Subject: tc-list Clarification

From: Timothy John Finney <[email-masked]>
Date: Thu, 29 Jan 1998 11:09:38 +0800 (WST)

I said the following. (By the way, sorry for the grammatical error in that
post. It should have been students', not student's): 

> >All this leads me to pose a question for a statistician to answer:
> >
> >If we have n judges with reliabilities r(n), what is the reliability of a
> >majority decision? Please give an answer for (a) independent judges,
> >and (b) judges which are not independent. (Many of the criteria tcers
> >use are not independent: they correlate.) Assume that the judges are only
> >judging between two possible states (although they are often judging
> >between more than two in real situations).

To which Bob Waltz replied,

> This needs to be clarified. How independent are the judges in case (b)?
> Also, what constitutes reliability? Accuracy in guessing the original
> reading? Or consistency in applying some set of rules?

For the general case, say that each judge may be correlated with each
other (i.e. the correlation coefficients for all cross combinations are
somewhere in the range of 0.0 to 1.0.) Reliability is accuracy in choosing
the original reading. There is no way to measure it directly -- we would
need the original Greek for that. Of Course! Use Westcott and Hort!  (Only
joking.) Otherwise we could estimate the reliability of a criterion by
seeing how often it selects the readings chosen by the majority vote of a
group of textual experts using diverse approaches. 

Bob also pointed out that old and new readings can coexist. I think that
Kurt Aland was recht when he said that NT readings are tenacious and that
the original readings are still there among the variant readings (my
paraphrase). What is interesting is when the relative frequency of
readings changes with time. This has happened with Heb 2.9. Now CARIS (C =
chi) is most frequent (among manuscripts), but in Origen's day CWRIS was
(according to Origen). So we see one reading being displaced by a more
'suitable' one. Now here's the rub. Was the trend caused by a corrupting
or restorative force? If corrupting, extrapolate backwards along the trend
line to get the originally more frequent reading and, consequently, the
reading with a higher probability of being original. The problem is that
uncertainties become very large in the earliest times because of the very
small sample size of extant manuscripts -- there are big error bars on
early relative frequencies. 

On the question of judges, I received this message from Steven Reed in
Japan:

> First, I know there are mathematical proofs in voting theory along the
> lines of if every voter has a greater than 0.5 probability of being
> correct on some issue, the majority will be more often right than any
> single individual.

If this is true, it means that we can be more confident of majority votes
than I thought. I think that the independence of voters would be a major
factor in the outcome. That is, I think that votes should be conducted by
secret ballot without comparing notes beforehand. Also, I suspect that the
foregoing result would rely on there being a large number of voters.  Many
textual experts with diverse approaches could participate in secret
ballots via the internet, providing a more reliable means of selecting the
most likely original reading (or the fittest reading for the present
paradigms). 

Yours megalomaniacally,

Tim Finney.

---

From: "Robert B. Waltz" <[email-masked]>
Date: Thu, 29 Jan 1998 08:38:13 -0600

On Thu, 29 Jan 1998, Timothy John Finney <[email-masked]>
wrote:

(I'm only going to reply to a few parts of this; I haven't had time
to think through the theory, so I'm just making obvious mathematical
points.)

>somewhere in the range of 0.0 to 1.0.)

I'm afraid this won't work. Correlation is not dependence. Correlation
can explain how *connected* things are, but not how. In other words,
it cannot explain; it's only an observation.

To give a comparison: Take two voters belonging to the same political
party, but in different cities. They have never met, and do not read
the same newspapers or watch the same news programs. Yet the correlation
between their voting records in national races will probably be in
excess of 80%. Correlated, but not dependent.

(Statisticians out there, *don't* give me grief about how party
affiliation is dependence. I'm trying to give a simple example,
even if it's imperfect. :-)

Given that we have arbitrarily (and falsely) said that all variants
are binary, chances are that all critics will show high correlations.
That does not mean we can in any way predict when they agree. So
I think we still need some clarification.

>Reliability is accuracy in choosing

Alternately, I suppose, we could simply take a section of the Bible
and list all readings supported by two or more "major" manuscripts
(define that as you will), and then see how the various editors
have felt at each point.

[ ... ]

>most likely original reading (or the fittest reading for the present

I believe the thesis is stated incorrectly. I believe it should
read

>> there are mathematical proofs in voting theory along the
>> correct on some issue, the majority will be more often right than THE
>> TYPICAL INDIVIDUAL [NOT, I repeat, NOT "any single individual."
One particular individual may very well "guess" the majority opinion
perfectly. (I can offer a sort of inverted proof of this, since I
have roughly an 80% record of disagreeing with the majority on
major issues, and close to a 100% record on issues involving the
long-term survival of the human race -- I tend to support it; the
rest of the population prefers short-term comfort.)

I also disagree that this increases our confidence of determining
the original reading. It merely increases the confidence we have
in getting scholars to agree on what they think is original. It's
not the same thing. :-)

-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-

                        Robert B. Waltz
                     [email-masked]

Want more loudmouthed opinions about textual criticism?
Try my web page: http://www.skypoint.com/~waltzmn
(A site inspired by the Encyclopedia of NT Textual Criticism)