Mediation in Long-Term Planning

Copyright © IFAC Supplemental Ways for Improving International Stability. Laxenburg. Austria . 19 8~

MEDIATION IN LONG-TERM PLANNING M. Grauer, E. Bischoff and A. Wierzbicki Int ernational Institute for Applied Systems Analysis, 2361 Laxenburg, Austria

Abstract . The aim in ma n y conflict situations is to move from a situation in which the goa ls of the co ntending parties are mutual l y i n compatible to one in which a comprom ise solution acceptable to all can be found . This is usually achieved through a series of co ncessions on b oth sides . This paper demonstrates how the concession- making process can be structured by a mediator using an interactive multiple - criteria programming system (DIDASS) based on aspiration point and achievement function methodology and linked t o a model of the system under study. The use of the approach is illustrated by simulated negotiations concerning the long-term de velopment of the Austrian energy system . Keywords . Long - term planning ; mediation; interactive decision support; energy systems .

INTRODUCTION

PROBLEM DESCRIPTION AND NOTATION

It is generally accepted that having a good mediator ca n be a crucia l factor in the suc cess or o th erwise of negotiations. Sometimes the mediator can confi n e his role to that of an organizer of mee tings ( " process mediation ", cf . Pruitt , 1981), contribu tin g t o a successful outcome simply by ensuring a continuing dialogue between the parties involved. In many cases , h owever , he might consider it desirable to become more actively involved in the actual ne go tiation process and to attempt to assist the participants through an analysis of the underlying conflict situation ( " cont e nt mediation " ) . This latter activ it y is the focus of th e present paper, which investigates the possibility of using a computer - based dec ision support system as an aid for mediation . The work is based on a macroeconomic planning mo d e l developed a t IIASA by the Energy Deve lopme nt, Economy an d Investments Group (Messner and Strubegger , 1983) . Built as par t of an investigation of different options for the long -t e rm development of the Aus trian energy system , the model portrays the interrelationships between the consumption sphere, the ene r gy production sector and the rest of the economy . It was desig ned as a means of ex amining the implica tions of different planning scenarios and as a vehicle for compa ring dif ferent views about the possible development of the energy system . The approach considered here goes beyond a mere comparison of opinions in that it attempts to provide support for a pr oc ess of concess i on - making which progresses from an initial situa tion of diverging views ( "incompatible aspirations") to a consensus acceptable to all of the parties involved ( " com patible aspirations") .

199

The Model The model of the Austrian energy system and economy mentioned above was developed, on the one hand, to allow the analysis of l on g -term interdependencies between ener gy and economic variables and , on the other , to give detailed insights into the energy co nsumpti on behavior of specific areas of the private and public sectors and of households. Special attention is paid to the changes in energy demand over the next 20 to 50 years resulting from changing consumption patterns ; these, in turn, are due to changes in the income structu re. Thus the pattern of household energy consumption can be determined . The inc ome st ru ctu r e also determines the activities of each sector of th e economy , in that ove rall production should meet the demands ar i sing from th e income structure . The model consists of three modules: a sub model of consumption behavior , a macroeconomic submodel (with eight sectors) and a n energy submodel . The system is of the dynam ic linear programming type and incorporates input - output techniques . The interrelationships between the state and decision variables of the model can, for the purposes of this paper, be stated in general form as follows: State equations

v

x(t+1) =

)J

L A(t - n.) · x(t -n.) + L 13 ( t -m . ) • u ( t -m . )

i=l

~

~

j =l

J

J (1)

200

M. Grauer, E. Bischoff and A. Wierzbicki

where

mented, i.e., usually

1.

for i

f

j. This

has been described above as a situation of incompatible aspirations. A (theoretically) mutually acceptable solution G to the problem can be characterized as a decision which is Pare to-optimal in the full space of the objectives of all parties, i.e., a solution of the vector maximization problem

0,1, ... ,T-1

t

G. f G.J

T - length of planning period x - vector of state variable u - vector of decision variables A,B - matrices of input data (n , .•• ,n) , (m , ••• ,m ) - sets of integers 1 1 w which characterize time lags in state or decision variables.

max ( f 1 (u) , f 2 ( u) , ... , f uEA

( u) )

(6)

n

The problem of mediation in this context is to encourage concessions leading from the set of U. to a single solutio~ U.

