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JS Weighted Voting

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  • E. Bruce Brooks
    Topic: JS Weighted Voting In Response To: Mahlon Smith From: Bruce I can only feel honored that Mahlon Smith, in reviewing the JS Voting material, has given as
    Message 1 of 2 , Jun 6, 1998
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      Topic: JS Weighted Voting
      In Response To: Mahlon Smith
      From: Bruce

      I can only feel honored that Mahlon Smith, in reviewing the JS Voting
      material, has given as much time as he has to my contribution. Since his
      response is in effect an official JS one, I am perhaps absolved from my
      announced intention of a few days ago to let the matter rest.

      For what it may be worth (Mahlon will presently encounter this in later
      messages to CrossTalk), I still feel that ANY weighting of votes in these
      matters is sooner or later problematic, that (for instance) alternate
      schemes of weighting might well be thought superior to the 3/2/1/0 system
      actually adopted, and that giving the actual breakdown of original votes
      next to the weighted color result, as was done in the Red Letter Mark, will
      inevitably cause reader confusion at every point where the plurality (the
      option getting the most votes) is different from the outcome (the final
      color). As Mahlon describes it, the four-option voting was essentially a
      refined way of getting to an IN or OUT verdict, but readers of the end
      product are going to take the FOUR tier system as a reality, not as a
      sophisticated device for reaching a TWO tier verdict respecting the
      intended Jesus data base.

      That double definition (note the double sets of color definitions on 5G,
      p36) seems to me a potential cause of reader confusion, and on considering
      Mahlon's comments, I think I see another one as well.

      Mahlon says:
      ----------

      1. "So a red vote meant one thing to me & another to
      Crossan & yet another to Borg. The only thing we were in total agreement
      on was R = IN & B = OUT & that every scholar's vote was to have the same
      weight."

      2. "A red vote counted the same whether it was cast
      by Funk, Crossan, Borg, Chilton, Kloppenborg or any of us lesser known
      scholars who did much of the research that provided the basis for
      debating the historical value of each item. But a red vote always
      carried more weight than a pink or gray for determining what was IN or
      OUT. It would take 3 gray votes to counteract 1 red vote."

      -----------
      #1 states the basic, and in fact (by 5G p36) the original, JS premise.
      However:

      In saying (#2) that 3 Gray votes counteract 1 Red vote, Mahlon is inviting
      us to notice that the weightings are respectively 1 (Gray) and 3 (Red).
      Notice the implication that a Gray vote will somehow offset, or pull down,
      the Red vote. I take this up below. In the meantime, there is a trap in the
      example itself, is there not? Let me ask it this way: On that same
      intuitive basis, how many Black votes (at 0 per vote) will it take to
      counteract 1 Red vote (at 3 per vote). This translates to: how many Zeroes
      make a Three? The answer comes out infinity. Therefore the example, or the
      process which it invites the reader to resort to, may be faulty.

      Now then, sneaking up on what I think may be a larger difficulty. I note
      that there is no Scotch or "Not Proven" verdict available in the voting.
      Did some Fellows simply abstain if they were not sure on a given vote? If
      they did, was the final "credibility" total (to use Bob Schacht's term)
      divided by the number of those present, or by the number of those voting?
      What would a system allowing for this "unsure" option have looked like? My
      own visualization is:
      Red +2
      Pink +1
      Unsure 0
      Gray -1
      Black -2
      Those who wish may play around with this system of equivalents and see what
      it does to sample outcomes. For one thing, they will find that it gives a
      literal meaning to the word "counteract." If 1 Fellow votes Red, it takes 2
      Grays to counteract that vote, AND THE RESULT ON ADDING THE WEIGHTING
      VALUES IS ZERO, that is, the verdict is truly cancelled out, leaving a
      neutral result. With no middle option available, as in the actual JS voting
      method, every saying is going to be either IN or OUT. Thus, it is not
      theoretically possible for any number of votes IN to exactly neutralize any
      other number of votes OUT. In that sense, the JS system or any other system
      without a middle will be intrinsically skewed in the direction of COMING TO
      A CONCLUSION; resting in doubt is not a final option (notice the rounding
      rules in the algorithm as stated).

      Now we approach the crux. Mahlon adds, later in his message:
      --------
      3. ". . . your analysis of a
      gray vote is not totally accurate. Gray does not simply mean that an
      item is dubious but also that it contained some element that could be
      historically useful in describing Jesus. This is clearly stated in every
      definition of gray used by the Seminar (5G p. 36)."
      --------
      I admit that this is different from the assumption of my previous notes. I
      think it is very important, as clarifying what the *specific* JS weighting
      system does. The centered system I mentioned above, or for that matter a
      noncentered system with weightings +2/+1/-1/-2 (allowing no zero-weighted
      VOTE but occasionally coming out with a zero or indeterminate RESULT),
      keeps to the spirit of Mahlon's first definitions; namely "R = IN and B =
      OUT." If we think of Pink and Gray as less positive versions of those
      options, then a Gray vote should pull the total DOWN, that is toward Black,
      but not so strongly as a literal Black vote (as Mahlon's above example, of
      3 Gray "counteracting" 1 Red, also assumed) . But as Mahlon has just stated
      it in the paragraph just quoted, Gray (with +1) is instead conceived of as
      pulling the total UP, just not as strongly UP as either Pink or Red. That
      is, there is an intrinsic skew UPWARD. To continue with Mahlon's own
      explanation:

      --------
      "In your illustration there is only 1 person [voting Black] who thought
      that this item
      was of no historical value for determining who Jesus was. 9 scholars
      thought [voting all other options] it was historically useful in some
      degree or other."
      --------

      In other words, all votes but Black are "in some degree or other" votes for
      INTO the database. This explanation of Mahlon's is exactly consistent with
      the JS weighting values (where all votes but Black have positive
      weightings). But I would still suggest that they are INconsistent with his
      original definition, namely Red = IN, Black = OUT, with Pink considered a
      subtype of Red and Gray a subtype of Black. The colors appropriate to this
      second definition, and to the JS weightings, might look rather more like
      the following:
      Red (3) = IN
      Hot Pink (2) = MODERATE IN
      Pale Pink (1) = FAINTLY IN
      Black (0) = OUT
      Gray may be *defined* as a mild NO, but it *computes*, as Mahlon has
      himself pointed out, like a mild YES. Or so it looks from here.

      This of course is analogous (more or less) to grading, where all results
      are simply different degrees of positive. Apart from the inward
      complexities of grading systems, it seems NOT analogous to a universe in
      which the two main options are pulling in opposite directions.

      In conclusion, I am very grateful to Mahlon for speaking so candidly to my
      political science question, about the effect of weighted vs unweighted
      voting on the group dynamic within JS. There is probably a good journal
      article in there somewhere.

      Bruce

      E Bruce Brooks
      University of Massachusetts
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