[EM] Weak Independence of Irrelevant Alternatives

[Forest Simmons]

Thanks, and see clarifications below.

Forest

On Wed, 28 Feb 2001, MIKE OSSIPOFF wrote:

> 
> 
> 
> Forest wrote:
> 
> >What I call "strong IIA" says (roughly) that the winner of an election
> >shouldn't change if any of the other candidates is removed.
> 
> Is it this?:
> 
> Deleting a loser from the ballots and then recounting those ballots
> should never change who wins.
> 
> [end of definition]

Forest: Yes, that's what I meant.

> 
> That criterion is passed by Approval & Plurality.
> 
> That's the version of IIAC that I sometimes refer to. I don't know
> if that's Arrow's own IIAC, but if IIAC were taken to mean that
> if everyone votes sincerely, then deleting a loser from the ballots
> and repeating the vote should never change the winner, I don't know
> if any method could pass.
> 
> >
> >Strong IIA may be too stiff a standard by which to judge common methods.
> >If you point out to IRV supporters that IRV doesn't satisfy strong IIA,
> >they will say, "So what? That's too strong a requirement."
> 
> The version I defined above is useful in discussions about IRV vs
> Approval, because Approval passes it & IRV fails it. It's especially
> useful when an IRVies brings up Arrow. Then I say that Approval passes
> all of Arrow's results criteria and IRV doesn't. That's if IIAC was
> as I defined it, where the same ballots are recounted after the deletion
> of a loser.
> 
> I don't bring up the Arrow issue, but IRVies often do, and so I
> point that out when they do. But I admit that I haven't seen Arrow's
> own article or book where he defines his criteria. I've only seen many
> accounts of them, each account different. I don't think that 2nd
> definition seems likely to be Arrow's IIAC, because if it's unmeetable,
> then what reason would there be for Arrow to include other criteria
> in his impossibility statement?
> 
> >
> >But it seems to me that we should be able to hold any decent method to
> >a "weak IIA" standard which says that a definite winner of an
> >election shouldn't change if a definite worst candidate is removed.
> >
> >Is anybody aware of previous work done on this weak version of
> >Independence of Irrelevant Alternatives?
> 
> Yes, Steve Eppley, a former member of this list proposed that criterion.
> He called it Indepence from Last Finishers Criterion (ILFC).
> He determined last finishers as you suggested, by repeatedly deleting
> the winner from the rankings and recounting, till only 1 candidate
> remains who hasn't been a winner.
> 
> Steve, it seems to me, said that, of the methods we were considering,
> only Tideman meets ILFC.
> 

Forest: If only Tideman meets ILFC, then ILFC is stronger than what I was
considering. The difference must be in my intended meaning of the word
"definite" as in definite winner and definite worst candidate.  If you
remove those words or interpret them too loosely, then the criterion is
harder to satisfy. 

I consider any CW method to satisfy my version of ILFC because I consider
true Condorcet Winners to be definite winners and that there are no
decisive winners when various other standards are used to break up
Condorcet cycles. All these other winners are compromises in one degree or
another.  (The confusion arises from the fact that there are degrees of
definiteness and decisiveness.) 

> >
> >This standard is intuitively fair, as well as easy to check, so it has a
> >chance of paring down the field of competing methods in a way that is
> >understandable to the average citizen.
> 
> Yes, but if it requires using Tideman, then it means giving up the
> Schwartz Criterion, and doing more overruling of voters than
> SSD or Cloneproof SSD would, and thereby having slightly lower SU.
> If the new recursive procedure you described meets ILFC, and does
> as well as SSD in other respects, that would argue strongly for it.
> 
> Of course it wouldn't take that much to argue strongly for it as
> a replacement of ordinary IRV.
> 
> Mike Ossipoff
> 
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