questions about IIAC & ICC

Thu Jan 10 21:53:10 PST 2002

I'd said:

>Then your definitions of those 2 criteria don't make any
>stipulations about how people vote? They don't have to
>vote sincerely, for instance? Or, if they have to vote
>sincerely, then what definition of sincere voting is used?

Markus replied:

Didn't we already have this discussion?

I reply:

I've probably mentioned before that I don't know how Arrow defined IIAC, and 
that I'm
not entirely sure about how ICC is defined. But we haven't had this same 
before, because I didn't before ask you what methods pass those criteria by 
particular definitions.

By the way, you didn't answer that question, but I won't press for
an answer. 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?

Anyway, my question about what methods meet the criteria that you defined 
a sincere question, and , I'd say, a fair question. 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'm not saying there isn't one just because I don't know of one.

Markus continued:

Similarily I could
ask whether the monotonicity resp. consistency resp.
participation criterion presumes sincere voting, whether
this or that election method is applied to sincere voting
or how you define sincere voting.

I reply:

Unless I've misunderstood the definitions of Monotonicity, Participation, &
Consistency, they don't stipulate sincere voting. Certainly the definitions 
have been posted here in recent days don't stipulate sincere voting. As 
posted here
recently, they're all defined according to actual ballots, with no mention 
about whether
they're sincere.

How I define sincere voting?:

A voter votes sincerely if s/he doesn't reverse a sincere preference or fail 
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.

[end of definition]

Of course reversing a sincere preference means voting B over A when you 
A to B. Voting a preference for A over B means voting A over B. You're then 
a sincere preference for A over B if you prefer A to B.

Maybe that should be called "sincere & complete voting" instead of just 
"sincere voting".

Markus continued:

You wrote (10 Jan 2002):
>Some of us agreed that ICC seems to work as expected when
>sincere voting is stipulated, and clones defined in terms
>of sincere preferences.

Clones are defined on the actually casted ballots. Whether
these ballots are sincere is irrelevant.

I reply:

So the newly-added candidate is a clone of some other candidate(s) according 
the ballots that are cast when the new candidate is added, but not 
necessarily in terms
of people's sincere preferences among the candidates.

When trying to write a failure example, can the example-writer have voters 
differently with & without the new candidate any way he chooses? Ordinarily
the example-writer can configure things any way that he wants to, provided 
that it
doesn't violate the criterion's stated premise conditions.

Markus continued:

By the way: Who is "some of us"?.

Norm Petry, Buddha Buck,  I, and some others were discussing ways of 
ICC, which includes the definition of a clone. I don't remember who it was 
who suggested
defining clones in terms of sincere preferences and stipulating sincere 
voting in the
ICC definition. But we as a group were satisfied with that way of defining 

Mike Ossipoff

Markus Schulze

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