[EM] CIBR examples, and its CC failure

[Ken Kuhlman]

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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