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Tradeoffs and oncessions
In
preparing
for
negotiations, either
bilateral
or multilateral, each
side should
try to
sort
out
its
own
preferences.
Bargainers
are
con-
tinually asked during negotiations whether they prefer one
constel-
lation of
outcomes
to
another: Would they rather
end up
with
this
or
that? Not only must they decide what they ultimately want, but
they
also
must
determine what
they would
be
willing
to give up in
order to
achieve
their goal.
How can
a
negotiator
assess the
values
of various tradeoffs, and what effect do these
values have on the
dynamics
of
negotiations?
Suppose that you are the administrator
of
he Environmental
Pro-
tection
Agency
and that you must choose
between Policy A
and
Policy B Your staff has prepared
atable
listing the
attributes that
are
of
concern
to
you
some
involvíng economíc
efficiency, some
economic equity, some
health
indices, some environmental
indices,
some
political indices) and has evaluated the two policies on
these
aUributes. A is better than B on
some
aUributes and
worse
on
others.
How can you think
systematically
about such composite
sets
of
evaluations?
This
issue
arises
not only in
negotiations, but
more
broadly in decision
and policy
making.
The
problem
is
mind-boggling in
its complexity, but formal anal-
ysis
can
help bring some order
to
the
morass.
One
approach
is to try
to
generate
scoring
systems that
assign points
to various levels
within each
attribute
and that
quantify
tradeoffs
between
issues.
This
is
not
easily
done, but values can
be
probed by
observing
pref-
erences between simple
hypothetical choice
s for
which aH
but
two
or three attributes have identical
scores,
and then by invoking
some
intuitively plausible
consistency
requirements. Most
decision and
policy makers
are skeptical and suspicious of this whole
approach.
They
just
don t
see the
need for formalization,
believing that the
decision maker can simply
make a
subjective choice among the
real
alternatives when they
are
presented at the time of the decision.
But now let
s
change the
setting.
Suppose that you
as
the EPA
ad-
ministrator
have
to give instructions to a
representative who must
negotiate a
complex contract with industry representatives. Several
issues
are involved
and
compromises
wiU
have
to be made during
negotiations.
What
s more,
you must handle dozens of these same
kinds
of
negotiations simultaneously.
At
this
point, the desire
to es-
tablish
the equivalent
of a formal
scoring system becomes more
compelling:
without
it,
the representative would be at
sea,
with no
way of
knowing how
to
make
tradeoffs between íssues, and
you
would not be able
to
delegate your
authority.
THE ADDITIVE MODEL
Assume
that prior
to its negotiations
with
AMPO, City
listed the ten
issues to
be discussed
and the
possible levels
on eaeh of the issues.
The City
negotiators
were concerned about
money,
real and
per
ceived security
of its
citizens, security of the police,
symbolic con-
sequenees with possible
ramifications for
other wage
negotiations,
polítical image,
and
so on.
Suppose that they started out monetizing
various issues,
sueh
as starting salaries,
maximum
salaries, vaca-
tions,
creation of the
rank of corporal, number
of sergeants;
but
that
they found it
hard
to put a
price
tag
on the reinstatement
of sus-
pended
officers
(there was
a
principIe at
stake),
on two-man
patrols
lives
were at
stake),
on the
Políce
Review Board
justice
and
alien
ation
were
at
stake),
on the
police
commissioner (the m ayor s job
may
have
been
at
stake). How
eould
they put a dollar figure on what
happened
to
the Police
Review
Board?
One
way
to
do
this would
be to
imagine
a
situation in which everything
was
settled except
the
issues
of
the Police
Review
Board
and the
stalting
salary
level.
The
negotiators
could then decide how they would be willing
to
trade
one against the
other-in effeet,
aeting
as if
they were
plae-
ing a
monetary
value
on
various Police
Review
Board options.
It
s
the
structure
of the problem
situation
that essentially
forces
this
evaluation.
When we turn our
aUention to
other applieations
such as
interna
tional
treaty
negotiations),
reducing everything
to
money may not
be
convenient
or
appealing.
