The consistency criterion requires that any candidate who wins both of two separate sets of voters must also win the combined electorate. Although it is not a logical requirement, generally speaking systems which satisfy the consistency criterion also satisfy the participation criterion. The reverse implication is also common, though slightly less so.
A voting system is consistent if, when the electorate is divided arbitrarily into two parts and separate elections in each part result in the same alternative being selected, an election of the entire electorate also selects that alternative. If a voting system is not consistent then it may be manipulated through the establishment of strategically configured election districts.