  Agents vote to choose a fair mixture of public outcomes; each agent likes or
dislikes each outcome. We discuss three outstanding voting rules. The
Conditional Utilitarian rule, a variant of the random dictator, is
Strategyproof and guarantees to any group of like-minded agents an influence
proportional to its size. It is easier to compute and more efficient than the
familiar Random Priority rule. Its worst case (resp. average) inefficiency is
provably (resp. in numerical experiments) low if the number of agents is low.
The efficient Egalitarian rule protects similarly individual agents but not
coalitions. It is Excludable Strategyproof: I do not want to lie if I cannot
consume outcomes I claim to dislike. The efficient Nash Max Product rule offers
the strongest welfare guarantees to coalitions, who can force any outcome with
a probability proportional to their size. But it fails even the excludable form
of Strategyproofness.
