Kotze-Pereira transformation: Difference between revisions
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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]]. |
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]]. |
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The KP transform often improves or at least doesn't worsen a voting method that it is applied to, but this isn't always the case. For example, [[SMV]] depends on being able to spend an entire ballot even if it didn't give full support to the winner. |
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The connection that the KP transform shows between Approval and Score ballots can most clearly be seen when the Score ballots are set to a scale of 0 to 1 (with in-between decimals allowed), because a voter who gives a middling score to a candidate is seen to be giving them a fractional approval. |
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==Further Reading== |
==Further Reading== |