[EM] Herve Moulin's proof not really a proof

[Kevin Venzke]

Hi Nicholas,

You seem to agree in your paper that Moulin's proof shows that in the
original scenario, the winner can only be A. If that is granted, then
we can simplify the proof by removing what we don't need.

Initial scenario (from case 4):

3 voters vote A > D > C > B.
3 voters vote A > D > B > C.
5 voters vote D > B > C > A.
4 voters vote B > C > A > D.
4 voters vote C > A > B > D.

Either A or C is elected (we agree on this yes?)

Step 2:
Say that A wins in the initial scenario.
Now add 6 voters for A > C > B > D.

Now C would be the Condorcet winner, do you agree?

So A cannot be the winner in the original scenario.

Step 3:
Say instead that C wins in the initial scenario.
Now add 4 voters for C > B > A > D.

Now B would be the Condorcet winner, do you agree?

So C can't be the winner in the original scenario, either.

No design can make it work.

Kevin