Scale invariance: Difference between revisions

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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.}}
{{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.
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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==Relevant Pages==
==See also==


* [[Single distributed vote]]
* [[Single distributed vote]]
Retrieved from "https://electowiki.org/wiki/Scale_invariance"