# [EM] Correlated Instant Borda Runoff, without Borda

Chris Benham chrisbenham at bigpond.com
Thu Dec 29 18:40:36 PST 2005

```Dan Bishop wrote:

>Months ago, someone proposed a method called "Correlated Instant Borda
>Runoff (CIBR)" in order to fix Borda's clone problem. But only now has
>it occurred to be that CIBR's clone-purging idea might be good for
>things other than improving on Borda.
>
>I've got a couple of examples below, but first I'd like to propose an
>improved defintion of "correlation".
>
>*** DEFINITIONS ***
>
>A candidate C is "voted between" A and B on a ballot if C is voted
>either both strictly higher than A and strictly lower than B, or vice-versa.
>
>The "correlation between X and Y with respect to Z" (where X, Y, and Z
>are candidates), denoted "corr(X, Y) wrt Z" is the proportion of the
>ballots on which Z is NOT voted between X and Y.
>
>The "correlation between D and E", denoted corr(D, E), is defined the
>minimum of corr(D, E) wrt F over all candidates F in the complement of
>{D, E}.
>
>
>
>
>
Dan (and Ken),
In  this way of determining "correlations", do you first symmetrically
complete truncated ballots?
Because if you allow truncation but don't symmetrically complete then it
seems to me that there
would be more frequent  ties for "most correlated pair of candidates".

How do you propose that such ties be broken?

49: A
24: B
27: C>B

For example in this (familiar to EMers) scenario, the AB pair and the CB
pair are tied each with
"100% correlation".

Chris  Benham

>
>
>

```