While the atomised voting to nominate representatives (who, in reality, held the real power in society) may be more than adequate to ensure bourgeois, i.e. minority, power, could it be used for working class, i.e. majority, power?
This seems highly unlikely because such institutions are designed to place policy-making in the hands of representatives and were created explicitly to exclude mass participation in order to ensure bourgeois control. They do not (indeed, cannot) constitute a “proletariat organised as a ruling class.” If public policy, as distinguished from administrative activities, is not made by the people themselves, in federations of self-managed assemblies, then a movement of the vast majority does not, cannot, exist. For people to acquire real power over their lives and society, they must establish institutions organised and run, as Bakunin constantly stressed, from below. This would necessitate that they themselves directly manage their own affairs, communities and workplaces and, for co-ordination, mandate federal assemblies of revocable and strictly controllable delegates, who will execute their decisions. Only in this sense can a majority class, especially one committed to the abolition of all classes, organise as a class to manage society.