Public Choice 85: 353-370, t995. @ 1995 Kluwer Academic Publishers'. Printed in the Netherlands.

PRIVATA: A model for privatization with multiple non-transitive

objectives W.K. BRAUERS Institute for Developing Countries and Faculty of Applied Economics, University of Antwerp (RUCA), Birontlaan 97, B 2600 Berchem-Antwerp, Belgium Accepted 30 January 1995

Abstract. Deregulation of punic enterprises and services by privatization is very fashionable nowadays. The aim of privatization is mainly to increase effectiveness, while the government itself likes to maximize its revenue at the occasion of the takeover. Most of these public enterprises show a shortage in investment while maintenance of a reasonable employment level in the new private firm is also strongly desirable, not to mention the ecological obligations imposed on the new private firm. It means that takeover bids have to face multiple nontransitive objectives and several parties interested in the issue even several decision makers. Traditionally the optimization of all these objectives are then judged upon case by case in a rather subjective way. Consequently there is a need for a more general and objective, not to say scientific, method which can compare several takeover bids for privatization optimizing multiple objectives sometimes with different units of measurement. With that purpose, the Privata model was developed. Privata takes into consideration upper limits, lower bounds, dominating and nondominating effects, ending up with a set of nondominated takeover bids, which are ranked by using the reference point theory based on the maximal criterion values. In this way objectivity and decreasing marginal utility are fuliy respected. A theoretical explanation is followed by a simulation on several takeover bids for a public enterprise given multiple objectives.

1. The theoretical approach of the proposed method 1.1. The problem N o w a d a y s a general tendency in the world exists towards pfivatization of public enterprises and services. Privatization m e a n s then that g o v e r n m e n t services or state enterprises are turned o v e r to private ownership. The purpose is m a i n l y to create a better m a n a g e m e n t for these institutions. The ultimate goal is h o w e v e r very v a g u e as multiple agents such as the g o v e r n m e n t and the eventual buyer, but also the e m p l o y e e s o f these institutions and even the whole population, g i v e n the repercussions on the general tax level, are interested in the issue. All these agents m a y pursue different, mostly non-transitive and e v e n contradictory, objectives. Non-transitivity is h o w e v e r also possible in the b e h a v i o r of an individual. A c o n s u m e r buying a car is facing several non-transitive objectives. Indeed

354 his objectives of safety, comfort, anti-pollution, petrol consumption are in fact separate from the price of the car. Transitivity means then that a common unit of measurement is found for all the objectives with their characteristics; non-transitivity that no common measurement is possible even starting from the axiom of economics that all objectives are measurable. 1 For the government the employment goal has to be a non-transitive objective separated from an optimal takeover price. This price could include a compensation for unemployment, but the unemployed may not be satisfied with a monetary compensation alone. The government may also ask for pollution abatement and for new investments as most of these public enterprises show a shortage in investment. As already said before several agents will try to influence the decision or even multiple decision makers could be present. Sometimes under the decision influencing agents pressure groups may be lobbying such as trade unions, ecologists and consumer organizations. It means that in fact Social Welfare and even Social Well-Being,think of pollution, has to be optimized given multiple non-transitive objectives. What does optimization mean in this context? Since multiple objective problems rarely have points that simultaneously maximize all of the objectives, we are typically in a situation of trying to maximize each objective to the greatest extent possible (Steuer, 1989a: 138).

1.2. Existing methods to approach the problem of multiple objectives The following methods will be taken into consideration: cost-benefit and cost-effectiveness analysis, weighting methods, voting, the scorecard method and the Delphi method.

1.2.1. Cost-benefit analysis Cost-benefit analysis is a typical transitive method with a monetary unit, such as the American dollar, as the common unit of measurement. Indeed even benefits are expressed in the chosen monetary unit, either in a direct or indirect way. 1.2.2. Cost-effectiveness analysis Cost-effectiveness may be called non-transitive, though limited to two objectives: on the one side the costs expressed in a common monetary unit and one effectiveness indicator on the other. For instance a weapon system could balance costs against the rate of kill (Brauers, 1976: 67-126). As initially optimality was absent in cost-effectiveness, several addenda were proposed.

