tradeoffs and concessions

7/25/2019 Tradeoffs and Concessions

http://slidepdf.com/reader/full/tradeoffs-and-concessions 1/5

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



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).



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-



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).



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

tradeoffs and concessions

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