[EM] A graphical description of Toby Pereira's Transformation of Range to Approval style ballots

[Forest Simmons]

OK, we can call it the KP (short for Kotze-Pereira) transformation, or
something like that.

On Fri, Dec 18, 2015 at 3:43 AM, Toby Pereira <tdp201b at yahoo.co.uk> wrote:

> I feel compelled to point out that although I independently encountered
> this method to convert score ballots to approval ballots, I wasn't the
> first to do so. After finding it myself, I found this post on a forum
> describing the same thing at an earlier time.
> http://www.revleft.com/vb/showpost.php?p=2030744&postcount=12
>
>
> ------------------------------
> *From:* Forest Simmons <fsimmons at pcc.edu>
> *To:* EM <election-methods at lists.electorama.com>; Jobst Heitzig <
> jobst.heitzig at posteo.de>; Brian Olson <bql at bolson.org>; Andrew Jennings <
> elections at jenningsstory.com>
> *Sent:* Thursday, 17 December 2015, 22:02
> *Subject:* [EM] A graphical description of Toby Pereira's Transformation
> of Range to Approval style ballots
>
> In a previous posting to the EM I promised to explain the Toby Pereira
> transformation of a cardinal ratings (aka "score" or "range") style ballot
> into a weighted sum of approval ballots.
>
> If you think of the ratings displayed graphically like a histogram (or
> vertical bar graph), then for each distinct bar height you make an
> horizontal slice of the bar graph at that height just grazing the tops of
> the bars at that height.
>
> The part of the bar graph between two consecutive slices will itself be a
> bar graph in its own right with all of its bars equal in height.  Divide by
> that common height h and you get a bar graph whose bars are all unit
> height, i.e. a bar graph of an approval vector.
>
> The weight of that approval vector is none other than the original height
> that we divided by.  If we add the approval vectors multiplied by their
> weights, we get back the original range/score vector, (assuming the
> original min score to be zero).
>
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