[EM] CIBR examples, and its CC failure
Ken Kuhlman
kskuhlman at gmail.com
Fri May 27 11:46:45 PDT 2005
On 5/27/05, Bishop, Daniel J wrote:
>
> 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 <http://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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