Constraints

~

G(t) • x(t)

+ D • u(t) < het)

(2)

\~here

G,D - matrices of input data h - vector of input data;

L ( t)

~

[u ( t) ] x (t)

~

U ( t)

Up to this point the vector u has been characterized merely as the set of "decision variables" without reference to who is responsible for the decision. There are three different possibilities:

1.

The set of decision variables is commo n to all parties, i.e., a decision can be made only by consensus, although the parties have different interests.

2.

The set of decision variables is split into subsets associated with the individual parties and a subset common to all parties.

3.

The set of decision variables is divided into non-intersecting subsets, each associated with one of the parties.

(3)

where L,U represent bounds on the variables. Initial condition x(O)

x

°

(4)

Relations (1)-(4) define the feasib l e region of model solutio ns, which will be denoted byA. The Mediation Problem Ideas concerni n g the future of the energy system can be expressed in the model in the form of scenario assumptions and also thr ough the objective functions chosen . It is assumed here that the parties involved agree upon the scenario assumptions , but that they have different views about the objectives. More precisely , let f . (u) ~ (f. l(u), ... ,f. (u)) 1 1, l,ri denote the objectives of party i, i~ 1,2, ... ,n, and assume, for the sake of s impli city , that f. .: A-+lR , i ~ 1,2, ... ,n, j ~ 1,2, ... ,r., ~,J

~

and that all object i ves are formulated so that they should be maximized. (Subscript j might be thought of as time t, in which case f. represents a trajectory of some criterion ~ith f. (u) ~ f.(u ,t ) .) Let F denote the image l,t

1

of the feasible region A in the space of the objectives of all parties, that is, F (f (A) , f (A) , ... ,fn( A)) . 1 2 If party i views the problem simply in terms of its own objectives , the following vector maximization problem is obtained: max fi (u)

(5)

uEA

Let ui' i ~ 1,2, ... ,n, represent the (Pareto) solut i ons of this problem for each party. Typically , the decisions that o ne party would regard as desirable are different from thos e which another party would like to see imp le-

While all three ways of looking at the problem are possible in principle, we deal here only with case 1 . For ease of presentation, the method will be described for a two-part y problem.

A COMPUTER-ASSISTED ME DIATION PROCEDURE The Concept Mediation is considered here as a three-stage process: Stage 1: Ag reement about the model. In order to start the proposed mediation process, the parties invol ved must first agree that the mathematical model adequately represents the problem under considera tion. Stage 2: Unilateral assessment of the problem. Both parties experiment with the model in order to formulate their objectives and to identify the solutions they would ideally like to achieve, i.e., the (usually incompatible) solutions and G • 1 2

u

Stage 3: Multilateral mediation. The point (f ),f )) can be viewed as a (not nor1 1 2 2 mally at tainable) 'utopia' (or 'ideal') solution in the space of the combined objectives of the two parties. This ideal solution is used by the mediator to construct a 'single negotiating proposal' (see Raiffa, 1982),

(u

(G

201

Mediation in Lo ng-T erm Planning which is put to both parties for discussion. The responses a re used to formulate a revised proposal and the process is then repeated until agreement is reached. The fo r mu lation ensures that the sequence of proposals l eads to a Pare to-optimal solution

n.

The Procedure

The rationale behind this approach is to allow a s uffi cient degree of freedom for co ncessions to be made. The single ne go tiating proposal marks the ent r y of t he mediator into the process . Both parties are asked to consider the proposal and to respond by specifying a new aspiration trajector y

The detailed procedure proposed for stages 2 and 3 is described below .

f~l).

Stage 2 . Using the DIDASS system (which is based on the referen ce point approach), the t wo parties determine th e ir preferred solutions to th e problem. More precisel y , let f. (u) = (u,t)!. t = 1,2, ... ,T denote the

The next step r equires the mediator to compu t e

l,

If.

t

l

trajectory considered by party i. (fi(u ,t ) could also be vector - valued , but for the sake of simplicity we will limit our co nsiderations to the case where th e re is only one trajectory for each party . ) Then the positions of the two parties at the beginning of the procedure can be characterized by their chosen solutions

G~O)

t o the two vec t o r maximization problems i

max fi(u)

1, 2

=

(7)

In formulating their response both partIes have access to the model via DIDASS .

