
27:B (>A=C)
23:C>A>B
22:C>B>A

A>B>C>A.  WV  Ranked Pairs and Minmax  elect  A,  but  (CC)SCRRIRVE 
 eliminates  A and elects B.
This result surprised me, but  I still think that on balance my method 
performs better. Note that  B is the Borda winner, and  that  B's 
pairwise loss to A was as narrow as possible (so this "loss" to WV was 
very narrow).

Chris Benham