Didn't we already do this? If you have 20 years of data, why not just take it from the data?
There remain only six outcomes:
Event(A>B) = U(ABC,ACB,CAB)
Event(B>C) = U(ABC,BAC,BCA)
Event(A>C) = U(ABC,ACB,BAC)
Event(A>Both) = U(ABC,ACB)
Off the top of this third rumination, I'd still say you need more information.