AO)

feasible solutions f1

The results in the objective space of each party are represented by

A(O) f.

which come as

close as possible to the new aspi ration points, i.e., he solves the two optimization problems ,

- 0)

max s (f. - f . uEA

l

)

01 )

1,2

i

l

where s is an app ro priate achievement scalarizing function in th e trajectory space of each party .

The solutions

G~1) l

can be conside r ed

as projections of the asp ir ation poin t s on t o the efficient fro nti er of F . = f.(A) . The re.

.

.

\"(1)

suIt lS a new ut o pla pOlnt f

uEA

l

"(1) " (1) T

= ( f1

,f 2 ) . Using this utopi a solution, the mediator co n-

struc ts an efficient feasible point [(1) by solving

(8)

l

max s " (f - f " ( 1 ) )

while the vec tor f

*(0)

,,(0)

= (f 1

~(O)

,r 2

)

T

Stage 3. This phase starts with the mediator investigating the implications of the preferred policies

(G~O» l

of each party for the

other , i . e ., he computes

where s is an achievement scalar i zing function in the full space spanned by the objectives of all parties . The next SNP to be put to the two parties is selected by th e mediator according to the formu l a f(k+l) = f(k) + a( f(k+1)_f(k» SNP SNP SNP

These trajector ies a r e us ed to provide the par ti es with a sing l e negotiating proposal (SNP) . If f(O) = (fi O) , fiO»T is feasible, then this will be put forward as the proposal; if not, a feasible proposal is computed which is as close as possible to 1(0). More formally,

.

1

'2

'

solution of minIl1(0) - (f (u),f (u»T lloo ; 1 2 uEA

otherwise (The actual calculations can be ca rried out by usin g DIDASS in a n inverse mode.)

,

k=0,1,2, ... (3)

where a (0 < a < 1) is an appropriately chosen "m ed iation coeffic i ent ". This coefficient en ables the mediator t o adapt to th e negotiation behav i or of the two parties . The coefficient should not normally be close to 1, at l east in the initial stages of the procedu r e , in order to allow fo r th e changi ng preference structures of the actors brought about by the process it self . The two parties are agai n asked to comment on the proposal by specifying new aspira -(k+1 )

tlon levels fi

f(O) = (f(O) f(O»T . i f 1(0) EF

(2)

uEA

repre -

sents a utopia trajectory in the full space of th e objectives of both parties.

f(O) SNP

,,0 )

, f2

.

and the process lS repeated

until the SNP is either on or sufficiently close t o the efficient frontier of F. This mediating procedure will obviously con ve r ge to a single Pareto point (in the space of all objectives) if both parties insist on keeping their aspiration trajectori es at the initial selected values f~O) . If, however, th e aspiration trajectories a?e modified during the negotiation process, the procedure mayor may not produce a mutually acceptable solution, depending on whether the parties behave con -

202

M. Grauer, E. Bischoff and A. Wierzbicki

structively or not (that is, whether they decrease or increase their aspirations).

Government (i

~

2)

Trade balance

RESULTS OBTAINED WITH THE AUSTRIAN MODEL

400

The mediation procedure described above can be used for various purposes. As well as employing it in actual negotiations, it can be used for model validation (since it reveals model solutions that might not have been considered beforehand) or as a means of teaching contending parties constructive negotiating behavior.

300

200

100 This section presents some numerical results obtained during experiments with the Austrian model, in which the procedure was first used as a validation tool. The numerical results are based on an assumed negotiation between representatives of 'Industry' (party 1) and 'the Government' (party 2). The former are assumed to be interested in minimizing a cost traje c tory f 1 (u,t) over the planning horizon t = O,l, oc, ,7, while it is assumed that the latter wish to maximize the trade balance traje c tory f (u,t). 2 Figure 1 shows some results obtained in this hypothetic a l negotiation process. The trajec-

~.~ f(O)

,_2

P

/,

8

-100

-200

- 300 Fig. 1 (b)

tory fiO) shown in Figure l(a) is the ideal policy from the viewpoint of 'Industry'

(Le.,

Fig. 1.

