[EM] IRV vs Plurality (back to the pile count controversy)

[Abd ul-Rahman Lomax]

At 01:48 AM 1/21/2010, robert bristow-johnson wrote:
>the fact is, transmitting the content (to a central counting
>location) of *every ballot* is the transfer of a finite amount of
>information.  that is even *more* general than sorting to piles and
>transmitting the tallies for piles.

Yes, of course. And this is an equivalent to carrying all the ballots 
to a central location, merely, if done, say, over the internet, faster.

But ... it raises some security issues. And with central counting 
there are other issues. This is a red herring, because we are talking 
about precinct summability, and when the number of candidates is very 
small, precinct summability isn't relevant, because the raw ballot 
data may be transmitted.

So, back to the real question: is precinct summability an important 
practical criterion to be applied to voting systems? A related 
question is the sensitivity of the method to small variations in 
votes. Noise, if you will. That can be seen with Yee diagrams, in the 
presence of chaotic regions in issue space, with IRV. But I won't 
address that here, beyond noting that IRV multiples the probability 
of ties, and many of the ties will drastically flip the overall 
result. With most other methods, there is only one relevant tie 
possible (beyond extraordinarily rare three-way ties) and when this 
happens, a coin flip doesn't change the expected voter satisfaction 
much, if at all. With IRV, the effect can be enormous, because the 
tie can affect a candidate elimination before all the votes for that 
candidate have been counted.

>but breaking it down to piles regarding every conceivable permutation
>of candidate preference is *still* breaking it down to a finite
>number of piles.

Sure. "Finite." I'll point out that a google is finite. With 
computers, this can be done even with moderately large numbers of 
candidates. It's still a problem with voting security, though. I've 
argued for Public Ballot Imaging, which would make available actual 
ballot images, transmitted from polling places, perhaps by fax or 
more likely through digital camera images -- no touching of ballots 
necessary except by election officers, all visible openly --, 
independently by voting watchdog organization through election 
observers, so that anyone can verify the count in a precinct or as 
many as they care, or can even just check one serialized ballot 
(serialized before counting) and mark it as reviewed, in a system 
that collects and displays such reviews. Many details omitted here!

>   for 3 candidates, that number is 9.

Okay, three candidates, A, B, C, the ballot possibilities are, to be 
complete, much more than 9. I'll assume that write-ins are illegal 
and void the ballot. Some of the possibilities are legally equivalent 
to others, and in actual IRV ballot imaging, they are collapsed and 
reported the same, to the displeasure of voting security people who 
do want to know the "error rate," which includes overvoting and exact 
overvoting patterns. So-called ballot images are not, generally. They 
are processed data reducing a ballot to legally equivalent votes. The 
reduced set is this:

A
B
C
A>B
A>C
B>A
B>C
C>A
C>B

Note that this assumes a 2-rank ballot. It also assumes that majority 
vote isn't important. If it's important, as it would be in an IRV 
election under Robert's Rules, we have some more possibilities. They 
are all the three-rank permutations.

A>B>C
A>C>B
B>A>C
B>C>A
C>A>B
C>B>A

Each of these is equivalent, for the purposes of finding a plurality 
winner, to a two-candidate combination.

>   if you or
>Kathy say it's 15, then you're wrong (and it's your slip that's
>showing).

Well, I won't speak about Kathy, but in terms of practical elections 
in the U.S., she's right. You did not state enough information to 
establish your reduced count, and you actually added language that 
indicated that a larger total would be necessary. You used the 
qualifier "credible" to indicate that there might be candidates not 
"credible," and you did not take care to define this. What you have 
asserted is true under two qualifications: there are only three 
candidates legally eligible to receive votes. And there are only two 
ranks on the ballot. If there are three ranks on the ballot, we have 
a poor situation, an invitation to voters to cast an irrelevant vote, 
if, in fact, that third rank has any effect on outcome, which, in the 
general case, it can. If it can affect outcome in some way, the piles 
must be reported separately.

>   for 4 candidates the number of necessary piles is 40.

