[EM] RE: CIBR

[Ken Kuhlman]

First, a reposting for Jobst:
CIBR stands for "Correlated Instant Borda Runoff," and is a tweak of Baldwin 
to solve the clone problem. 

Individual ballots are scored according to the Borda count, and then all 
possible candidate pairs are ranked according to correlation. The Borda 
loser of highest correlated pair is eliminated, and the next round proceeds 
with the remaining candidates. 

Under this method, clones can be seen as a special case of correlated pairs 
(they're perfectly correlated), and so the Borda loser of a clone pair is 
eliminated immediately, before they can spoil the election. 

Now to answer Forest's questions: 
On 5/25/05, Simmons, Forest <simmonfo at up.edu> wrote:
> 
> This looks promising. I like this kind of creativity.
> 
> Three Questions:
> 
> 1. Exactly how do you define correlation?
> 
> 2. Do you re-calculate the correlations after each elimination?
> 
> 3. What about clone triplets, quintuplets, etc.?
> 
> Forest
> 
> 
I have to admit that I struggled with how to define correlation. 
I looked at the standard formulas, and decided that I was either not smart
or patient enough to determine how to apply them to ballots. So for my 
working model, I came up with a custom function that works as follows: 

For each possible candidate pair on each ballot, I calculate the Borda value
of the rank difference between the two candidates to get their "team score". 

For example, if candidate "A" is in position 1 & candidate "C" is in 
position 3,
their rank difference is 2. With 5 candidates, the Borda value of position 2 
is 3,
so that's the "AC" team score for that ballot.

The team scores across all ballots are then summed, and the team with the 
highest score is the most correlated. 

Let's work through a full election involving a clone (BC): 
51:A>B>C
49:B>C>A

This results in the following first round counts: 
Ballots Borda Value Team Points
A B C AB AC BC 
51:A>B>C 102 51 0 102 51 102 
49:B>C>A 0 98 49 49 98 98
------------------- ----------------------
Totals: 102 149 49 151 149 200

BC has the most team points, so the Borda loser between them,
C, is eliminated. 

In the next round, we recalculate the correlations (I think this is 
necessary to compensate for clone triplets & multiples), so the 
tally goes: 

Ballots Borda Value Team Points
A B AB
51:A>B 51 0 51
49:B>A 0 49 49
------------------- --------------
Totals: 51 49 100


Since there's only one team left, it's Borda loser, B, is eliminated 
and A wins the election.

-Ken
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