[EM] IRV vs Plurality
robert bristow-johnson
rbj at audioimagination.com
Sat Jan 16 15:40:09 PST 2010
On Jan 16, 2010, at 5:26 PM, Kathy Dopp wrote:
> On Sat, Jan 16, 2010 at 5:22 PM,
> <election-methods-request at lists.electorama.com> wrote:
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> I give up. Both Abd ul and I have tried to explain this to Robert
better leave Abd ul out of your claim, Kathy. let him speak for
himself.
> with Abd ul even listing all the possible unique ballot orderings when
> there are 3 candidates, and Robert still doesn't get it.
Kathy, you failed about the numerical stuff because it is *you* that
do not understand.
you said, for 3 candidates, there would be 9 Condorcet tallies
(thinking that i mixed it up) and i corrected you with the number 6.
there are 6 head-to-head tallies to count and send up the pike to the
central election authority if the election were known to be decided
by Condorcet rules. not 9.
and, for 3 candidates, there are only 9 consequentially different
manners to mark relative preferences. assuming (and that is the case
in Burlington) that some dumb voter ranks A as 2nd, B as 3rd and D as
4th and leaves the ballot unmarked otherwise, that is treated no
differently than if the voter marked it A 1st, B 2nd, and C 3rd. and
*that* is *no* different (as a ballot counting consequence) than if
the voter marked it A 1st, B 2nd, and left the ballot otherwise
unmarked. by being unmarked, C still comes in last in any manner of
counting.
> Can anyone else that Robert may be more willing to comprehend, please
> try to explain how to list and count or how to caculate the number of
> unique ballot combinations with rank choice voting to him?
they won't be able to do it, Kathy. and it's not because i "doesn't
get it". i does.
i don't want to make "appeal to authority" arguments, particularly if
such would appear to be a self-referential appeal to authority.
but i've had a few university courses in mathematics. not so many in
discrete mathematics, but several in probability, random numbers, and
random processes. in such courses, we learn how to formally count.
we learn how to count how many ways to put N balls into n bins.
that's where you get those nifty little factorial expressions. and,
Kathy, you have a handle on it, sorta. your "15" was a meaningful
count, but considering how any of the tabulation procedures would,
you didn't realize that some piles can be combined, and then how to
use that knowledge to adjust the count.
you're implying that, for N candidates, that the number of
consequentially differentiable ways to mark the ballot is
N-1
SUM{ N!/n! }
n=0
but, i'm saying one of the terms in that summation (the n=1 term) is
for permutations that have no consequential counting difference to
other permutations being counted (by the n=0 term). so i subtract
out the n=1 term, and it's the correct thing to do.
N-1
SUM{ N!/n! } - N!/1!
n=0
hell, since 1! is the same as 0!, we could say that that we'll keep
the A>B label and fold all the A>B>C ballots into the A>B pile. then
it's the equivalent
N-1
SUM{ N!/n! } - N!/0!
n=0
or simply,
N-1
SUM{ N!/n! }
n=1
With N candidates, that is how many consequently different manners
one can mark a ranked ballot. there can be tallies for each, those
tallies are precinct summable, and those are the only numbers that
need percolate upward to the central counting facility. it doesn't
matter what the counting method is, IRV, Condorcet, Borda, Plurality
of 1st choices (or other rank threshold). all of the information is
in those piles, and if N=3 the number of piles is 9.
take a course in probability, Kathy. learn how many different hands
in poker can be a pair or three-of-a-kind or a full house. learn to
count, formally.
> Also, someone else besides myself needs to tell Robert how many
> tallies there are with the Condorcet method as well because he insists
> on using a nonsensical formula for that too.
>
> Thanks. Robert obviously thinks he is too smart to learn anything
> from me,
no Kathy, it is precisely the other way around. you *think* yourself
as some sort of "expert" (and Abd ul seems to accept that
uncritically). and maybe you are about some things regarding
security. but you actually *don't* understand the mathematics of
"permutations and combinations". when talking about "precinct
summability", and the complexity (i.e. number of piles) of an
information processing method (and that is what we *are* talking
about, it's about processing information) it is *you* who do not know
who you are up against.
i realize that there are some mathematicians on this list and i know
that Warren Smith is one of them. you might have noticed in the past
that i haven't locked horns with Smith about specific mathematics,
only about political or electoral philosophy (that sets the rules
that the math deals with later) and i've been arguing with everyone
on this list about making the case for some system and defending it
with *specific* examples with vote counts that they had dreamed up.
the professor i had in Real Analysis 3 decades ago had this to say
about some of our "proofs" that he marked wrong. it would be one of
these "given an epsilon>0, find a delta so that..." sorta proof (like
for continuity or differentiability). he said "*You* don't get to
choose the epsilon. The Devil hands you an epsilon>0 and you still
have to find a delta that can still beat the Devil." that's the
philosophy that you guys need to take here regarding supporting
election systems. it's okay to create counter examples to disprove
someone else's sweeping claim, but creating nicely chosen scenarios
to show how well some system works doesn't carry water for me.
BTW, my background is that of a signal processing algorithmist for
audio and music. for a quarter century, i've been ABD for a PhD in
electrical engineering. i've taught at Northwestern University, the
U of Southern Maine, and once at UVM (the "VM" stands for VerMont) as
an adjunct. i have never met Prof Tony Gierzynski, a committed IRV
opponent who has done some nice vote counting that confirms the
numbers i have (to within 4 ballots, but it doesn't change any outcome).
we study this discipline called "information theory" (Claude Shannon)
that also contributes some formal methods in determining "how many
bits" a particular message inherently requires. whether it's the
President getting on the phone to the Strategic Air Command to tell
them to "bomb the hell outa them" or it's voters getting on their
ballots that "we like Candidate A, then B, then C", it's a very
similar information theory kind of problem. similar to how to
reliably transmit information from ballots to election officials.
> so someone else will have to try to educate him.
unlike you, Kathy, i'm a lifelong student. and, at 54, i've also
seen a few things and dealt with systems of significant complexity
(and gotten paid for it). one of my favorite contributions i like to
make to the scholarly pile is to cut through unnecessary complexity
and boil something down to the kernel of the issue. for audio signal
processing geeks, an example that's public-domain is http://
www.musicdsp.org/files/EQ-Coefficients.pdf which has later become
http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt and has about
6900 references on the web and 1000 in Google Scholar (none that i
know of are negative references). i dunno how many hits i get in
Google Scholar, far less than a "real" academic. i just checked and
it's 9 more hits than you get Kathy.
it's *you* that do not get it, Kathy. neither quantitative nor
qualitatively.
and you're not very forthright, either. you said earlier that you
weren't attached to any partisan party (and given your definition,
you meant like Dems and GOPs and Progs). i've just been to http://
kathydopp.com . it says you're a Greenie. you implied earlier that
you had no party affiliation (and here i was only accusing you of
being a rabid anti-IRV partisan) and that was not true. your
credibility just took a nasty hit. now we're gonna have to verify
*every* claim you make that isn't ostensibly taken for granted.
> Cheers,
why, thank you.
and may your evening be as the same.
L8r,
--
r b-j rbj at audioimagination.com
"Imagination is more important than knowledge."
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