Under the restricted conditions, perhaps. I haven't checked the math. 
I distrust formulas compared to exhaustive enumeration, they take 
more work and there is more room for error. My lists, which I 
provided before, showed what is shown above, though it may be better 
explained this time.

The "slip" is an assumption that one's analysis is more complete than 
that of another, when it may be, instead, ignorant of some of the 
possibilities and implications. The slip betrays both ignorance and 
arrogance, a dangerous combination.

Hint: the smartest response, if it's a possible one, is "Oops! Never 
mind!" And then you move on to more substance, having learned 
something. Maybe even something very important. If it's not possible, 
if, for example, I'm the ignorant and arrogant one, then, I'd 
suggest, you probably will have to become much more cautious and 
careful in your expression. Or I'm ready for the old folk's home. An 
appealing idea, sometimes. Am I ready for it yet?

>   for
>N candidates, the number of piles necessary, P(N) is
>
>            N-1
>     P(N) = SUM{ N!/n! }
>            n=1
>
>not
>
>            N-1
>     P(N) = SUM{ N!/n! }
>            n=0
>
>which is appears to be the formula you and Kathy continue to insist
>is correct.

Which it is under some conditions and yours is correct under some 
conditions. I assume. I haven't checked them because it's more work 
than I can put in now.

>   and whether Kathy has an MS in Mathematics or not,
>whether you do or not, this error is demonstrable.

Cool. Examine the arguments and evidence I provided, and see if you 
can sustain that position. Hint: there are many people who have tried 
to do that, the roadside is littered with their virtual bodies, they 
managed to convince none but themselves. Easily, I make mistakes, but 
... I *love* it when someone can point them out. Please. Be my guest.

>   you and Kathy
>continue to insist that there is a consequential difference between
>ranking all candidates and ranking all but 1 and leaving one
>candidate unranked and i continue to say there is no consequential
>difference.

Under some conditions you are correct. However, the conditions under 
which you are correct won't occur in actual U.S. primary elections 
unless there are only three candidates legally eligible to receive 
votes. Which means, in practice, a maximum of two on the ballot. And 
often, in such elections, IRV isn't used anyway, the rules provide 
for a preferential ballot only if there are more than two ballot 
candidates. Wake up, Robert, you are debating with people who 
frequently know much more than you, and if you want to survive that 
with some benefit for yourself, you will need to, much more rapidly, 
come up with "Ooops! Thanks for pointing that out!"

>   this is a difference of falsifiable claims that form a
>dichotomy.    we can test which claim is correct.

Sure. But I'd already enumerated the ballot possibilities, and, now, 
you have made your claim in such a way that the difference is a 
little more visible, but you still haven't accurately stated the 
conditions and restrictions. Chalk it up to inexperience, we all 
start there, but it's what we do then that determines whether we 
learn or not, or merely practice bluster and entrenched belief in 
personal rightness.

Okay, back to meta even more:

>>In person, face-to-face, people would fall over laughing, and
>>whatever value there was in your position would be lost.
>
>you've never used humor to make a point?

That's what I did. What was your humor?

>   or to make clear the
>lameness of an irrelevant reference?

Really worked, eh? Robert, your views and approach are quite narrow. 
If you want to be effectively politically, you will need to learn to 
see yourself as others see you. Not easy, I'm sure. But necessary.

>whether one responds to an irrelevant distraction with humor or not
>changes nothing regarding the core issues.

Absolutely. Unless you are engaged in advocacy and care about 
results. For that, you will have to deal with people as they are, not 
as you wish them to be.

>certainly if a ridiculously large number of candidates are on the
>ballot, manually separating ballots into piles (without grouping
>together minor or non-credible candidates) is not practical.

How large is ridiculously large?

>   even
>with 4 salient candidates, 40 piles gets pretty nasty for sorting by
>*hand*.

Indeed. But notice the incorrect assumption: "salient." Robert still 
has not faced this issue, even though it's been covered in these 
discussions. How do we know if a candidate is "salient" or not?