355 Firstly Lange launched his economic principle. Either costs are kept constant with maximization of effectiveness, or effectiveness is kept constant with minimization of costs, i.e., efficiency (Lange, 1968). From linear programming it is known that for this dual the solution is identical, which is only an assumption for nonlinear functions. The question remains however if the unique solution found is also optimal. Secondly fractional programming was proposed for the dual problem (Nykowski and Zolkiewski, 1983). E max. effectiveness max.~ = min. costs For privatization research the fractional programming formula has to be reversed. C max. takeover price at the government side max.- = E rain. unemployment It is however not sure that fractional programming produces the non-utopian optimal solution in the Steuer sense. Moreover other attributes for privatization are excluded such as: return on equity and investment commitments for the new firm, the change in the general tax level, the expected value added, the influence on the balance of payments, other financial, monetary, regional and ecological repercussions, etc. 1.2.3. Weightingmethods Weighting methods being by definition transitive have to be excluded. We follow therefore the definition of Schlaifer (1959) concerning weights. 2 1.2.4. Voting If non-transitive objectives are present in the mind of different people interested in the issue one could think of voting, or even expected voting. Voting in this context is however rejected as a reverse order in the ranking of the results is possible as demonstrated in the Condorcet probtems (see, e.g., Kast, 1993) and later in Arrow's theorem (Arrow, 1951). An example of a reverse order in ranking will be demonstrated later in this paper. Instead of voting convergency in opinions as much as possible, even in an optimal way, has to be aimed at. Therefore the following methods will produce a better result. 1.2.5. The scorecard method In 1953 the islands of the province of Zeetand in the Netherlands were flooded causing the death of thousands and thousands of persons and billions

356 of Guilders in material losses. Closing the islands with one huge dam, making the island a part of the continent and changing the Ooster-Schelde estuarium in a huge sweet water reservoir presented a good solution for the safety people but was found very harmful by the ecologists. Higher dikes on the islands were accepted by the ecologists but not by the safety people. In this way the Ooster-Schelde problem was a good example of antagonistic opinions defended by several groups. The breakthrough would come by finding a solution acceptable for all the parties and their objectives. It means an effort of creative thinking. Brainstorming may be useful in this context, but also the scorecard method. This method was invented by Rand Corporation in the case of the Ooster-Schelde (Rand, 1977). All the advantages and disadvantages of the two propositions were detailed in a systematic way with tables, graphs etc. On basis of this information, new solutions were looked after bringing a kind of greatest possible divisor for all opinions. The solution found consisted of storm dams in front of the islands which would weaken the floods, but keep the OosterSchelde as an open estuarium with salt water. This solution was satisfactory to both security officers and ecologists, and the proposition finally passed in the Dutch Parliament. Perhaps another objective was overlooked at that time, namely the minimization of the budget costs given the increasing cost price of these gigantic public works. It is clear however that it will not always be possible to find a compromise solution. 1.2.6. The Delphi method Delphi is based on a meeting organized in such a way that communication among the participants is impossible. The same effect can be obtained by sending questionnaires. The opinions quantitatively expressed are evaluated with statistical index numbers such as the median and the quartiles. Several successive rounds are possible showing after a while convergence due to the anonymity and the expertise of the participants (see also Brauers, 1987a: 244-245, 1979 and 1976: 45-52). Though the Delphi solution may not be optimal, anyway it is a satisficing one. 3

1.3. The multi-objective case Most of the time with privatization multiple non-transitive objectives are faced such as selling price, employment, new investments and pollution abatement. The optimization of these objectives is then judged upon case by case sometimes in a rather subjective way namely by feeling (Fingerspitzengefiihl). Consequently there is a need for a more general and objective method, that is to say a scientific method, which can compare several takeover

