Before revision:  Unlike other methods in this family,  Split Cycle satisfies a new criterion we call immunity to spoilers, which concerns adding candidates to elections, as well as the known criteria of positive involvement and negative involvement, which concern adding voters to elections.
After revision:  Unlike other methods in this family, only Split Cycle satisfies a new criterion we call immunity to spoilers, which concerns adding candidates to elections, as well as the known criteria of positive involvement and negative involvement, which concern adding voters to elections.