[EM] Banks//Approval fulfils INI/ICI

[Jobst Heitzig]

Banks//Approval: The most approved candidate from the Banks set wins.

fulfils the following strong version of INI/ICI: if X and not Y wins, Y has beatpath to X through Z, and X has no beatpath to Y through Z, then, after removing Z: not (Y and not X wins).

Proof.
X wins => is in Banks set => ex. max. chain c1 with X on top => Z not in c1, and ex. A in c1 with A>Z (otherwise Z could be added on top of c1). After removing Z, c1 is still max. => X is still Banks. Assume Y but not X wins. Then Y is more approved than X and is Banks after removal of Z => ex. max. chain c2 with Y on top. Since Y is more approved than X, it was not Banks originally => c2 was not max. originally => Z can be added to c2 originally (all other additions would also be possible after removing Z) => Z>Y => X>A>Z>Y => X has beatpath to Y through Z -- a contradiction.

Jobst
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