Demarchy, or lottocracy, involves randomly-selected decision-makers who are chosen from an inclusive group of citizens to form a government, and make policy decisions.
Problems and Purpose
Demarchy (or lottocracy) is a form of government in which the state is governed by randomly selected decision makers who have been selected by sortition (lot) from a broadly inclusive pool of eligible citizens. These groups, sometimes termed policy juries, citizens' juries, or consensus conferences, deliberately make decisions about public policies in much the same way that juries decide criminal cases.
Demarchy, in theory, could overcome some of the functional problems of conventional representative democracy, which is widely subject to manipulation by special interests and a division between professional policymakers (politicians and lobbyists) vs. a largely passive, uninvolved and often uninformed electorate. According to Australian philosopher John Burnheim, random selection of policymakers would make it easier for everyday citizens to meaningfully participate, and harder for special interests to corrupt the process. 
A related method is Civic Lottery.
Origins and Development
Participant Recruitment and Selection
How it Works: Process, Interaction, and Decision-Making
Influence, Outcomes, and Effects
Analysis and Lessons Learned
The Demarchy Manifesto for better public policy
Demarchy: A Dubious Conception of Global Democracy
Demarchy: A Democratic Alternative to Electoral Politics
Demarchy: a flexible deliberative process for contemporary democracies
Lead Image: Lottocracy http://tinyurl.com/y2jneduc