Gene Gallagher <[EMAIL PROTECTED]> wrote:
> Date: Thu, 30 Nov 2000 12:57:30 GMT
> From: Gene Gallagher <[EMAIL PROTECTED]>
> Subject: Florida votes and statistical errors
>
> There seems to be some misunderstanding in the press about a fundamental
> difference between a sample of a larger population and a complete
> census.
>
> J. A. Paulos in his NY Times article ‘We're Measuring Bacteria With a
> Yardstick'
> http://www.nytimes.com/2000/11/22/opinion/22PAUL.html
> stated:
> "Not to be too cryptic, let me simply state that the vote in Florida is
> essentially a tie. The totals for Al Gore and George W. Bush, out of
> nearly six million votes, are so close that the results are
> [snip]
>
> Steven J. Gould has seconded this opinion in today's (11/30) Boston
> Globe:
> http://www.boston.com/dailyglobe2/335/oped/Heads_or_tails_+.shtml
> "Unfortunately, in making a deadly serious, even prayerful, case for the
> fairness of coin flipping in this circumstance, we must fight both the
> greatest failure of education and the deepest foible of the human mind;
> our propensity to misunderstand probability ... So flip a quarter ...
> Let the fortunate man win, and the United States triumph."
>
> [snip] When it
> comes down to counting a finite and relatively small number of ballots,
> with strict standards, there need be NO sampling error. Debate the
> standards about dimpled chads and what counts as a vote, but don't throw
> up your hands citing inappropriate probability theory and argue that
> Supreme Court Justice Rhenquist should toss a quarter in the air to
> decide who will be president.
>
> Reference
> Pielou, E. C. 1969. An introduction to mathematical ecology.
> Wiley-Interscience, New York.
>
> - --
> Dr. Eugene D. Gallagher
> ECOS, UMASS/Boston
>
1) Thanks for the refs, especially to one of my favorite authors, Steven J. Gould.
2) Suppose we define the population as the ballots cast, and we wish to assess
the "peoples' will" as recorded. In this case, if we do a full count, a binomial
dist. is not an issue, as you pointed out.
3) However, as Dennis Roberts pointed out, there remains an error to contend
with. This is the measurement error which all inspectors contend with. Below is a
short piece in which I used the occasion of the election to remind practicing
Quality people (some of whom do statistics!) of the _measurement_ error, which
doesn't go away, no matter how you design the ballots, paper or electronic.
4) The problem the election commissions in each state face is to minimize the
'gray zone' of uncertainty about the voter's choice(s). For the famous punch paper
ballots, I heard regions of uncertainty between 0.002 and 0.05 (5%) of ballots
cast. 500 of 6 million votes is under 0.0001 error, under even the lower
uncertainty assessment. On this _physical_ basis, we could claim the election a
tossup. In Colorado a tie vote was decided by high hand in 5 card stud poker. A
tossed coin is no different, if it really has different faces, and is tossed
correctly.
5) Electronics isn't the total answer. Cases have been noted of poll workers
accidentally erasing electronic records for whole precincts - hundreds of votes.
6) In addition, what we really need is for some _feedback_. Give the voter a
device that will read the ballot, and tell the voter what will be recorded,
_before_ adding to the tally. That way, they will have increased confidence that
their vote will be recorded as they want. Do we really believe that 'every vote
counts'?
Ballot Counting, Inspections, and ‘Gray Zones’ of Uncertainty
Jay Warner, Ph. D., CQE, CQA, Warner Consulting, Inc.
Yes, the vote counting in Florida is a mess. Exactly what sort of mess seems to
depend mostly on ones political persuasion. (As I write, the legal beagles are
proving to be more pit bulls than beagles.) Students in statistics courses should
plan on analyzing the Florida vote counts and miscounts for years to come. We who
regularly do careful measurements and evaluations can draw a lesson from the
excitement.
When a ballot is received the counter, a machine or person, has to decide if the
vote is valid or invalid. Friends, this is a dichotomy ? the inspected ballot is
either one way or another. A ballot cannot count as half a vote.
However, in the physical world there is no such thing as a pure dichotomy. There
is always a gray zone, when the choice ? one side or the other ? is not clear. In
the case of an ink ballot counted by machine, the machine has to decide if a mark
is dark and large enough to qualify as a vote for one candidate, or none. Two
marks or one very large mark, of course disqualify the ballot altogether.
One may think of this gray zone as a band between clearly one side and clearly the
other side of the dichotomy. The gray zone is always there. It won't go away.
This is reality.
In the case of punched ballots, we are all learning about the facts. If a hole is
punched cleanly and cleared of ‘chad,’ the material from the hole, it is clearly
punched. If the chad clings to the sheet long enough for the counting machine to
‘see’ it, then the vote is not tabulated. When a hand assessment of the
non-tabulated ballots is made, the person may record the 'pregnant chad' or even
dimple, as a vote. At some point the depression which is a dimple will be so small
it is counted by the person as a non vote. The gray zone appears again, between
these two amounts of dimple. Let's let the Florida poll workers decide how much
dimple is a vote.
Now, what about the situations we _can_ control? The ballot counting problem is
the same situation as an inspector who must decide if a product is OK to accept.
The bookkeeper working out sales commissions must decide who contributed to each
sale. One of my uncles was final inspector for airplanes about to go on
international flights. Same type of question, same kind of decision. The stakes
may be arguably less for a product inspector than for a Florida poll worker, but
the issue is identical.
The inspector and those supporting the inspector must set up clear measures and
guides, plus ensure the inspector is properly trained, with the aim to minimize the
gray zone. Then we all must stand back and let the inspector decide. We can
change the inspection criteria so inspectors will make different decisions in
future, but don’t change an inspector’s past decision. If someone changes a
decision, then that person has taken over the inspector’s job. We might as well
let the inspector go on to other activities.
One thing is for sure. We don’t want our production areas and offices to get mired
the way Florida is, or is not, recounting ballots. Recognize that gray zones
always exist. Give the ‘inspectors’ clear instructions and training, then let them
do their jobs. Meddling with inspectors is nonproductive. Management’s job is to
plan for and deal with the results, not deny them.
Jay
--
Jay Warner
Principal Scientist
Warner Consulting, Inc.
4444 North Green Bay Road
Racine, WI 53404-1216
USA
Ph: (262) 634-9100
FAX: (262) 681-1133
email: [EMAIL PROTECTED]
web: http://www.a2q.com
The A2Q Method (tm). What do you want to improve today?
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