[EM] Re: Reversed rankings, symetrically completed

[Chris Benham]

Mike,
On the subject of this method I suggested,

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.

you asked me (Sun.Jan.18,2004):
"In step 2, the rankings are reversed, and then IRV applied to them, and then 
the IRV winner eliminated, right?"

Yes.

"But what is meant by symetrically completed?"

Quoting Woodall (in the context of equal preferences not being allowed except for truncation),

"Symetric Completion.
A truncated ballot should be treated in the same way as its symetric completion. (The symetric 
completion of a ballot is obtained by replacing it by all possible completions of it with 
equal weight chosen so that the total weight is 1. For example,if there are five candidates 
a,b,c,d,e, then the symetric completion of a ballot marked ab consists of six ballots, each 
with weight 1/6, marked abcde, abced, abdce, abdec,abecd, and abedc.)"

In effect what I mean is that equal preferences should be split into equal fractions that sum
to 1, and that truncated ballots should be counted as if the unranked candidates were explicitly
ranked equal last.

Chris Benham