357 bids for privatization of a public service or enterprise optimizing multiple objectives sometimes with different units of measurement. Additionally from what is concluded above, stress is laid upon convergency, including eventually the opinions of minority groups and on optimality to the greatest extent possible in the Steuer sense. Keeping all this in mind Privata was developed considering multiple objectives expressed in different units of measurement, facing the most general case of several private propositions for the takeover of a public enterprise or service. Privata takes into consideration upper limits, lower bounds, dominating and nondominating effects in order to end up with a ranking of all propositions for privatization of a public enterprise or service. Pfivata is composed of two stages: first the filtering stage and then either the indifference or the ranking stage. 1.4. The filtering stage in Privata At this stage several hard constraints are put as a threshold (a lower bound) or as a ceiling (an upper limit), in the case of privatization the filter can be either of a qualitative or of a quantitative nature. As an example of a qualitative limit let us give the example of the takeover of a public enterprise by a daughter of a multinational. In that case the multinational has to accept responsibility for the eventual bankruptcy of the daughter let us say for the next ten years. Indeed out of past experience it is known that bankruptcy of a daughter firm is the cheapest way to liquidate that firm. Another example is the obligation to invest in a well defined region. Quantitative limits could be for instance: a minimum bottom price, a minimum of guaranteed employment, a minimum of new investment, maxima for pollution emissions (CO2, CO, NOx, SO2, particulates, etc.), the liquidity position of the applicant, the obligation to accept the government as a majority or as a minority shareholder, the consideration of a risk factor, etcfi Of course antecedent to the fixation of thresholds and ceilings the necessary feasibility studies have to be made on market capacity, material inputs and human resources and on the evaluation of the necessary investment and financing (Brauers, 1987b and 1990a). In the presence of a single takeover proposition for a public enterprise or service the Privata model stops after the filtering stage (see therefore also Brauers, 1990a). It happens sometimes that a private partner discussed in advance the privatization with the public enterprise or service to be privatized. In this way many difficulties are already solved before the offer is officially introduced. Nevertheless the government or its representatives have to decide if a public auction is not better for the general interest.

358 With several takeover bids which already passed the filtering stage the next step will be that they have to face either the indifference or the ranking stage. Let us discuss first the indifference stage.

1.5. The indifference stage in Privata (indifference method, Brauers, 1977, 1988a) In real life many decision makers are indifferent about alternative solutions at the moment some thresholds or ceilings are respected. 5 Most of the commodities however are no free commodities and services and in the traditional scarce economy the cost side takes then a decisive position. Therefore in the indifference stage, when the alternative solutions pass the filtering stage and the decision makers are indifferent about the solutions, the cost side will determine a ranking of altemative solutions. 6 In the case of Privata government decision makers are indifferent if thresholds are respected by the several propositions conceming employment, investments, liquidity etc. At that moment the takeover bid alone will be decisive for the ranking of propositions with a maximum possible price for the government. In the 1991-drive for privatization the Brazilian government was indifferent about new investments in and the effective way of working of the new private firm and about the decrease in employment (Brauers, 1991). Indeed it was assumed that a private firm will automatically provide new investments, with a multiplier effect on the national income and on the government income through taxation. The decrease in employment was not considered as important, due to the fact that in 1991 ten years of restrictions on hiring new personnel were already existing for the public sector. The firing of 10 till 15% of personnel from the firms being privatized was considered as normal. In this way for the Brazilian government the selling price ofthefirm remained then the only objective to be maximized. The bottom price for the public auction was then the economic value of capital for production, i.e., the sum of the discounted expected cash flows as well known from project management. 7 The economic value of capital for production of a firm was estimated by two separate consulting firms. In case of strong differences in the estimation a third consulting firm was approached.

1.6. The ranking stage in Privata After the filtering stage and when the indifference stage is not applicable the remaining propositions for privatization have to be ranked for the several objectives considered at the same time.

