There are versions of Gibbard's theorem for outputting a single winner too. The famous one is Gibbard-Satterthwaite: https://en.wikipedia.org/wiki/Gibbard%E2%80

There are versions of Gibbard's theorem for outputting a single winner too. The famous one is Gibbard-Satterthwaite: https://en.wikipedia.org/wiki/Gibbard%E2%80%93Satterthwaite_theorem https://en.wikipedia.org/wiki/Gibbard%E2%80%93Satterthwaite_...