In most of the world there is already a democratically-elected power that can be seen as an alternative to the power of the state: it is local authorities at the city, town and regional levels.
They may be corrupt or incompetent, but at least local authorities do not base their power on the culture of war, at least not since the days of the medieval city-state. This is true because over time the state has has come to monopolize the culture of war. The United Nations could be transformed to work for a culture of peace if it were based on local authorities instead of the state.
The linkage of civil society and elected authorities at the local and regional levels could make up for the lack of democracy in social movements and civil society organizations and allow them to realize their full potential contribution to a culture of peace.
The state would put up great resistance to its power being replaced by local authorities! It's hard to imagine how could this be overcome, unless it were to take place at a moment of history when state power was greatly weakened.
But most local authorities are not linked up to each other on a regional and global basis and are not ready to assume the powers of the state!