Some
abstract
scoring
system
may be
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150/ TWO
PARTIES,
MANY
ISSUES
easier
to
work with. In the case
of
AMPO versus City we could
have
evaluated City's reactions
for
nonmonetary issues in terms
ol'
equivalent
salary concessions,
and thereby monetized these
non
monetary concems. This
might, in fact, have been
the
more natu
ral
approach.
But
the
introduction
of abstract scores for City
served
a
useful purpose: they
will
be easier and
more
comfortable
to
handle
when
we deal with subsequent
examples like
the Panama
Canal Treaty
and the Camp
David
negotiations.
In the laboratory
experiment,
we assumed
that
City and AMPO
assigned
a specific
point score
to
each outcome level on each
issue
and then added these
to
get an entire contract evaluation.We'll
call
this
an
additíve scoring
system although
there
was
one small
de
viation from
this system. Remember that
if City held AMPO to zero
additional vacation days
for all officers,
City achieved
a boIius of
10
points. In this case we
simply
could not add up City's score for
these two issues.
The
bonus introduced what
is
known
as an
inter-
action
effect between
the vacation issues.
If
we combined
thetwo
separate vacation issues into
a single composite
issue, then we
would have strict additivity among
the nine
resulting issues.
Considering just
two
issues-starting
salary
and number
of ser
geants-suppose
that the other seven
issues
(treating
vacations as a
composite
issue)
are already
fixed.
We're now
investigating trade
offs between
starting salary and
sergeants only.
In the scoring
sys
tem we are using, notice that any
tradeoff
comparisons between
levels
on these two
issues do
not depend on
the
levels
of
the
re
maining seven
issues: the tradeoffs between starting salaries and
sergeants can be said
to be
preferentially independent
of
the
levels
of the
remaining
issues. Indeed, it
can
easily be seen
that with
an
additive
scoring system,
the
tradeoffs
between the
levels
of any
two
issues
are
preferentially
independent of the levels of
the
remaining
issues.
t
can
also
be seen (but not
so easily )
that the converse is
true: i f here are more thantwo issues and
ifthe
tradeoffs between
the levels on any two issues are preferentially independent of the
remainin g issues then an additive scoring system is appropriate.
Let'
s look
at one particular technique
for
obtaining
scores for the
additive case, using
a fictitious situation
that
is just complicated
enough to illustrate
the
complexities 1
wish
to address. Suppose
that
you,
the manager
of
an expanding business,
are
entering
into
negotiations
with
a building contractor for the construction of a fac-
TRADEOFFS AND CONCESSIONS
/
151
tOly. You
are concemed about three
factors: cost,
time
to
comple
tion,
and
quality.
From preliminary discussions you limit the
ranges
of
these
factors to, respectively,
$3.0-4.5 million,
250-400
days,
and
a best
value
of 1 to a
worst value
of 5 (on
an
ordinal
scale). You
would most prefer
a
cost
of $3.0
million,
a
time
of
250
days,
and the best
quality
(an
index of
1).
But you
realize
that
it' s
highly unlikely you will be
able
to negotiate
such
a de al.
Assume that your tradeoffs between
the
levels of any two factors,
keeping the
level
of
the
third
factor fixed,
do not
depend on the
level
of
this third
factor.
For example, your
tradeoffs between cost
and
time
do
not
depend on quality, as
long
as
the
level of
quality
is
he Id fixed. So it' s legitimate in
this
case for
you
to seek an
additive
scoring system. You agree for nOlmalization
purposes
to give
the
best
contract ($3.0 million, 250 days,
quality
1 a score of 100 points
and the worst contract
($4.5
million, 400 days, quality
5) a score of
zero points.
This
is like an exam
with
three
questions,
in
which
the
scorer must decide how much weight should be given
to
each
ques
tion
and how
many points
should be given
to
each
paItially correct
answer.
You
decide
to
score individual
factors in
the
same
way
(100
=
best,
O
= worst),
and
to
combine the
scores
with propor
tional weights
that
sum to 1.
