Here's one way that idea could be applied to the obstreperous ballot set
49 C 24 B 27 A>B :
First we introduce the lotteries A', B', and C' :
A' means a toss up between B and C. B' means a toss up between C and A. C' means a toss up between A and B.
Next we deduce the most likely relative rankings of the candidates and lotteries:
49 C>A'=B'>C'=A=B 24 B>A'=C'>B'=C=A 27 A>C'>B=B'>A'>C
Now notice that in every case X' is ranked above X on more ballots than not:
A' beats A 73 to 27. B' beats B 49 to 24. C' beats C 51 to 49.
This suggests that we should throw out A, B, and C, and choose from among A', B', and C'.
We now have
49 A'=B'>C' 24 C'=A'>B' 27 C'>B'>A'
Here C' beats B' (51 to 49), B' beats A' (27 to 24), and A' beats C' (49 to 27).
So the wv lottery winner is A' and the margins lottery winner is B'.
If we took the average of these (A'+ B')/2, the respective probabilities for A, B, and C would be 25%, 25%, and 50%, which is very close to the set of probabilities that random ballot would give: 27%, 24%, and 49%.
It is interesting to note that if we applied Rob's ballot-by-ballot DSV using Strategy A to the contest among A',B', and C', then B' would be the most likely winner (a sure winner if we multiplied this ballot set by 100), even though it would make B the winner of the original ballot set.
This corresponds to the fact that the original ballot set and its reverse comprise an example showing that this version of DSV fails the Reverse Symmetry Criterion.
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