[EM] questions about IIAC & ICC

[MIKE OSSIPOFF]

Markus wrote:

An election method violates "Independence from Irrelevant
Alternatives" when there are situations where you can
increase the winning probability of a given already running
candidate by introducing an additional candidate.

An election method violates "Independence from Clones"
when there are situations where you can (1) increase or
decrease the probability that a candidate of a given set
of clones is elected by introducing additional clones to
this set of clones or (2) increase or decrease the
probability that a given candidate is elected by introducing
additional clones to a set of clones to which this candidate
doesn't belong.

I reply:

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?

Does Approval pass your IIAC? Your ICC?

If a stipulation about how people vote isn't added to your IIAC definition, 
then what
method passes it? What method passes your ICC, copied above, if no 
stipulation about
how people vote is added to it?

Some of us agreed that ICC seems to work as expected when sincere voting is 
stipulated,
and clones defined in terms of sincere preferences. That's also true of the 
Condorcet
Criterion, by the way.

I've heard lots of definitions of IIAC, most or all  incomplete. If anyone 
knows how Arrow
himself defined it, could they post an English translation of it?

I state it in terms of actual votes:

Deleting a loser from the ballots and
recounting those ballots should never change who wins.

[end of definition]

But I don't claim that that correctly represent's Arrow's IIAC.

Mike Ossipoff


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