[EM] independence form covered alternatives is incompatible with monotonicity

[fsimmons at pcc.edu]

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.