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

Abd ul-Rahman Lomax abd at lomaxdesign.com
Thu Jan 25 06:08:50 PST 2007

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.