I, too, hope that our disagreement will soon disappear. But as far as I can see, it's clearly not a semantic disagreement; one of us is just wrong. I'd say it's you.

So. Say there are 3 voters, and without loss of generality, voter 1 prefers A>B>C. Now, for every one of the 21 distinct combinations for the other two, you have to write down who wins, and I will find either an (a priori, determinative; not mirror) dictator or a non-IIA scenario.

ABC ABC: A

ABC ACB: A

ABC BAC: ?... you fill in these here

ABC BCA: ?

ABC CAB: .

ABC CBA: .

ACB ACB: .

ACB BAC:

ACB BCA:

ACB CAB:

ACB CBA:

BAC BAC:

BAC BCA:

BAC CAB:

BAC CBA:

BCA BCA:

BCA CAB: .... this one's really the key, but please fill in the rest too.

BCA CBA:

CAB CAB:

CAB CBA:

CBA CBA:

Once you've copied these to your comment I will delete my copies.