Scale invariance: Difference between revisions
Added in "additive" scale invariance an addition to multiplicative scale invariance.
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(Added in "additive" scale invariance an addition to multiplicative scale invariance.) |
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Scale invariance can refer to one of two criteria: a cardinal voting method criterion and an ordinal one, and these can be multiplicative or additive.
The [[Cardinal voting systems#Scale%20invariance|cardinal method criterion]]
{{Definition|Multiplying every ballot's score of every candidate by a constant <math>\alpha>0</math> should not change the outcome.}}The additive version:
{{Definition|Adding a constant <math>\alpha</math> to every ballot's score of every candidate should not change the outcome.}}
with a stronger variant being (multiplicative):▼
{{Definition|Multiplying one or more ballot's score of every candidate by a constant <math>\alpha>0</math> should not change the outcome.}}Additive:
▲with a stronger variant being
{{Definition|Adding a constant <math>\alpha</math> to one or more ballot's score of every candidate should not change the outcome.}}
The ordinal method criterion is also called the [[homogeneity criterion]]. It is (multiplicative):▼
{{Definition|
Additive:
▲The ordinal method criterion is also called the [[homogeneity criterion]]. It is:
{{Definition|For every way of ranking the candidates,
These criteria represent a desideratum that the method should not rely on absolute numbers when selecting a winner, just on the candidates' or factions' relative support.
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