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From: bts@unc.UUCP
Newsgroups: net.religion
Subject: Playing games with God, II
Message-ID: <5646@unc.UUCP>
Date: Tue, 2-Aug-83 03:22:41 EDT
Article-I.D.: unc.5646
Posted: Tue Aug  2 03:22:41 1983
Date-Received: Wed, 3-Aug-83 04:00:55 EDT
Lines: 131


     I haven't been able to find either of Steven J. Brams'
books in the Math/Physics Library at UNC.  This past Satur-
day night, however, I found a volume titled "Applied Game
Theory", edited by S.J.Brams, A.Schotter, and G.Schwodiauer,
published by Physica-Verlag in 1979.  The last article in
the book is "Faith versus rationality in the Bible: game-
theoretic interpretations of sacrifice in the Old Testa-
ment", by Brams.  In the interest of continuing this discus-
sion, I'll summarize parts of the article.  (The book,
according to a card on the inside cover, cost $80.00.  The
other articles are more mundane game theory.  Given that it
was until re-bound a paperback, however, I'd say the book's
interesting.) All biblical quotes will be from the KJV,
other quotes from Brams.

     Brams studies two stories in the Old Testament wherein
God tested the faith of fathers by seeing if they would
sacrifice their children.  The first story is well known to
all of us: Abraham and Isaac (Genesis 22:1-18).  There, God
called off the sacrifice at the last minute.  The second
story is about Jephthah's sacrifice of his daughter (Judges
11:30-40).  Since the latter story is not so familiar, I'll
start with a synopsis.  During a battle, Jephthah

     vowed a vow to the Lord and said, If You shall without
     fail deliver the children of Ammon into my hands, then
     whatever comes out of my house to meet me when I return
     in peace from the children of Ammon, surely it shall
     belong to the Lord, or I will offer it up for a burnt
     offering. (Judges 11:30-31)

When Jephthah returned home, he was first greeted by his
daughter, his only child.  Despite his grief and with his
daughter's consent, Jephthah went ahead with the sacrifice.
(He did give her a two month's delay (Judges 11:37) so that
she might "go up and down on the mountains and weep for
[her] virginity.")  This time God did not intervene.

     (At this point, by the way, there is an intriguing quo-
tation from the Encyclopedia Judaica, vol. 9, p. 1342, on
"Jephthah".  It says that this story is "exceptional and
cannot be treated as indicative of the norm of human sacri-
fice in Israel".  Would any scholars care to enlighten us as
to what that norm might have been?)

     Brams models these stories as two-player games.  In
each game, the father has two choices: to offer the sacri-
fice or to refuse.  Since God moves second, He may make His
move based on the father's.  Therefore, He has four choices:
He may

(1)  reject the sacrifice if offered/forgive if the father
     refuses,

(2)  reject the sacrifice if offered/not forgive if the
     father refuses,

(3)  accept the sacrifice if offered/forgive if the father
     refuses, or

(4)  accept the sacrifice if offered/not forgive if the
     father refuses.

Hence, there are eight outcomes to each game.  Under the
assumptions that God would prefer not to have Isaac sacri-
ficed but would rather Jephthah kept his promise, Brams
ranks these outcomes from God's point of view. (This seems
weak to me.  Brams rationalizes by saying that "since
Abraham's time, the Israelites had caused God much grief...
so He was not inclined to be sympathetic with people...  who
were too quick to make solemn vows." (p. 440)  The rankings
of outcomes according to the fathers can be disputed, too.)
Next, he ranks the outcomes for the fathers' under three
levels of faith: "faithful regardless", "wavers somewhat",
and "wavers seriously".

     If the father is "faithful regardless", there is a
clear choice, in the sense of a dominant strategy.  In the
other two cases, neither strategy is dominant.  In those
cases, according to Brams, the father must try to anticipate
God's choice by assuming that God is a "rational" player.
Abraham will, in all cases, decide on just the strategy he
chose: to sacrifice Isaac.  Jephthah, on the other hand,
will make the sacrifice in the "faithful regardless" and the
"wavers somewhat" cases, but he will refuse in the "wavers
seriously" case.  By now, there are any number of holes in
Brams' arguments.  Let's take his analysis for granted, how-
ever, and look at his conclusions.

     All that this leads to is the following:

     [It] is impossible to ascertain whether biblical char-
     acters are blindly faithful or wavering.  Thus a major
     alternative explanation of their actions might be that
     they did indeed waver, but anticipating God's rational
     strategy, they were compelled by their own rationality
     to demonstrate their faith by offering to sacrifice
     their children.  (p. 443)

Contrasting the two stories:

     If God is sympathetic, as in Abraham's case, Abraham
     can waver seriously and still rationalize the offering
     of his son.  Some wavering is possible if God is less
     sympathetic, as in Jephthah's case, but if Jephthah
     prizes his daughter above everything else, it is not
     rational for him to offer to sacrifice her, given the
     two sets of preferences I have postulated for God, and
     Jephthah's awareness of these. (p. 443)

My feeling is that I don't need to bother pointing out the
holes in Brams' reasoning, if this is all it can offer
should I accept it.  Perhaps the arguments presented in his
books are more compelling, and I suspect I'll look for them
in our main library next time I'm there.

     Finally, for anyone who might be tempted to read Brams
for himself, some reassurance.  I saw nothing at all in his
article which anyone might consider blasphemous-- except
possibly the idea that we can gain an understanding of how
God thinks by analyzing stories from the Bible.

	Bruce Smith, UNC-CH
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     Next: If my keyboard isn't incinerated by the flames
after this one, a review of Martin Gardner's 1961 religious
novel "The Flight of Peter Fromm".