universal conscription system
A formal term for a system in which all citizens are liable for military service. Often used in historical or political contexts.
That country has adopted a system of universal conscription.
徴兵制度 is the more common term for conscription or draft system, while 皆兵制度 emphasizes the universality of the obligation.
Compound of 皆 (all, everyone), 兵 (soldier), and 制度 (system). The term is a straightforward Sino-Japanese construction.