by Lee Adams Young
The algorithm for tallying the consensus of Jesus Seminar votes has been erroneous. Suppose 100 Jesus Seminar scholars voted whether a given statement attributed to Jesus in one of the five gospels is authentic. If 74 scholars voted "doubtful" (gray) and 26 scholars voted "no" (black), the algorithm used by the seminar would declare that the black votes had won!
Casting Votes
The Five Gospels: The Search for the Authentic Words of Jesus by Robert W. Funk, Roy W. Hoover, and the Jesus Seminar (Macmillan, 1993) describes the voting of the Jesus Seminar on statements attributed to Jesus in the four canonical gospels and the Gospel of Thomas. Each Fellow of the Seminar personally judged whether each saying was originally made by Jesus according to the following scheme:
Red Doubtless authentic Pink Probably authentic Gray Doubtful (or not characteristic of Jesus) Black Not authentic
Each vote earned the following points: Red 3, Pink 2, Gray 1, Black 0. The average point count for the voting group was determined by adding up all the point counts and dividing by the number of persons voting. Thus the average point count ranged from 0 to 3.
The Faulty Algorithm
In addition, the average point counts were divided by three to provide an average score ranging from 0 to 1. This range was divided into four intervals for determining the consensus of the group. The following ranges, which appear unbiased but are actually biased, were used:
Average score Result (Erroneous) -------------- ------------------ .7501 - 1.0000 Red .5001 - .7500 Pink .2501 - .5000 Gray .0000 - .2500 Black
Let's multiply these numbers by 3, to convert back to a 0 - 3 range. We have .25 x 3 = .75, .5 x 3 = 1.5, and .75 x 3 = 2.25. The faulty algorithm is shown on this chart:
Scoring chart (erroneous):
. . . . . . and the winner is . . . . . .
|<---Red--->|<---Pink-->|<--Gray--->|<--Black-->|
| 2.25 1.5 .75 |
|.......|...|...|.......|.......|...|...|.......|
3 2.5 2 1.5 1 0.5 0
All tie All tie All tie All
Red Pink Gray Black
If all Fellows of the Seminar voted Pink, the average point score would be 2. But suppose there were a tie between Red and Pink. The average point score would be 2.5, yet the algorithm would erroneously declare the consensus of the Seminar to be well in the Red range. The algorithm is faulty because the Red/Pink breakpoint does not coincide with the Red/Pink tie score. And the Gray/Black breakpoint does not coincide with the Gray/Black tie score.
We now develop a correct algorithm.
Consider various votes of the Seminar, in which those voting voted all Red, or were split 50/50 between Red and Pink, and so on. We have the following results. (The numbers in the third column are simply those of the second divided by three.)
Average Average
points score
Vote (0 - 3) (0 - 1)
----- ------- --------
All Red 3 1.000
Tied Red/Pink 2.5 .833
All Pink 2 .667
Tied Pink/Gray 1.5 .500
All Gray 1 .333
Tied Gray/Black 0.5 .167
All Black 0 0.000
The critical aspect of this table are the scores on a 0 - 1 scale for tie votes. Note that these scores are unbiased. The tie scores lie equidistant between the scores for all one color. In determining the consensus of the voters, the following ranges should be used:
Average
score Result (corrected)
--------- -------------------
.834 - 1.000 Red
.501 - .833 Pink
.168 - .500 Gray
.000 - .167 Black
The use of the erroneous tallying table near the top of this page awarded all votes with an average score in the .750 - .833 range to the Red category, when the nod for these should have been given to the Pink category. Likewise in The Five Gospels, statements attributed to Jesus earning scores in the .167 - .250 range were printed in Black, whereas they should have been printed in Gray. The latter would have elevated many statements into the "possible (but unlikely)" category.
The Five Gospels contains a table of sayings rated Red or Pink by the seminar. 25 sayings were accorded a Red status, as shown on p. 549. Of these, 17 had average scores in the .751 - .833 range; these were erroneously printed in Red; they would have a Pink status if the correct cutoffs were used. Only 8 of the sayings of Jesus deserved to be printed in Red.
