Kotze-Pereira transformation: Difference between revisions

The '''Kotze-Pereira transformation''' ('''KP transform''') converts scored ballots into Approval ballots, which allows any Approval PR method to be run on scored ballots. Because the score winner will always have the most approvals after the transformation, a PR method that elects the approval winner in the single-winner case will also elect the score winner in the single-winner case when converted to a score method using the transformation. Score methods using this transformation are also generally scalesatisfy invariant[[Scale invariance]] (multiplying all score by a constant leaves the result unaffected), except when the change in score causes differences in surplus handling due to quotas being met or not met. The transformation was independently invented by Kotze in 2011<ref>{{cite web |url=https://www.revleft.space/vb/threads/143429-Voting-with-ratings?s=f9288911a893930199498f370d9e4825&p=2030744#post2030744 |date=2011-02-23 |access-date=2020-02-10 |title=Voting with ratings|author=Kotze}}</ref> and [[Toby Pereira]] in 2015.<ref>https://groups.google.com/forum/#!msg/electionscience/BURkyIxZaBM/GdAcH2z7XkEJ</ref> It was named by [[Forest Simmons]] in 2015.<ref>http://election-methods.5485.n7.nabble.com/EM-A-graphical-description-of-Toby-Pereira-s-Transformation-of-Range-to-Approval-style-ballots-tp33047p33051.html</ref>

[[Reweighted Range Voting]] is one example of a method that is made scale invariant bywhere the Kotze-Pereira Transformation will provide [[Scale invariance]]. This example will use Jefferson RRV because it's marginally easier to work with, but it's basically the same with any divisors.

Imagine A1, A2, B1, A3 are already elected. The new weighted total approvals for A4 would be 1800 x 1/4 = 450. For B2 it would be 900 x 1/2 = 450. This is the exact tie we want. So scale[[Scale invariance]] is preserved.