[EM] [RangeVoting] Problem solved (for pure rank ballots): ICC & AFB incompatible (essentially)

[Abd ul-Rahman Lomax]

At 12:11 AM 1/25/2007, Dave Ketchum wrote:
>How is this supposed to make sense?
>
>You have the voters voting a perfect rank tie.  You do not show the range
>votes but, to be comparable, they would ALSO have to express a tie.

Yes. Indeed, that's the point. If there is a tie in Range, then there 
is no basis for choosing one candidate over another, thus satisfying 
criterion 5.

The example is a maximally simple election showing what Warren thinks 
he has found. If a single election scenario can be constructed where 
a criterion is violated, the general agreement is that the method 
used does not satisfy the criterion. So Warren claiming that a set of 
six criteria are mutually incompatible, given a pure ranked ballot. 
He may be correct, but it looks to me at this point that the proof is 
defective. We'll see.

>Starting with identical triplets you do some dancing assuming NONidentity.
>   Even with NONidentity, any one of them would have been equally likely to
>do the same dance steps.

That's not the problem. Yes, any voter could have done it. If even 
one voter can change his or her vote to betray a favorite, and this 
causes the election outcome to be more favorable for that voter, then 
FB is violated. Yes, it is true that if every voter makes this same 
change, the election is still tied. I've got a pre-migraine right now 
and I don't want to figure out what happens if two voters Favorite 
betray.... but it's moot for this proof. One voter is enough.

The problem is in the definition of clone. The definition does not 
depend on the how voters vote, unless we assume that the voters vote 
sincerely. It depends on the actual preferences of the voters. So 
there are no clones in the initial case, and this does not change 
merely because a voter changes a vote to Favorite Betray.

As I wrote last night, I think this is fatal to the proof. Warren 
suffered a brain fault. But let's see what he says. My own brain has 
frequent earthquakes. But, like California, it can be a nice place to 
live when it isn't shaking.