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

[Abd ul-Rahman Lomax]

Dave, you have totally misunderstood what's going on here. This is 
not about public elections, it is about an election method, in the 
abstract. This election has three candidates and three voters. It's a 
*test* election, to show properties of ranked methods.

At 11:01 PM 1/25/2007, Dave Ketchum wrote:
>Assuming this is a public election and, therefore, the votes are secret.

Irrelevant.

>Warren assumes identical triplets as voters, thus producing a tie.

Well, not identical. Permuted. You could say symmetrical.

>To me this is an argument for a random selection of winner from tied
>leaders, especially since rank and rating methods permit voters to clearly
>state their preferences (and ties being rare and reruns expensive in real
>public elections).

This, again, is totally irrelevant.

>I would expect these voters to be as likely to vote a tie with Range.

Yes. Indeed, to see if Range has the same properties, one would set 
up a Range election with exactly the same rankings, and, to be 
comparable, with the same preference strengths.

>Apparently Warren assumes a rerun in response to the tie.

He assumes nothing of the kind. I think that random choice is 
assumed, with the probability of victory being spread among the tied 
candidates. I.e., 1/3 for each.

>   These being
>identical triplets, I claim their response to a rerun call could be to
>repeat the same votes - or to each make the SAME modification to their
>votes - letting the tie continue until the authorities amended THEIR
>responses.

No rerun. One of the assumptions, I think, is that the method is 
deterministic. That is, it *will* choose a winner, but random choice 
is only allowed if there is a tie (or more than one tie).

This is abstract voting method stuff. There may be some significance 
for practical elections, but the fact is that there is a much simpler 
proof that ranked methods suffer from a limitation that Range does 
not. And that may *still* not "prove" that Range is better, for there 
is more to an election method, when it is applied, than its 
theoretical compliance with election criteria -- which is what this is about.

Normally, I wouldn't be following this. I just happened to notice the 
problem with how ICC was being considered.