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Re: tc-list Clarification

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  • Robert B. Waltz
    On Thu, 29 Jan 1998, Timothy John Finney wrote: (I m only going to reply to a few parts of this; I haven t had time to think
    Message 1 of 2 , Jan 29, 1998
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      On Thu, 29 Jan 1998, Timothy John Finney <finney@...>
      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.)

      >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.)

      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
      >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.

      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.

      [ ... ]

      >> 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).

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

      >> 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 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
      waltzmn@...

      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)
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