Scale invariance: Difference between revisions

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Scale invariance can refer to one of two criteria: a cardinal voting method criterion and an ordinal one.

The cardinal method criterion is:

Multiplying every ballot's score of every candidate by a constant $\alpha >0$ should not change the outcome.

with a stronger variant being

Multiplying one or more ballot's score of every candidate by a constant $\alpha >0$ should not change the outcome.

The ordinal method criterion is also called the homogeneity criterion. It is:

For every way of ranking the candidates, multiplying the number of voters who express this preference by a constant $\alpha >0$ should not change the outcome.

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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 {{Definition|Multiplying every ballot's score of every candidate by a constant <math>\alpha>0</math> should not change the outcome.}}
+with a stronger variant being
-The ordinal method criterion is also called the [[homogeneity criterion]]. It is:
-{{Definition|For every way of ranking the candidates, multiplying the number of voters who express this preference by a constant <math>\alpha>0</math> should not change the outcome.}}
+{{Definition|Multiplying one or more ballot's score of every candidate by a constant <math>\alpha>0</math> should not change the outcome.}}
+The ordinal method criterion is also called the [[homogeneity criterion]]. It is:
-Strong variant, for [[Cardinal voting systems#Scale%20invariance|cardinal method]] is:
-{{Definition|Multiplying one or more ballot's score of every candidate by a constant <math>\alpha>0</math> should not change the outcome.}}
+{{Definition|For every way of ranking the candidates, multiplying the number of voters who express this preference by a constant <math>\alpha>0</math> should not change the outcome.}}
 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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 {{stub}}
-==Relevant Pages==
+==See also==
 * [[Single distributed vote]]