Permissionless-consensus-based Decentralised Autonomous Organisations (DAOs) are the prevailing paradigm for participant-governed digital organisations. As participants have verified resources but no trusted identities, this ecosystem is necessarily plutocratic (one coin -- one vote). Here we offer, for the first time, a democratic (one person -- one vote) paradigm for the governance of digital communities and organisations, based on permissioned consensus and egalitarian decision processes. In line with Lamport's vision of consensus as a self-governing parliament, in the democratic paradigm a constitution specifies both a decision making protocol as well as a consensus protocol, combined to let participants amend the constitution through constitutionally-valid decisions that are ratified by consensus. To meaningfully instantiate this paradigm we integrate the disciplines of distributed computing and computational social choice, with the goal of providing a practical and efficient smartphone-based solution for the democratic self-governance of grassroots sovereign digital communities and organisations. The resulting Constitutional Consensus protocol employs (1) state-of-the-art Sybil-resilient democratic decision processes for amending the set of participants, supermajority threshold, and timeout; and (2) a novel Byzantine-fault tolerant consensus protocol that is DAG-based (following Cordial Miners) thus eschewing reliable broadcast, with dual-mode operation (following Morpheus) that is quiescent when idle, has spontaneous leaders for isolated transactions, and formal round-robin leadership during high throughput.