[EM] Cardinal Pairwise fails SFC.

MIKE OSSIPOFF nkklrp at hotmail.com
Mon May 2 21:44:38 PDT 2005


When you posted that Cardinal Pairwise meets SFC, I took your word for it, 
because I didn't know exactly the definition of Cardinal Pairwise. I still 
don't know that definition for sure, but this posting's claim is based on 
this guess:

Cardinal Pairwise:

Same as wv, except that, if every candidate has a pairwise defeat, then, for 
any particular voter and for any two particular candidates, that voter's 
pairwise vote for one of those candidates over the other is weighted 
according to the difference between that voter's points-assignments to those 
two candidates.

[end of guessed Cardinal-Pairwise definition]

An example:

Four candidates, A, B, C, D. Point ratings from 0 to 100.

Preferences of voters numbered in left margin:

28: CBAD
27: BCAD
23: ADBC
22: D

B is the CW.


28: C100, B99, A99
27: B100, C100, A100
23: A100  (truncated ballot)
22: D100

A wins in Cardinal Pairwise.

The 55 B voters and C voters are a majority. They prefer B to A, and vote 
No one falsifies a preference. A wins. Cardinal Pairwise fails SFC.

And no, this isn't just failure by technicality. In Cardinal Pairwise, those 
{B,C} voters need to know what rating strategy to use, to get their best 
result. SFC-complying methods, under these plausible conditions, don't 
require them to do other than rank sincerely.

Of course some don't recognize or accept SFC, presumably because some don't 
think that it's desirable to not need to do other than rank sincerely, when 
that freedom from strategy need can be guaranteed.

But whether you recognize SFS or not, you've benefited from it in EM polls. 
EM polls and other Internet wv polls, such as the ones at masquilier.org  
That's because truncation commonly happens in polls. Sometimes a lot of 
truncation, in some EM polls. That hasn't caused a circular tie, but it 
could have. You couldn't have known that it wouldn't. Because of the unique 
stability of SFC-complying methods, you had the assurance that even if 
truncation caused a circular tie, it wouldn't cause the kinds of failures 
that noncomplying methods such as Margins and Cardinal Pairwise can cause 
under conditions such as in the above example.

Some Rankings-Approval hybrids meet WDSC. Some weakly meet SDSC. I don't 
know of any that meet SFC. For instance DMC fails SFC. A method meets a 
criterion weakly, in regards to balloting modes, if it meets that criterion, 
but wouldn't meet it if "Votes X over Y" were replaced with "Votes X over Y 
with respect to every balloting mode used by that method".

The Rankings-Approval hybrids that meet WDSC would at least weakly meet SDSC 
if they had AERLO.

SFC and GSFC are the pinnacle of the promise of rank methods. If you propose 
or use a rank method, why use less than the best? Why propose or use one 
that doesn't deliver on rank-balloting's promise?

Of course Bucklin requires less handcount labor than wv, when there are many 
candidates. But that doesn't mean that a handcount of Bucklin or IRV is 
necessarily faster than a handcount of wv: The wv handcount is faster than 
the IRV and Bucklin counts if separate count-teams are assigned to the 
pairwise comparisons. Faster handcount, but still a more expensive one, in 
terms of person-hours of labor.

If no count computer were available, and ballots had to be counted by hand, 
and if count labor expense were critical, then Bucklin coud be the best 
feasible method.

Bucklin meets SDSC, but not SFC.

Mike Ossipoff

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