In its suggested form Maximal Lottery-Lotteries is still a majoritarian system in the sense that a mere majority of 51% of the voters can make sure that candidate A wins regardless how the other 49% vote. For this, they only need to give A a rating of 1 and all other candidates a rating of 0.
One can also turn the system into a non-majoritarian system in which power is distributed proportionally in the sense that any group of x% of the voters can make sure that candidate A gets at least x% winning probability, similar to what is true of the MaxParC voting system used in vodle
The only modification needed to achieve this is to replace Δ(C) (the set of all lotteries on C) in your formula by the set of those lotteries on C which every single ballot rates at least as good as the benchmark lottery. In this, the benchmark lottery is the lottery of drawing one ballot uniformly at random and electing the highest-rated candidate (as in the “random ballot” or “random dictator” method).
In its suggested form Maximal Lottery-Lotteries is still a majoritarian system in the sense that a mere majority of 51% of the voters can make sure that candidate A wins regardless how the other 49% vote. For this, they only need to give A a rating of 1 and all other candidates a rating of 0.
One can also turn the system into a non-majoritarian system in which power is distributed proportionally in the sense that any group of x% of the voters can make sure that candidate A gets at least x% winning probability, similar to what is true of the MaxParC voting system used in vodle
The only modification needed to achieve this is to replace Δ(C) (the set of all lotteries on C) in your formula by the set of those lotteries on C which every single ballot rates at least as good as the benchmark lottery. In this, the benchmark lottery is the lottery of drawing one ballot uniformly at random and electing the highest-rated candidate (as in the “random ballot” or “random dictator” method).