it's been pretty quiet around here, lately.
Jameson, you had an example to illustrate a point, and when i examined
it, it appeared to not do (change the winner) what you were
suggesting. would you look that over and maybe adjust the numbers to
illustrate the point you wanted? also, i would like to know what the
"trembling-hand equilibrium" strategy is?
i'm not asking any of this rhetorically or to challenge. just curious.
L8r,
--
r b-j [email protected]
"Imagination is more important than knowledge."
On May 29, 2010, at 2:30 PM, robert bristow-johnson wrote:
On May 27, 2010, at 1:09 PM, Jameson Quinn wrote:
now ask yourself the question whether or not Condorcet satisfies
these criteria (assuming a CW exists).
Of course it does, because you only included the anti-strategy
criteria which it does pass.
they're more like basic principles of a fair and predictable (in
behavior) election system. they're almost axiomatic. if one were
to take issue with any one of those 6 principles, i would ask them
to defend their objection or devaluation (relative to other criteria
that might be seen to compete against those 6) of any of those 6
principles on a fundamental philosophical level. i know there are
other election criteria of "goodness", but those are the salient ones.
But what do you call this:
Hypothetical true preferences:
39.4: D>H=C
30.8: H>C>D
27.6: C>H>D
2.5: NOTA
H is the condorcet winner. But if just 8% from the C voters instead
vote C>H=D (or 4% of them vote C>D>H, if equal rankings aren't
allowed), then there is no Condorcet winner, and C could win.
so, you're saying that if 4% of the voters bump their preference of
H down, then H no longer wins outright. that might be expected.
i'm gonna scale this to integer quantities (dunno what to do with
NOTA):
394: D>H=C
308: H>C>D
276: C>H>D
the "NxN" matrix in my preferred triangular form:
H>D 584
D>H 394
H>C 308 C>D 584
C>H 276 D>C 394
now 80 C voters hypothetically change their mind to:
394: D>H=C
308: H>C>D
196: C>H>D
80: C>H=D
H>D 504
D>H 394
H>C 308 C>D 584
C>H 276 D>C 394
i dunno, but i still see H as the Condorcet winner. what am i doing
wrong, Jameson?
My APV proposal does very well on this and other scenarios.
Specifically, for this scenario, the pure strategy which is closest
to being a trembling-hand equilibrium is the "good" situation where
H wins in one round (Not true of Approval, Bucklin, margins
Condorcet, Range; IRV is the only "major" system I know of which
passes this test). And it is monotonic, and, unlike IRV, unilkely
to fail to find a centrist Condorcet winner.
again, even though Condorcet seems to favor the centrist over either
extreme, that is not the reason Condorcet is fairer than methods
(like IRV) that favor the centrist less. the main reason the
Condorcet winner (if one exists) should be elected to office is,
compared to any other candidate, the CW is the candidate the
majority of voters prefer when asked to choose between the two. it
is the simplest extension of the concept of "simple majority" rule
from the two-candidate context (where we all agree how the votes
should be counted) to the multi-candidate context. i don't think
centrism is such a bad byproduct of Condorcet, but i would still be
plugging Condorcet even if it tended to favor the centrist less.
In fact, I can't think of a single scenario where the pure strategy
closest to being trembling-hand equilibrium doesn't give an very-
arguably "right" answer in one round for APV. And I can easily get
IRV to give the wrong answer, so APV is the only system I know of
which pass this test.
what is the "trembling-hand equilibrium" strategy? i dunno what
that is.
bestest,
--
r b-j [email protected]
"Imagination is more important than knowledge."
----
Election-Methods mailing list - see http://electorama.com/em for list info
