The random ballot method is decisive, in that there is no possibility of a tied vote, assuming that the selected voted has expressed a preference (if not then another ballot can be selected at random). It is unbiased in that the probability of a particular result is equal to the proportion of total support that that result has in all the votes. It is also strategy-free in that there is no advantage in tactical voting.
But it is not deterministic, in that a different random selection could have produced a different result, and it undermines majority rule since there is a substantial possibility that the selected voter may be in the minority.
It is less a practical form of democracy and more a theoretical method designed to explain some of the properties of other voting methods.