Hylland's theorem
See Aanund Hylland.
See also: "Strategy Proofness of Voting Procedures with Lotteries as Outcomes and Infinite Sets of Strategies" -- Aanund Hyllund -- January 1980 https://www.sv.uio.no/econ/personer/vit/aanundh/upubliserte-artikler-og-notater/Strategy%20Proofness%5B1%5D.pdf