Suppose that we have a method that satisfies independence form covered
alternatives, and that gives
greater winning probability to alternative B in this scenario
40 B>C>A
30 C>A>B
30 A>B>C
than in this scenario
40 D>B>C
30 B>C>D
30 C>D>B
as any decent method would.
Then consider the scenario
40 D>B>C>A
30 A>B>C>D
30 C>A>D>B
The uncovered set is {A,B,C} and so by independence from covered alternatives
the winner is chosen
according to the first scenario above.
Now switch A and B in the second faction to get
40 D>B>C>A
30 B>A>C>D
30 C>A>D>B .
The uncovered set becomes {D,B,C}.and so by independence from covered
alternatives the winner is
chosen according to the second scenario above.
In summary, soley by raising B relative to A , the winning probability of B
decreased.
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