The asari have no government, per se. Policy is decided through the ebb and flow of public opinion in a sprawling but well-organized electronic democracy. The closest analogue to an executive decision-making body is the opinion of the Matriarchs. In a crisis, the public turns to the experience of these millennia-old "wise women" for advice.
The asari military resembles a collection of tribal warrior bands with no national structure. Each community organizes its own unit as the locals see fit, and elect a leader to command them. Units from populous cities are large and well-equipped, while those from farm villages may be only a few women with small arms. There is no uniform; everyone wears what they like. The asari military is not an irregular militia, however; those who serve are full-time professionals.