Consistency criterion

A voting system is consistent if, whenever the electorate is divided (arbitrarily) into several parts and elections in those parts garner the same result, then an election of the entire electorate also garners that result. Smith calls this property separability and Woodall calls it convexity.

It has been proven a ranked voting system is "consistent if and only if it is a scoring function", i.e. a positional voting system. Borda count is an example of this.

The failure of the consistency criterion can be seen as an example of Simpson's paradox.

As shown below under Kemeny-Young, passing or failing the consistency criterion can depend on whether the election selects a single winner or a full ranking of the candidates (sometimes referred to as ranking consistency); in fact, the specific examples below rely on finding single winner inconsistency by choosing two different rankings with the same overall winner, which means they do not apply to ranking consistency.