[EM] Weak Independence of Irrelevant Alternatives

[MIKE OSSIPOFF]

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]

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.

>
>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

_________________________________________________________________
Get your FREE download of MSN Explorer at http://explorer.msn.com