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 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 should not change the outcome.
Both 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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