Droop-PSC implies Hare-PSC, since a Hare quota is simply a large Droop quota, but the same doesn't hold the other way around. Hare-PSC is equivalent to the unanimity criterion and Droop-PSC to the mutual majority criterion in the single-winner case. Note that this means cardinal PR methods can only pass Hare-PSC and not Droop-PSC in order to reduce to cardinal methods that fail the mutual majority criterion in the single-winner case, which is most of them.
Methods that reduce to [[D'Hondt]] in the [[Party list case|party list case]]<nowiki/>tend to pass at least a weak form of Droop-PSC; this is because D'Hondt guarantees every party will get at least the number of HB quotas it has rounded down.
Note that PSC doesn't hold if some voters in a coalition back out-of-coalition candidates i.e. 1-winner example with Droop quota of 51: