[EM] IRV vs Plurality

[robert bristow-johnson]

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."