Illustration of the proposed mediation support procedure.

it minimizes costs) and trajectory fiO) in Figure l(b) represents the implications of this policy for 'the Government'. It is clear that Industry's preferred policy would result in a negative trade balance for the last seven years of the planning period. Industry (i

~

1)

Figure l(b) shows the - again assumed - ideal '" (0)

policy f2

of the Government.

plications t iO)

This has im-

(see Fig. 1 (a)) f o r th e tra-

jectory of interest to Industry.

Cost function

The procedure calls for the ve c tor f(O)

1500

(fiO) ,fiO))T to be checked for feasibility

............... i (1) - (0) f 1

'(0)

1000

fl

using DIDASS; in our c ase it turns out to be a feasible point. This vector is then proposed to the two parties as an SNP. Making the assumption that n e ither part y is prepared (at this stage) to make any deviations from its previous position, the ut o pia point f

1(0)

-;.(0) ",(0) T .

(r

,f2 ) 1S used as a re f er1 ence point in the objective function space F . =

This leads to the solution f(l) which lies on the efficient frontier of F. This vector is then used to define a new SNP. A value of "mediation coefficient"

500

proposal f

O+--+--~~~--~-+--+--+

o

2

4 Fig. 1 (a)

6

8

(1)

SNP

Cl.

=

0.5 leads to the

'

Experiments of this kind with a number of different objective functions highlighted several shortcomings of the model itself. Since it had been developed on the basis of an aggregated single-criterion philosophy it did not always produce realistic results when reference points were set for only a few narrowly defined objectives (as can be the

Mediation in Long-Term Planning case when one of the parties has very specific interests). This necessitated several modifications to the model which have not yet been completed. Thus, the procedure has at least proven its usefulness in model validation; further work needs to be done before the procedure can be employed as a teaching aid or used in computer-supported negotiations. CONCLUSIONS In a long-term planning situation, the parties involved often do not think in terms of a utility function, but rather try to balance intuitively a number of qualitative objectives under specific time preferences. Also, they do not necessarily behave as maximizers, but may rather exhibit satisficing behavior (see Wierzbicki, 1983). The approach suggested here takes this type of behavior into account. This paper describes an approach to the problem of understanding and resolving the conflicting objectives of several parties. The approach is based on an opt~mization-oriented decision support system, but is nevertheless pragmatic and heuristic in nature. As such, its merits will depend on aspects of the concrete problems to which it is applied. One of the weak points of the approach lies in the choice of the initial proposal or starting point. In problems of type (3) it might be more desirable to take a status-quo point defined by the conditions of a Nash equilibrium as a starting proposal. However, since the set of Nash equilibria typically contains more than one point, there is still the problem of how to select one of these equilibria. Furthermore, the concept of an SNP, although sometimes used in mediation processes, is not the only one that could have been adopted. A process whereby the parties put forward separate proposals, which are then modified in an iterative fashion, could also be considered. It should also be mentioned that national policies are usually developed using a singlecriterion modeling approach. Thus the traditional modelling methodology has to be modified to allow for the existence of several objectives and interest groups. Nevertheless, we believe that the type of interactive decision-supported gaming proposed here can be of considerable use in various fields which involve issues of conflict resolution. The model of the Austrian energy economic system on which this study was based is deterministic in nature. Long-term planning, however, is typically concerned with problems of a highly stochastic nature. How the procedure could be adapted to this kind of situation is another useful area for further research.

203

REFERENCES Grauer, M. (1983). A Dynamic Interactive Decision Analysis and Support System (DIDASS) - User's Guide. Working Paper WP-83-60, International Institute for Applied Systems Analysis, Laxenburg, Austria. Messner, S., and M. Strubegger (1983). Ein Modell zur Untersuchung der AbhMngigkeiten zwischen Warenkerben, Industrie und Energieversorgung. Unpublished report. Pruitt, D.G. (1981). Negotiation Behavior. Academic Press, New York. Raiffa, H. (1982). The Art and Science of Negotiation. Harvard University Press, Cambridge, Mass. Wierzbicki, A.P. (1981). A mathematical basis for satisficing decision making. In J.N. Morse (Ed.), Organizations: Multiple Agents with Multiple Criteria, SpringerVerlag, Berlin, pp. 465-485. Wierzbicki, A.P. (1983). Negotiation and Mediation in Conflicts. I: The Role of Mathematical Approaches and Methods. This volume.