The asari came late to the concept of world government. For centuries, their homeworld of Thessia was dotted with loose confederacies of great republican cities. The closest Earthly equivalent would be the ancient Mediterranean city-states. Since the asari culture values consensus and accommodation, there was little impetus to form larger principalities. Rather than hoard resources, the asari bartered freely. Rather than attack one another over differing philosophies, they sought to understand one another.
Only in the information age did the city-states grow close. Communication over internet evolved into an "electronic democracy". Asari have no politicians or elections, but a free-wheeling, all-inclusive legislature that citizens can participate in at will. Policy debates take place at all hours of the day, in official chat rooms and forums moderated by specially-programmed virtual intelligences. All aspects of policy are opened to plebiscite at any time. In any given debate, the asari tend to lend the most credence to the opinions of any Matriarchs present, nearly always deferring to the experience of these millennia-old "wise women".
Achieving consensus through public debate may take too long in a crisis. In cases where prompt, decisive action is required, the asari defer to the wisdom of local Matriarchs.