Random Ballot fails IIAC

MIKE OSSIPOFF nkklrp at hotmail.com
Sun Jan 20 21:02:43 PST 2002

I'd said:

>This is why I asked Markus if anything was stipulated about how people
>vote. He indicated that there's no such assumption. For that reason,
>Random Ballot fails IIAC, as Markus defined it.

Markus replied:

Of course, when you presume that criteria should be defined on the
sincere opinions of the voters and that the voters don't vote sincerely,
then there is also no method that meets Condorcet, Pareto, monotonicity,
participation, consistency or clone-independence.

I reply:

How anyone presumes that criteria should be defined is irrelevant
to the matter of whether Random Ballot fails IIAC as you defined it.

I asked you if you if your criterion [unpokenly] assumes sincere
voting or makes other stipulations about how people vote. You
indicated that it doesn't.

Since your IIAC doesn't stipulate sincere voting, or otherwise
make stipulations about how people vote, and since you confirmed,
when I asked, that nothing of the sort is assumed, then when
my example has a voter voting insincerely, that doesn't violate the
premise of your IIAC criterion. And so, when the addition of a
candidate increases the probability that a previously-existing
candidate will win, given the inclusion of such a voter, in my
example, that is an IIAC failure by Random Ballot, as you define

As for Pareto, Condorcet's Criterion, Montonicity, Participation,
Consistency, and Clone Independence, the only one of those that
is often defined so that no method complies is Condorcet's Criterion
(CC). It's often defined in terms of sincere preferences, without
stipulation of sincere voting or any other specifications about
voting strategy.

But my Condorcet's Criterion & Smith Criterion, defined in terms
of sincere preferences, and stipulating sincere voting, are
complied with by the methods that people expect to meet them, and
failed by the methods that people don't expect to meet the, including

Some define CC in terms of actual votes, with the result that
Plurality passes, and so, to keep Plurality from passing, they
say that the criterion, by their definition, applies only to rank
methods. That greatly reduces the meaningfulness and usefulness
of CC, and it's a shabby contrivance to avoid an undesired result.

But of course you're right to say that it would be asinine to
define a criterion that specifies that everyone votes sincerely, and
then use, with that criterion, an example in which someone votes
insincerely. I'm not aware of an instance of that, however.

Mike Ossipoff

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