>   but 40 is still a pretty small number for a computer and a
>modern network.

Thus raising the hackles of every voting security expert.

>a national election with 3 credible candidates can easily be
>"precinct summable" with 9 salient piles and 31 less important
>piles.

There are no national elections, to start with. It just looks like 
that. But if we are discussing proposals, including some hypothetical 
national presidential election using IRV, requiring either a federal 
constitutional change or changes in many state constitions, a very 
complex matter, in fact, we can now ask, again, what is 'credible.' 
Whose votes get transmitted to central counting as sums in piles? 
This situation requires one central counting facility for the entire 
United States, it can't be done state by state. And an error in a 
single precinct could flip the result.

"Less important piles." A world of error is covered under these 
words, that are undefined by Robert. Were he to attempt to define 
them explicitly, he'd see his error. "Credible." Same thing. How do 
we know which candidates are credible? What is the algorithm, specify 
it, such that all information necessary to determine an election can 
be transmitted for central counting with no more reference to the 
precincts where ballots are actually sorted.

>   it doesn't matter if it is IRV, Condorcet, Borda or what.
>the issue of summing pile count is not dependent on what tabulation
>method is used (and what, *i* think, should be what the debate is
>about).
>
>neither you nor Kathy have shown *any* problem of "precinct
>summability" regarding IRV or any other ranked-ballot method.

Robert ought to know that this is a dangerously ignorant statement, 
because of the broad acceptance of the summability criterion as 
important, by those who have considered the issue. In a real U.S. 
election using IRV, the method must be able to handle any number of 
candidates in short order. Robert has made a drastically simplifying 
assumption, without specifying how this assumption would be 
established, what it actually means. It's true if and only if there 
are only three candidates eligible to receive votes. We can make one 
simplifying assumption: write-in votes, in a two-candidate election 
(two on the ballot) can be summed, but this will require a contingent 
recounting under some conditions. Might be tolerable. This is the 
only situation where the drastically simple precinct sum is what 
Robert claims. With three "credible candidates," it's actually four 
that must be considered. And there are frequently more. In general, 
the number of candidates who must be totalled are minimum four in an 
"IRV" election, if we except the occasional use of IRV when there are 
only one or two candidates on the ballot.

A vote of A>B>C, is that the same as A>B? Robert assumes, yes. But 
what about write-ins? A>B>C is equivalent to A>B>C>W. Not to A>B>C. 
The former is a vote that is C>W, the latter is truncated. (Pointing 
out one of the problems of IRV, by the way, its behavior with 
write-in candidates. It slaughters them, by providing a default vote 
against then from every ballot that doesn't explicitly rank them.... 
whereas with a candidate on the ballot, behavior is different. but 
that's another story.)

>not that i am a defender of IRV.  but, you haven't laid a hand on it
>regarding "precinct summability".

I didn't use my hand. I used my head.

>   IRV has a few pathologies, which i
>think i understand better than either you or Kathy, simply from the
>lame and partisan arguments (and wholly verbose) i read coming from
>that direction.

As to Kathy, she's a voting security expert, not a voting systems 
expert, and she comes here to learn as well as to express her 
security concerns. As to me, let's, say, Yes. You think so. 
Obviously. Now, what does that mean?

>even though *now* Kathy seems to be paying some attention to
>Condorcet, before this last week, i haven't noticed any such
>attention about that from her.  it was always just how bad IRV is,
>and that it's worse than any other method, including FPTP.  and when
>she (or you) says that, then i am convinced that she (or you) are
>simply anti-IRV partisans that don't really consider what the
>*commonly* *known* problems are that associated with the traditional
>FPTP (or even 2-round with runoff) methods for which motivated us to
>adopt IRV in the first place.

I'm fairly sure that you understand very little about the problems 
and benefits of runoff methods; some of what you think is a problem 
is actually a benefit. That's another story.

>so, before pointing out that someone's slip is showing, it might be
>safer to adjust where one's own fig leaf is hanging.

I threw the fig leaf away years ago. What you see is what you get. 
Take it or leave it.