359 If one proposition dominates all the others for all objectives then this proposition is ranked first (strong dominance). 8 If there exists no dominance but indifference for some objectives, but dominance for some other objectives then the propositions are ranked in accordance with this partial dominance (weak dominance). 9 Propositions which are seen to be dominated by the others for all objectives are ranked last. A ranking remains then to be done for those propositions which under these definitions are neither dominating nor being dominated for all objectives considered at the same time. Let us call it the set of till now uncomparable alternatives. 1°

1.7. The solution for the set of till now uncomparable alternatives 1.7.1. The normalization procedure Due to the different units of measurement a non-transitive normalization for the objectives has to occur. Normalization means that the decision makers are asked in a Delphi kind of operation to give a non-additive score to each objective, at the same time leading to (see, for this theory, Brauers, 1993): 1. an expected aggregate utility function which is nonlinear; 2. a utility having a well defined meaning as a measurement of effectiveness; 3. learning taking place due to successive Delphi rounds between the decision makers determining a non-additive score for each objective; 4. decision makers agreeing with the outcome as they participated in its formulation.

1.7.2. The reference point theory with maximal criterion values The following conclusions are drawn from a theoretical research on the multiobjective utility function (Brauers, 1993). 1. A simple weighting of the normalized data or any linearity has to be excluded being in contradiction with diminishing marginal utility. 2. Instead a multi-objective utility function has to be assumed being nonlinear and showing new dominance effects. 3. As it is difficult to determine the exact shape of this utility function an approximation is used under the form of the reference point theory with maximal criterion values. This reference point theory responds indeed to decreasing marginal utility, to nonlinearity and to an objective choice of the reference point. Suppose for instance two alternatives, A with as co-ordinates respectively 20, 10 and 5 and B with as co-ordinates 12, 15, 7, then the co-ordinates of the reference point d* will be respectively 20, 15 and 7 (maximal criterion values). This approach results in an optimum which is realistic as all the chosen co-ordinates of the reference

360 point are realized at least in one of the alternatives and is consequently non-subjective) 1 4. The most effective distance function for the reference point is used at this occasion. 12 The deviations from the co-ordinates of the alternatives to the corresponding co-ordinates of the reference point are presented in a table; the largest deviations are indicated and finally the ranking of the alternatives is made after the smallest size of these deviations.

2.

Simulation exercise on Privata

2.1. The problem The government or his proxies are supposed to fix for instance the following objectives: 13 A. In the micro-economic field: 1. maximization of the selling price for the public enterprise or service; 2. maximization of guaranteed employment; 3. maximization of new investments over a ten year period; 4. minimization of the payback period of Net Present Value; 14 B. In the macro-economic field: 1. maximization of discounted Value Added in constant prices over a ten year period; 2. maximization of total employment (direct, indirect and secondary); 3. maximization of discounted net exports in constant prices over a ten year period; C. In the social-economic field: - minimization of the emission of sulphur dioxide content taken as a typical example of pollution. 2.2. The filtering stage Suppose the govemment or his proxies fix the following thresholds or ceilings for eventual takeover bids on public enterprises or services beside qualitative requirements such as qualitative filters on location, financial responsibility of multinationals for their daughters, etc.: - a minimum bottom price for the takeover bid; - a minimum of guaranteed employment; - a minimum of new investments over a ten year period;

361 - a maximum on the emission of sulphur dioxide; a minimum of Internal Rate of Return, e.g., the rate for getting a loan from the World Bank; - a maximum on the payback period of Net Present Value. Suppose that seven takeover bids are made which will be called A, B, C, D, E, F and G. Takeover bid D does not guarantee the threshold and ceiling concerning respectively Internal Rate of Return and payback period, E cannot guarantee the employment level and refuses to invest in the indicated region, F the new investments and G does not accept any anti-pollution rule and the financial responsibility of the mother firm. It means that after the filtering stage takeover bids A, B and C remain. Only on these takeover bids the reference point theory will be applied. -

