[EM] "Instant Runoff Normalized Ratings" question

[Chris Benham]

Brian,
I am a bit puzzled as to exactly how your IRNR method works.
From part of your site:

Instant Runoff Normalized Ratings
Each ballot is normalized so that all ballots have the same magnitude. 
The modified ballots are summed, and the choice with the lowest 
sumarry rating is disqualified. Each ballot is then normalized again as if 
the disqualified choice was not there, redistributing the vote across the 
choices in proportion to the original ballot. The new modified ballots 
are summed and the process is repeated until there are two choices 
remaining and one choice wins over the other. 
IRNR slide show: PDF (219KB), QuickTime (2.3MB)
 
 
Even after looking up the words "normalize" and "magnitude" in the
dictionary, I don't fully understand the first sentence above.

As an example you give a ballot that allows the voter to score the
candidates on a scale of 10 to -10, filled out thus:

A10,  B6,  C-3,  D-10,  E4

This you then "normalize" to:

A.62,  B.37,  C-.19,  D-.62,  E.25

For what it's worth, these numbers sum to the not-very-round 0.43.

How exactly were these numbers derived from the scores on the 
original ballot?


Chris Benham
Example: one voteTo make things fair,
each vote is
normalized to have
the same magnitude
A B C D E0.62 0.37 -0.19 -0.2 0.25A B C D E0 6 -3 -10 4


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