Efficient democratic decisions via nondeterministic proportional consensus

Are there voting methods which (i) give everyone, including minorities, an equal share of effective power even if voters act strategically, (ii) promote consensus rather than polarization and inequality, and (iii) do not favour the status quo or rely too much on chance? We show the answer is yes by describing two nondeterministic voting methods, one based on automatic bargaining over lotteries, the other on conditional commitments to approve compromise options. Our theoretical analysis and agent-based simulation experiments suggest that with these, majorities cannot consistently suppress minorities as with deterministic methods, proponents of the status quo cannot block decisions as in consensus-based approaches, the resulting aggregate welfare is comparable to existing methods, and average randomness is lower than for other nondeterministic methods.