[EM] RE : Re: Problem solved (for pure ranked ballot)

[Abd ul-Rahman Lomax]

At 11:15 AM 1/26/2007, Kevin Venzke wrote:
>Hmm.
>
>Well, looking at the RangeVoting list, it looks like this is important
>to what you're saying:
>
> >You cannot test FB and ICC together, because one requires constant
> >voting from all voters and the other requires a change of one vote.
>
>It's true that you probably can't take just two scenarios and make a
>point about both FBC and ICC. But nothing stops you from saying that
>in the change from some scenario 1 to scenario 2, FBC requires something
>of the result, and that in a further change from scenario 2 to scenario
>3, ICC requires something about the result. Of course this is only
>meaningful if you declare in advance that you're talking about a method
>that is supposed to satisfy both criteria.

Yes. We are applying FB to election 1. This produces election 2.

We are then applying ICC to election 2. This produces election 3.

FB tells us about the interchange between 1 and 2.
ICC tells us about the interchange between 2 and 3.

Insert a clone into election 1, the result does not change if ICC is 
satisfied. This says nothing about what happens if you insert a clone 
into election 2.

Favorite Betrayal with election 1 does not change the result if FB is 
satisfied.

What has been done here is to apply FB to one election and then apply 
ICC to a *different* election. This different election happens to be 
the FB election (the one with FB incorporated), which makes it seem 
reasonable to link them. It's a logical error; I've seen various 
false proofs constructed with such errors, I'm sure Warren has seen them too.

To show a contradiction between ICC and FB, there must be *one* 
election which shows ICC, either by the insertion or removal of a 
clone, and FB failure, where the election result improves for a voter who FBs.

What you've done is to create a new criterion: If FB creates a new 
election which satisfies ICC, the FB has been successful and thus the 
FB+SecondElectionICC Criterion fails. You can show that FB can do 
that, therefore no ranked method (and maybe no method at all) can 
satisfy the FB+SecondElectionICC Criterion. Or something like that.

Which we can promptly forget about. I'm certainly not going to add it 
to Wikipeda or the EM wiki!