On Jun 21, 2011, at 7:56 AM, Markus Schulze wrote:
Hallo,
Eric Maskin, a Nobel laureate, is currently very
active in promoting the Black method.
i have to confess, even though i had heard of ranked-choice voting
before and had myself thought that what would later to be learned is
called "Condorcet compliant" was the only logical and consistent (with
a simple majority binary vote in all binary cases) manner to decide
it. and i thought of the possible problem that there was no single
candidate who wins every pair they're in, didn't know what to call it,
and didn't even know if there were any theorems that spoke to it, and
decided not to worry about it.
anyway, because i'm a real neophyte to this, it wasn't until sometime
last decade that i read anything about it until i read a Scientific
American article of his titled "The fairest vote of all" that promoted
Condorcet, but didn't really call it that. Maskin labeled the method
"true majority rule" and only obliquely raised the issue that a cycle
could happen and mentioned Condorcet in that context. soon after i
learned the terms from the Wikipedia articles and at about the same
time, we voted in IRV by about 65% (which was repealed in 2010 in a
dramatic but really stupid slugfest between the one true faith "One
person, one vote" crowd and those who denied anything went wrong in
the 2009 election).
anyway, especially after reviewing his bio again, i can't help by
admire the guy and it was an article of his that first got me thinking
analytically about the voting systems issue. but i wonder if he was
using terminology that was more neology, even pre-neology. i think he
was trying to coin a term that would end up getting attached to his
name.
and we've all been groping for a name for this primary voting criteria
that is not this non-American, Frenchie, probably sorta pinko-
socialist secular humanist "intellectual" (did i mention *not*
American?) whose heresy is leading us away from the One True Faith of
the Single Affirmative Vote. we have sects in the One True Faith,
some of us believe in the sanctity of the Two Party System: "if yer
ain't fer us, you agin' us. and pass da ammunition, Ma."
i don't have a better idea than "true majority rule". but there must
be a better one than that. Warren, i remember you like "beats-all
winner" for the CW. i wonder if the "beats-all method" is a good label.
The Black
method says: If there is a Condorcet winner, then
the Condorcet winner should win; if there is no
Condorcet winner, then the Borda winner should win.
i hadn't heard of the Black method before, but just reading this shows
pretty superficially a problem. above is one way to say something...
See e.g.:
1 Sep 2009: http://research.microsoft.com/apps/video/default.aspx?id=143268
8 Apr 2011: http://www.youtube.com/watch?v=Bx_lt06W9Ww
Maskin argues as follows:
If election method X is the best possible
election method in domain X and if election
method Y is the best possible election method
in domain Y and if domain X and domain Y are
disjoint and if domain X and domain Y together
cover all possible situations, then the best
possible election method is to use election
method X in domain X and election method Y in
domain Y.
Maskin argues: "domain X" = "situations with a
Condorcet winner"; "election method X" = "any
Condorcet method"; "domain Y" = "situations
without a Condorcet winner"; "election method Y"
= "Borda method".
... and this is another way to say the same thing. so, right away,
Maskin is just restating an assertion as some sort of argument
supportive of the assertion, but it is nothing new. just a re-
assertion. (is that what is "begging the question" is?)
at the core, let's assume that we are already disciples of Condorcet,
we all agree that method X is best for domain X, he doesn't say squat
about why method Y is preferred in domain Y. if we're nowhere near to
a conclusion that Borda is good for anything (he might have been a
good general, i dunno), then how do we conclude that it is preferable
to everything else when there is no CW? sorry, i haven't even got
past this block.
Maskin's argumentation doesn't work because
of the following reason: Whether an election
method is good or bad depends on which criteria
it satisfies. Most criteria say how the result
should change when the profile changes. Now it
can happen that the original profile and the
new profile are in different domains. This
means that, to satisfy some criterion, election
method X for domain X and election method Y for
domain Y must not be chosen independent from
each other.
but, this is the fundamental argument of those who claim that it is
natural for an election to be spoiled, to be dependent upon irrelevant
alternatives. isn't that what the fundamental issue is about for why
Condorcet (assuming a CW exists) is consistent with any simple-
majority, two-candidate election where every vote carries equal
weight? that's what's fundamental about it, it is consistent to the
concept that if Candidate A is preferred to Candidate B, Candidate B
is not a winner, and being consistent with the result when the profile
changes in that manner is both tangible and operational (we can get a
handle on it and doing it differently, like using IRV instead, makes a
difference).
Example:
The participation criterion says that adding
some ballots, that rank candidate A above
candidate B, must not change the winner from
candidate A to candidate B.
does Black do this?
Election method X satisfies the participation
criterion in domain X. Reason: If candidate A
was the winner in the original profile and if
the original profile was in domain X, then this
means that candidate A was the Condorcet winner
and, therefore, that candidate A pairwise beat
candidate B. If candidate B is the winner in
the new profile and if the new profile is in
domain X, then this means that candidate B
is the Condorcet winner and, therefore, that
candidate B pairwise beats candidate A. If
candidate A pairwise beat candidate B in the
original profile and if candidate B pairwise
beats candidate A in the new profile, then
this means that the added ballots rank
candidate B above candidate A.
okay, since adding a positive number to the margin increases the size
of the margin, and since, if there is no cycle (domain X), the
Condorcet winner is decided *solely* by the margins (even the signum
function of the margins), that sufficiently satisfies the
participation criterion, no?
Election method Y satisfies the participation
criterion in domain Y, because the Borda method
satisfies the participation criterion in general.
However, election method Z doesn't satisfy the
participation criterion since the Condorcet
criterion and the participation criterion are
incompatible.
whoa. the Condorcet criterion is not assumed for Z unless domain Y is
empty. and isn't participation and Condorcet with no cycle
compatible? of course it's not guaranteed to satisfy participation
for all possible situations in domain Y. that's not even the point is
it? Maskin isn't saying that the participation criterion makes Borda
the *best* alternative method from the POV of disciples of Condorcet,
is he?
In short: Even if election method X satisfies
criterion A in domain X and election method Y
satisfies criterion A in domain Y, it doesn't
mean that election method Z satisfies
criterion A. Therefore, Maskin's argumentation
doesn't work.
but is Masking saying that? i'm groping for a definition of what he
means by "best possible election method". i can't tell that he means
"participation criterion" when he says that in his construction that
you apparently quoted.
***********************************
I also question the claim that the Borda
method is the best possible election method
in situations without a Condorcet winner.
Bingo!
to mix metaphors, that's where the argument never really gets off the
ground at square 1. and restating it over and over does not provide
evidence nor proof.
not that i can't accept some principles as axiomatic. like
fundamentally the "one person, one vote" value for all persons of
franchise. all i can say is "why shouldn't that be the case?" for
that one.
interesting, Markus, to bring Maskin back to our attention.
thank you.
--
r b-j [email protected]
"Imagination is more important than knowledge."
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