Questions about IIAC & ICC

[MIKE OSSIPOFF]

>But if IIAC, as Arrow intended it, isn't met by any method,
>then why wouldn't he mention that? If nothing meets IIAC,
>then there'd be no point in listing those other criteria,
>the ones in his impossibility theorem. If nothing meets IIAC,
>then why bother saying that nothing meets all the criteria
>in some list that includes IIAC? I really don't know of a method that meets 
>that particular IIAC, and so I was just
>asking. If you know of one, tell me of it.

Markus wrote:

I have already mentioned in one of my last mails that there
are election methods that meet IIAC. I wrote (9 Jan 2002):

>Random Candidate meets "Independence from Irrelevant
>Alternatives" and violates "Independence from Clones".
>Tideman's Ranked Pairs method meets "Independence from Clones"
>and violates "Independence from Irrelevant Alternatives".

I reply:

OK, but though Random Candidate can be called a choice method, it can't
be called a voting system.

Markus continued:

Also Random Dictatorship meets IIAC. So there are election
methods that meet IIAC.

I reply:

Fine. I just asked what they were, and you've answered. Some choice methods 
that
aren't proposed meet that version of IIAC.

I don't have your IIAC wording before me right now, so for now I'll take 
your word for that.

I'd said:

>How I define sincere voting?:
>A voter votes sincerely if s/he doesn't reverse a sincere
>preference or fail to vote a sincere preference that the
>balloting system in use would allow hir to vote in addition
>to the preferences that s/he actually did vote.
>Of course reversing a sincere preference means voting B over
>A when you prefer A to B. Voting a preference for A over B
>means voting A over B. You're then voting a sincere preference
>for A over B if you prefer A to B.

Markus replied:

How do you define "sincere voting" for other election methods
than preferential election methods?

I reply:

I use that definition for all voting systems, not just rank methods. It 
means just
as expected with rank methods, Plurality, & Approval (as Brams & Fishburn 
use
the term "sincere" in reference to Approval). I apply it to CR too, though 
it only looks
at the order of the candidates' ratings on your ballot. I admit that I 
haven't checked
if that causes unexpected criterion compliance results. We don't expect CR 
to meet
SFC, CC, or ICC, as I define them,  3 criteria of mine that refer to sincere 
voting.

This more lax voting requirement, for CR, when the criterion's premise 
requires sincere
voting, would make it easier for CR to fail a criterion, since we have more 
ways to
try to make it fail, and so I expect that, with that looser meaning for 
sincere voting in
CR, CR would still fail SFC, and my versions of CC & ICC. In other words, 
that definition
gives the expected results for CR.

If necessary, that definition of sincere voting maybe could be changed so 
that
it would mean, in CR, voting sincere ratings--but without seeming to contain 
wording
specifically for CR. If that's needed then it would be something to work on.

Mike Ossipoff

******

You wrote (12 Jan 2002):

>Most rank methods, even if monotonic, fail Participation &
>Consistency. Borda is the only rank method that I know to pass
>those 2 criteria.

All positional election methods meet monotonicity, participation
and consistency.

Markus Schulze




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