Non-compulsory support criterion
The Non-compulsory support criterion was devised in 2005 by Thomas Smith. A voting method satisfies the Non-compulsory Support criterion if the ballot provides a means for the voter to exclude one or more candidates from supportive ranking or rating, and by doing so, not causing harm to any supported candidates or help to non-supported candidates. Methods that satisfy this criterion include Approval voting, Range voting, Bucklin voting, truncatable STV methods and Borda count that is voter truncated from the low rankings. Methods that do not satisfy this criterion include Condorcet methods, plurality voting, standard Borda count, and modified Borda count (voter truncated from the high rankings). For example, Approval and Range voting allow the voter to rate any candidate with a zero, which effectively does not give those candidates any advantage and does not harm the chances of the positively rated candidates. Voter-truncated Borda count from the low rankings allows the voter to not rank any candidate, thus giving those candidates no points in the tallies, but gives the supported candidates the same high-ranking point values as a standard Borda count. Plurality voting does not satisfy ncsc because only one candidate can be selected for a ballot slot, so there is no means to exclude even one candidate without not voting at all in that ballot slot. Standard STV methods (like standard IRV) satisfy ncsc because the voter is allowed to truncate, neither harming ranked candidates, nor helping those that are truncated away on the ballot. However, because STV methods do not satisfy the monotonicity criterion or the participation criterion, not ranking a candidate can lead to an outcome where a ranked candidate was harmed or a unranked candidate was helped as a result of a particular truncated ballot.
A voting methods that satisfies the non-compulsory support criterion provides some incentive for the voter to sincerely disapprove, rate as 0, or not rank a candidate, because those that voters support will never be harmed by the non-support of a candidate, nor will those candidates who are non-supported ever be helped by non-support of a candidate.