Simmons, Forest wrote:
>1. Exactly how do you define correlation?
My suggestion is this:
The "absolute Borda difference" (ABD) between two candidates on one
ballot is the absolute value of the difference of their Borda scores on
that Ballot.
The "total absolute Borda difference" (TABD) between two candidates is
the sum of their ABDs on all ballots. "Correlation" is the inverse of
the TABD.
(I had intended to send this on Wednesday night, only to find out that
neo.tamu.edu no longer lets me log in as "dbishop". In the meantime, Ken
posted his suggestion. It looks like mine is identical, but simpler.)
Agreed. Thank you for the simplified statement.
Daniel continues:
In this particular example, the Condorcet Winner is elected. However, this is
not always the case.
Again, absolutely true. However, it should come as no surprise that I consider
"failing" CC to be a positive. Failing CC stems from obeying symmetry, which is
a Borda property I tried to maintain.
While your CC failure example is helpful, my favorite is Condorcet's original
critique of Borda:
30:A>B>C
10:B>C>A
10:C>A>B
1:C>B>A
29:B>A>C
1:A>C>B
Condorcet picks A & Borda & CIBR pick B. Here's the explanation (summarized
from Saari): If symmetrical ballots, (which represent ties & should cancel),
are factored out, the election outcome should be unchanged.
The symmetrical ballots in Condorcet's critique are:
10:A>B>C
10:B>C>A
10:C>A>B
and
1:C>B>A
1:B>A>C
1:A>C>B
The reduced profile is then:
20:A>B>C
28:B>A>C
All reasonable methods pick B in this election. Since Condorcet picked A from the
original profile, it is not "symmetry proof."
CIBR is both symmetry & clone proof, which is what is exciting about it.
-Ken
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