Advisory bodies of randomly chosen citizens already are becoming commonplace. The more these examples demonstrate the wisdom of ‘the people’, the sooner such bodies can graduate from advisers to policy makers.

See, among others, The Center for Deliberative Democracy, The Jefferson Center for New Democratic Processes, Citizen Consensus Councils, National Issues Forum, The National Initiative for Democracy, Everyday Democracy, Public Agenda, International Association for Public Participation, National Coalition for Dialogue and Deliberation, America Speaks and the Deliberative Democracy Consortium.

For bicameral legislatures some thinkers propose replacing the upper chamber with an allotted one and keeping the lower elected chamber.
In the U.S. Congress the Senate would be replaced by a sortitionally-chosen Citizens Chamber. Current procedural rules would remain as they are. [It is worth noting that under present U.S. Senate rules of filibuster, 40 Senators representing less than 10% of the population can block legislation.]
It is assumed that the Citizens Chamber would prove its worth over time and would likely stimulate demand for a unicameral Citizens Legislature.