Mike refers to this scenario:
The Approval bad-example is an example of that. I'll give it again here:
Sincere preferences:
49: C
27: A>B
24: B>A
A majority _equally strongly_ prefer A and B to C.
Actual votes:
The A voters defect, in order to take advantage of the
co-operativeness and
responsibility of the A voters:
49: C
27: A>B
24: B
I agree that *if* the sincere preferences are as Mike specifies then a
just interventionist mind-reading God
should award the election to A.
But a voting method's decisions and philosophical justification should
be based on information that is actually
on the ballots, not on some guess or arbitrary assumption about some
maybe-existing "information" that isn't.
I think a very reasonable tenet is that if, based on the information on
the ballots, candidate X utterly dominates
candidate Y then we should not elect Y.
For several reasons (for those who can pooh-pooh this as "merely
aesthetic"): electing Y gives the supporters
of X a very strong post-election complaint with no common-sense or
philosophically cogent answer, X is highly
likely to be higher Social Utility (SU), Y's victory will have
compromised legitimacy.
The Plurality criterion is one very reasonable criterion that says that
C is so much stronger than A that the election
of A can't be justified. . There are other criteria I find reasonable
that say the same thing:
"Strong Minimal Defense": If the number of ballots on which both X is
voted above bottom and Y isn't is greater than
the total number of ballots on which Y is voted above bottom, then don't
elect Y.
And 2 that only use information from the normal gross pairwise matrix:
"Pairwise Plurality": If X's smallest pairwise score is larger than Y's
largest pairwise score, then don't elect Y".
"Pairwise Strong Minimal Defense" : If X's pairwise score versus Y is
larger than Y's largest pairwise score, then
don't elect Y.
The election of A is unacceptable because C's domination of A is
vastly more impressive than A's pairwise win over
B. The Plurality criterion plus the three other criteria I define above
all loudly say "not A".
Minimal Defense and Strong Minimal Defense and "Pairwise Strong Minimal
Defense" all say "not C" (due to B), and
I find that message very reasonable but nothing like as compelling as
the "not A" message.
The A voters defect, in order to take advantage of the
co-operativeness and
responsibility of the A voters:
The plausibility of arbitrary claims about the voters' sincere
preferences and motivations can weighed in the light of the
used election method's incentives. How is it so "co-operative and
responsible" of the A voters to rank B when doing
so (versus truncating) can only help their favourite? And why would the
B voters be insincerely truncating ("defecting")
when doing so can only harm their favourite?
Given the incentives of the MDD,TR method that Mike is advocating, it is
only reasonable to assume that the truncators
are all sincere and that the A>B voters' sincere preferences could be
A>B or A>C or A. It's a bit like Mike is assuming that
the voters were all deceived into thinking that their votes would be
counted using a method like Bucklin or MCA (which have
truncation and defection incentives, failing Later-no-Harm and meeting
Later-no-Help).
(I might comment on IRV in another post).
Chris Benham
Mike Ossipoff wrote (16 Nov 2011):
Votes-only criteria vs preference criteria:
____________________________________________
Kevin, you objected to my preference-mentioning criteria on the grounds
that no one knows what the voters'
true preferences really are. But so what?
As I said before, my criteria indirectly stipulate votes. They do that
when they stipulate that people have
a certain preference and vote sincerely; or have a certain preference
and don't vote anyone equal to or over
their favorite. Etc.
Are you saying that methods meeting my preference-mentioning criteria
can act wrongly when the preferences aren't
as stipulated? If so, then say so explicitly, and show how that can happen.
As a matter of fact, that _can_ happen with some votes-only criteria,
such as the Plurality Criterion:
The Approval bad-example is an example of that. I'll give it again here:
Sincere preferences:
49: C
27: AB
24: BA
A majority _equally strongly_ prefer A and B to C.
Actual votes:
The A voters defect, in order to take advantage of the co-operativeness and
responsibility of the A voters:
49: C
27: AB
24: B
Now, in MDDTR and MMPO, A wins. According to the Plurality Criterion,
that's wrong.
But it's only wrong if the B voters aren't voting for A because they
don't prefer A to C
as much as the A voters prefer B to C.
Given the preferences, and the explanation for the actual votes, the
Plurality Criterion is wrong
when it calls the election of A a wrong result.
So yes: A criterion can rule wrongly, based on an incorrect built-in
assumption about true preferences.
But the Plurality Criterion is a votes-only criterion. So that problem
certainly isn't peculiar to
my preference-mentioning criteria.
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