Kotze-Pereira transformation: Difference between revisions
→Notes
(→Notes) |
(→Notes) |
||
Line 104:
== Notes ==
Using the "ranked KP transform" on Score ballots (converting them into Approval ballots which are then converted into ranked ballots, with approved candidates ranked 1st and all others last) and running this through [[Smith-efficient]] [[Condorcet methods]] yields a [[Smith set]] with only the candidates who originally had the most points i.e. the [[Score voting]] winner.
Something similar to the KP transform can be done using randomness: if a voter approves a candidate with a probability proportional to their utility from that candidate, then with probability approaching 1 with many voters, the candidate will have the same [[approval rating]] as they would if every voter had simply scored that candidate.
One way to visualize the KP transform is as follows: imagine that for each voter, 9 additional voters are added to the election, whose ballots are treated as "under the control of" that voter. If the voter decided to make 8 of the 10 ballots under their control approve their favorite candidate, while not doing anything with the remaining 2, then this would be equivalent to them giving that candidate an 8 out of 10 on a rated ballot. Thus, the KP transform helps with [[scale invariance]].
==Further Reading==
| |||