[EM] Questions about IIAC & ICC

[Markus Schulze]

Dear Mike,

you wrote (14 Jan 2002):
> Markus wrote (13 Jan 2002):
> > Mike wrote (11 Jan 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.
> >
> > I have already mentioned in one of my last mails that there
> > are election methods that meet IIAC. Markus 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".
> >
> > Also Random Dictatorship meets IIAC. So there are election
> > methods that meet IIAC.
>
> OK, but though Random Candidate can be called a choice method,
> it can't be called a voting system.

When you want to prove an impossibility theorem, then of course
you must not only consider all those methods you consider acceptable,
you must also exclude (by using appropriate axioms) those methods
you don't consider acceptable.

Otherwise, somebody would use Random Candidate or Random Dictatorship
as examples that your impossibility theorem is false.

******

You wrote (14 Jan 2002):
> Markus wrote (13 Jan 2002):
> > Mike wrote (11 Jan 2002):
> > > 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.
> >
> > How do you define "sincere voting" for other election methods
> > than preferential election methods?
>
> 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.

So you say that when someone exaggerates his opinion under average rating
then this is still "sincere voting" as long as the casted _order_ of the
candidates' ratings reflects the sincere opinion of this voter?

How do you define "sincere voting" for cumulative voting?

Markus Schulze