I found this paper earlier today: https://www.science4all.org/wp-content/uploads/RandomizedCondorcet.pdf >From my light skimming through it, it appears to define a relation between lotteries so that a Condorcet winner always exists, and that the (nondeterministic) voting method that elects this CW lottery is always individually strategy-proof and is group strategy-proof under singlepeaked preferences. It might be possible to generalize the majority lottery concept when given strength of preference data so that the comparison between lotteries take that strength of preference into account. If so, that would provide a more natural "cardinal Condorcet" method than my STAR generalization. Although the method would be nondeterministic, it would be pretty simple to define a nonzero chance of victory set and then run a conventional Condorcet method on top. This would destroy the strategy-proofness, but I don't know if the cardinal generalization would retain it in the first place. It's an interesting concept that could be useful to investigate :-) -km