# [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
> 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.

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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