For
example,
suppose that
you
give
a
weight
of.5
to
factor
e
(cost), a
weight
of.3 to factor
T
(time),
and
a
weight
of .2 to factor (qual ity).
Suppose that the internal compo
nent
scoring is as
shown
in
Figure
25. A
contract that
gives you $4
million,
350
days,
and
quality
2
would then receive-multiplying
weight times
score for
each factor-a total
score of (.5 x 50) (.3 x
25) (.2 x 80), or 48.5 points.
How should you
detennine
the weights
of
the
factors
(reflecting
the impoItance of each) and the component scoring within each
fac
tor?
Following
are
some observations
that should provide
insights
into
these questions.
1
StaIting from
the worst case
($4.5
million, 400
days,
quality
5),
if
you have
the
choice of improving
one
factor from
the worst
to
the
best level, let'
s
suppose that
you
would most prefer
to
improve the
cost factor first,
the time
factor second,
and the quality
factor third.
This reflects the
ordinal ranking
of the weights.
Suppose, fmther
more,
that you would be indifferent between improving the cost
1. For a systematic discussion, see
Keeney
and Raiffa (1976).
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TRADEOFFS
AND
CONCESSlONS /
153
factor
alone
and
improving
both the
time
and
quality
factor
together,
Score
reflecting the fact that.5
=
.3 + .2.
Using the exam
analogy:
getting
(J
the cost
question
perfect
and the other
questions completely wrong
o
CI
....
would
be as
desirable
as
getting
the
cost
question
completely wrong
S'
o
and the
others completely
right.
:3
The cost jactor
The
more
you
spend, the more important
it is
(1)
p
oq
o
'
hat you save
a given
increment
of
money. Reducing your
costs
::r-
...
::l
CI
from 4.5 million to 4.0
million
is just as
important
as
reducing
o
your
costs from 4.0
million
to 3.0 million, which accounts for the
en
.....
o
Q..
shape
of
your
cost function.
2-
SO
The time jactor Improving the time value
from
400 days
down-
...
'
j
ward
is
not very important at
first,
but improvements become
more
¡:::
Score
important
as
the value
goes from
350
days to 300;
the
reafte
1', the
iil
value of
time reductions decreases (which accounts
for the
shape
of
to
....
S11
to
'
8o:>o
'
<:>
'
our
time
function).
rJJ
( )
o
The quality jactor Going
from
one quality index
to the
next
is
::l,
::l
:1
approximately
worth the same
as
moving
between any other two in-
OQ
3
(JJ
(1)
8
JO
oq
<b
dices, except that quality index
2 is
doser in value
to
quality index
<
::r-
JO
.....
... .
S
( )
1 than to
quality index
3.
:3
Q..
(JJ
'
oughly, the way to go
about constructing any
scoring
system
is O'
c..
pj
o
<
...
to formulate sorne
rough guidelines,
and then to tune the
system by g:.
.¡:..
manipulating numbers and curves and by testing the implied
re-
Ol
8
)
sults. There are fancier and
more systematic methods,
but
the task
sr'
( )
Score
hould
be approached in the
same way
one would
grade
an exam
...
o
...
....
with
several
questions.
f
you are
sol
el
y
responsible
for giving a
'
....
grade and you don't
have
to
explain your grading
to
anyone
else or
8
to the
student,
then
you
might want merely to respond
intuitively
......
to
::l
Q..
I
aJ
and
impressionistically to
the
entire exam.
But
if you want
someone
(1)
<b
o
oq
><
el
se
to
do
the
grading
for you, then sorne
scoring
system, even if it
:r
o
.....
(JJ
is
not
perfect,
can be
a
great help.
A
case can
also
be made
for
..o
::
adopting
sorne formal
system
of
grading
even
if
you
are not ac-
to
countable
to
anyone
and do not plan to delegate
authority
to
an
....
.¡:..
<
I
to:>
agent. A formal
scheme
of
your own devising might help you de-
'
cide how
to
grade each question separately and how
to
combine the
, ' o
scores
of different questions.
