Piketty has a brief paper here
'Condorcet’s basic result, the so-called ‘Condorcet Jury Theorem’,
states under which conditions majority-rule voting yields efficient information
aggregation. But Condorcet also examines what information structures imply
the informational efficiency of other electoral systems (indirect democracy,
multi-stage voting, etc. . . .). In a sense, the recent literature surveyed in this
paper represents a come-back to the original Condorcet approach.'
The problem with his approach is that, if voting uses up scarce resources, there must always be either a superior stochastic or formal Muth Rational solution.
Furthermore, concurrency deadlocks endow valuable inertial properties to Institutions. Finally, with hindsight from the vantage point of regret minimisation, it is vital that noise obtains.