Thus the saying, "Render to Caesar the things that are Caesar's, and to God the things that are God's" (Mark 12:17 etc.) as well as the story of the Good Samaritan (Luke 10:30-35) are printed in red in The Five Gospels, but to reflect the views of the Seminar should have been printed in pink.
You might object that the table of corrected cutoff scores seems biased, because the Pink and Gray ranges are twice as large as those for Red and Black. This apparent bias would be removed if the scholars has been allowed to vote -2,-1, 0, 1, 2, 3, 4, . . . Then the interval for a 0 consensus would be -.167 to + .167; that for a 1 consensus would be .167 to .500; that for a 2 vote would be .500 to .833; and that for a 3 vote would be .833 to 1.167. Then parity would be restored. The apparent disparity results from the fact that a Pink vote lies in the 1.5 to 2.5 point range, but a Red vote lies in the smaller 2.5 to 3 point range.
Let's check out my claim made at the top of this page. Suppose there are 74 Gray votes and 26 Black votes. The latter earn zero points. Thus the average point score for this vote is (74 x 1)/100 = .74. Converting to a 0 - 1 scale yields a score of .74/3 = .2467. This is less than the (erroneous) cutoff value of .2500, and black wins!
Using the corrected table, one finds that the score of .2467 falls well within the Gray range, where it should.
The correct scoring chart looks like this:
Scoring chart (corrected):
. . . . . . and the winner is . . . . . .
|<-Red->|<-----Pink---->|<-----Gray---->|<Black>|
| | | | |
|.......|...|...|.......|.......|...|...|.......|
3 2.5 2 1.5 1 0.5 0
All tie All tie All tie All
Red Pink Gray Black
The error would probably have never arisen if the weighted average vote had been left on a scale of 0 to 3. Even a classics professor can recognize that 2.5 is the breakpoint between 2 and 3. The Devil got into the mathematics when somebody had the bright idea of dividing all tally scores by 3.
The faulty algorithm continues to be used in The Acts of Jesus by Funk and the Jesus Seminar (HarperSanFrancisco 1998). Old algorithms never die. . . .
Even using the correct table, the Red and Black voters have plenty of clout. Suppose one day fifty scholars showed up early for the seminar, and were divided 25/25 between Red and Pink on a given saying. Now imagine that 14 more scholars march in, who intend to vote Red. One of Pinkers says to his allies, "I have some friends who could help us. They would vote Black, but they're still asleep in bed. I'll call them up."
Question: How many Black votes does it take to counter the 14 Red votes, to swing the consensus to Pink, relative to a Red/Pink tie?
Answer: Only 3.
Think of the voters as sitting on a see-saw. When it is balanced, 25 scholars sit at the 3 mark (Red); 25 scholars sit at the 2 mark (Pink); and the fulcrum for the balanced seesaw is at 2.5. (2.5 is the weighted average vote.) An additional scholar sitting at the 0 mark (Black) has five times the leverage as an additional scholar at the 3 mark (Red).
40 25 3
Reds Pinks Blacks
-------------------------------------------------
^
3 2.5 2 1 0
[(40 x 3) + (25 x 2) + (3 x 0)]/68 = 2.5
If a vote is close to a Pink/Gray tie, a Red or Black vote has three times the leverage of a Pink or Gray vote.
The extremists always have the loudest voices.
Determining the Seminar consensus is exactly analogous to calculating Grade Point Averages in school.
For a more complete discussion, go to Jesus Seminar Voting Algorithm.
Lee A. Young, PhD
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Lincoln, Massachusetts 01773
781-259-9563
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Are you a Fellow or Associate of the Jesus Seminar? Robert Funk has ignored messages from me about this error. The Seminar is still using the erroneous algorithm as of October 1999. Please ask Dr. Funk about the algorithm.
The error is very simple to explain. If there were a committee of four people, and three voted Gray, and one voted Black, Dr. Funk would declare that Gray and Black were tied! Calculate the score! IT'S CRAZY!!!
Posted May 4, 1998. Revised February 10, 2000.
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