Questions about IIAC & ICC

Sun Jan 13 21:46:51 PST 2002

>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 
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 
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 

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 
it would mean, in CR, voting sincere ratings--but without seeming to contain 
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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