An
additive
scoring
system sometimes
falls far
short
of what is
reasonable. This may be a result
of
the interdependence between
factors,
an
extreme example being the
case
where preference
rank-
ing
of
levels within one
factor
depends on the level
of
another
fac-
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154/ TWO PARTIES, MANY ISSUES
toro
For example, the
better
the military defenses of an ally of Coun
try X, the
better
offCountry X will be; however, X's preferences or
the ally's military
defenses
(the
more
the
better) might reverse
(to
the
less the
better)
if the level of their
friendship
slips below sorne
critical point.
Factors
may
also
be
interdependent when there
is a
need
for bal
ance
or
equity. Suppose that you are a negotiator, acting in a benev
olent
way so as to favor two groups (A and B) internal to your side.
For
any contract
you
negotiate,
you are primarily
concerned
with
the
benefits
to groups A and B. For political reasons you must make
sure, however,
that the
benefits
to A are
commensurate with
those
accruing to B. The
value
of an
increase
in
benefits
to A may depend
critically on the level ofbenefits to B; indeed, ifbenefits to B are at
a very low level, the increase in already high benefits to A may be
deemed undesirable. An additive scheme that scores the benefits
independently for A and for B and
adds these together
misses the
need
for
balance.
In
cases
such
as
these,
a
non dditive
scoring
system
can
be
used.
Nonadditive
systems are not too difficult for current state-of-the-art
measurement, but
they
are
too difficult and too
involved
to be
di
cussed heTe. Suffice
it
to say
that
often there may be
many
factors
under
consideration,
but
only
a few
will be
interdependent; nego
tiators can derive
advantage
from grouping them together and treat
ing
them
as one composite factor in an othelwise additive scheme.
. VALUE AND UTILITY FUNCTIONS
Researchers sometimes distinguish
between a
v lue
scoring
scheme and a
ut l ty
scoring scheme (see Keeney and Raiffa, 1976),
but this distinction is not standard. In the case involving cost, time,
and
quality, the scoring system, as
we
have seen, allows you to as
sign an
overall
numerical value
to
any
contracto The scoring system
has been
tuned
in such a way that contracts with higher scores are
prefe
rred. No
uncertainties are
involved.
Such
a
system
can
be
caBed a
v lue
scoring system.
Now suppose that you must decide
between
a compromise con
tract ($4 million, 350 days, quality 2) and a gamble in which, witb
equal probability, you could end up wíth the best
contract
($3 mil
lion, 250 days, quality 1) or with the worst contraet ($4.5 million,
TRADEOFFS AND CONCESSIONS /155
400 days, quality 5).
The
value scores
of
the
best
and worst eon
tracts are, respectively, 100
and
O, and
therefore
the
gamble has an
expeeted value return of -50. But regardless of
what
the
numbers
imply, you might strongly prefer the
certainty
of the
contract
with a
score of 48.5 to the
uncertainty of
the gamble with the higher ex
pected score of 50. This is not surprising, beeause
the
scoring sys
tem was constructed
on
the basis of nongambling tradeoffoptions:
the derived numbers do not reflect any attitudes toward risk.
Here
is where the advantages of utility scoring become apparent. Such
techniques enable one to find
suitable
scoring
procedures
that not
only
reflect preferences under certainty, but that
appropriately use
expected utility calculations as guidelines forchoices between lot
teries with well-specified probabilities.
2
In negotiations, probabilities may become relevant in several
ways. The consequences associatred with an
agreed-upon
final con
tract might involve
uncertainties
not
under
the control of the nego
tiators.
Differences
in
probability
assessments might be exploited
in terms
of
contingency
contracts.
But even in idealized cases
where there are no external uncertainties outside the control of the
negotiators,
each negotiator
is
uncertain about
what
his adversary
ultimately
will
do.
Should Steve
hold out for $350,000
in
the
Elm
tree House sale, instead of settling for 300,OOO? Should a union,
which can secure a given contract from management, refuse to
accept the contract and submit to the uncertainties of voluntary
arbitration?
