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 scale invariant (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]].{{citation needed}}in 2015.<ref>https://groups.google.com/forum/#!--msg/electionscience/BURkyIxZaBM/GdAcH2z7XkEJ</ref> needsIt datewas ofnamed inventionby and[[Forest referenceSimmons]] toin it, e2015.g<ref>http://election-methods. mailing list post 5485.n7.nabble.com/EM-A-graphical-description-of-Toby-Pereira-s-Transformation-of-Range-to-Approval-style-ballots-tp33047p33051.html</ref>

In the whole ballot formulation there is never any farctionalfractional approval ballots. All score ballots are turned into the same number of whole approval ballots. The number of ballots is the same as the maximum score.

==Scale Invariance example for RRV==

Aside[[Reweighted fromRange makingVoting]] approvalis systemsone beexample apleof toa bemethod run on score ballots therethat is anmade interestingscale effectinvariant onby [[Reweightedthe RangeKotze-Pereira Voting]]Transformation. This example will use Jefferson RRV because it's marginally easier to work with, but it's basically the same with any divisors.