A well-developed theory of utility analysis has been devised to
handle both uncertainties and multiple
attributes,
but
the theory,
while
operational, is
not easy
to
use
and
requires
a
level
of co
herency that few individuals, and still fewer groups, achieve. Most
people, even in simple
risky situations,
don t
behave the way the
theory of utility would have them behave.
There
are a few re
searchers
who
prefer to
trust
the
recommendations
of formal utility
analysis rather than their own
intuition,
even though this behavior
would not occur without the existence ofthe theory. A larger num-
2. Many analysts as sume that a value scoring system-designed for tradeo l's
under
certainty-can
also
be used
for probabilistic choice (using expected values).
Such an assumption is wrong theoretically,
but
as 1 become more experienced 1
gain more
tolerance
for these analytical simplifications. This is, 1believe, a relatively
benign mistake in practice (see Bell and Raiffa, 1980).
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156/ TWO PARTIES, MANY ISSUES
ber
of analysts
who
understand
the theory simply
don t
trust
it; tht
point to
examples
of situations (the Allais Paradox, the
E l l s h t ~ l
Paradox, the experimental results of Kahneman and Tversky
f
~ : : ;
which
they,
even
knowing
the
theory, would deliberately act out ui
accord
with it. Sorne
are probably confused
and
will eventually s c;lC
the value
of
utility analysis. Sorne are
not confused,
but
have
d(,t,; l>
psycholo'gical
concerns;
they
may anticípate
that a
given
act mig.tJ&1
lead to an unfortunate
outcome,
which
will
result in persistel4
deeply
felt pangs of regret. Such psychólogical concems are
usuaH:.
not
accommodated in applications
of the
theory
of utility,
but
,,¡;
principIe they could be-wi th further complexities in the
theOf)
Even though you, as a negotiator, might want to act r e f l e c t i v e l ~ .
coherently, and rationally,
your adversaries
in alllikelihood will Jtól
with
very
limited rationality. Don t
be naive
and
expect them
to
l)t>,
have
like you may
want to
behave.
However,
if
they
are
prone
the gambler s fallacy; to an excessive zeal for certainty, to an tol
cessive
avoidance
of potential ex post
regret,
to misperceptions > ti
small probabilities
(one
could come up with
a litany
of
so-call<:'>:
nonrational, descriptive behaviors),
then
you might
be
able to
t"L'
ploit such behavior
in
negotiations.
TRADEOFFS WITH TWO CONTINUOUS ISSUES
Mr. Hee and Ms. Shee are negotiating over two continuous issllt,,,.
cost
and
time.
The
ranges
under
discussion are 3.0-4.5 millic.,l,
and 250-400 days. He wants high dollars and high days; she want.,
low dollars apd
low
days. Figure
26
indicates by
means
of ndifTc:::,z·
ence (iso-value) curves their
respective
tradeoffs. He, for exampit:
deems contracts V Q and P equally desirable, and thus they are ~ . t
his same
iso-value
curve;
he
prefers contract
R to any
of
the
v a l l i i : ~
equivalent contracts V Q and P,
and
hence R is on a higher ¡SoY-
value curve. He wants to go northeasterly; she southwesterly. Let '
suppose that they have tentatively settled on a contract agreeme.,OOi
of 4.0 million
and
275 days, which is depicted as point Pan :,
which is scored 20 for him
and
50 for her (see Figure 27).
Notice
from Figure 26 that if the final contract were to be mO\'6:::
from point P along Mr. Hee s iso-value contour (along the are PQ\ \
3. See Raiffa (1968) and Kahneman
and
Tversky (1979).
60
400
rn
>.
35
á
e
t ::
300
I I • I
25 I 85 70
1
5
3
3.0 3.5 4.0
4.5
Cost
(in
millions of dollars)
¡ngure 26. Iso-value curves for Mr. Hee (solid lines) and Ms. Shee (bro
kn
lines). Her direction of preference
is
southwest; his
is
northeast.
lOOr
75
c:
Vl
..;
50
8
Vl
25
o 25 5 75
100
Score
for
Mr. Hee
figure 27. The efficient frontier. (Point P represents theioint scores for a