2.3. The ranking stage 2.3.1. Dominance After the available information none of the remaining takeover bids seems to dominate strongly or weakly the others for all objectives (see Table 1). The table also shows the different units of measurement of the objectives. In order to normalize the objectives the decision makers are asked in a Delphi exercise to indicate a non-additive score for each of the proposed objectives which are expressed in different units of measurement. The result of the score exercise is given in column (7) of Table t. 2.3.2. The reference point theory with maximal criterion values After the maximal criterion values the co-ordinates of the reference point are equal to the highest co-ordinate found per objective as indicated in Table 2. In case of linearity the totals of Table 2 would have a meaning, but due to the law of diminishing marginal utility, nonlinearity is the rule. In conformity with these requirements the reference point theory is used with the maximal criterion values as the co-ordinates for the reference point. In Table 3 the deviations of the co-ordinates are given. The ranking is made after the smallest size of the deviations (see 1.7.2. above). At that moment the ranking for the best choice is as follows: 1. takeover bid C 2. takeover bid B 3. takeover bid A though the differences are not velN large between the three propositions.

> 0,8 mid $ _>. 750 jobs _< 9 years > 2,5 mid $ over 10 years > 13% over 10 years

> 0 over 10 years > 350 rain over t0 years < 50% of exports

< 8 ton per year

in region I yes

4acro-economics :. Total employment ;, V,A, (discounted) '. Exports (discounted) ;. Risk factor: deterioration of the terms of trade

'ocial economics ,. Emission of sulphur dioxide

)uatitative attributes • Regional :. Financial responsibility

Thresholds or ceilings (filtering) (2)

, Takeover bid , Guaranteed employment ,. Payback period , New investments • Internal Rate of Return

~,ntrepreneurial economics

~ttributes 1)

min. in tons

max. jobs max. in $ max in $ re_in, in %

max, in $ max, jobs rain. in years max, in $ -

Objectives (3)

"able I. Reaction of the several takeover bids on the proposed objectives (with i = 1, 2 , . . . , 9)

yes yes

8 tons

1,300 j. 800 mln $ 450 mln $ 30%

0,8 mid $ 750 j. 5 y. 4.5 mid $ yes

A (4)

yes yes

7 tons

1,200 j. 600 mln $ 400 mln $ 50%

1 mid $ 800 j, 7 y. 3 mid $ yes

B (5)

yes yes

5 tons

1,100 j. 400 mln $ 350 mln $ 20%

1.5 mid $ 900 j, 9 y. 2.5 told $ yes

C (6)

yes yes

1,000 per ton less

5 per job 1 per 80,000 $ 1 per 100,000 $ 100 per % point less

I per 100,000 $ 10 per job 100 per year earlier 1 per 100,000 $ yes

Non-additive scores (u0 (7)

to

¢2r,

363

Table 2. Co-ordinates of the takeover bids and of the reference point. The last ones being equal to the maximal criterion values~ Attributes

A

B

C

d*

1. Takeover bid 2. Guaranteed employment 3. Payback period 4. New investments 5. Total employment 6. V.A. 7. Exports 8. Risk factor 9. Pollution Totals

8,000 7,500 400 4,500 6,500 10,000 4,500 2,000 0 43,400

10,000 8,000 200 3,000 6,000 7,500 4,000 0 1,000 39,700

15,000 9,000 0 2,500 5,500 5,000 3,500 3,000 3,000 46,500

15,000 9,000 400 4,500 6,500 10,000 4,500 3,000 3,000 55,900

aAttributes are multiplied with ul for A, B and C in Table 1.

Table 3. Deviations of the co-ordinates of the takeover bids from the co-ordinates of the reference point Attributes

d*

A

B

C

1. Takeover bid 2. Guaranteed employment 3. Payback period 4. New investments 5. Total employment 6. V.A. 7. Exports 8. Risk factor 9. Pollution Largest deviation

15,000 9,000 400 4,500 6,500 10,000 4,500 3,000 3,000

7,000 1,500 0 0 0 0 0 1,000 3,000 7,(100

5,000 1,{}00 200 1,500 500 2,500 500 3,000 2,tI0t) 6,000

0 {} 400 2,000 1,000 5,000 1.000 0 0 5,000

The indifference method results in the same ranking: C P B P A. Indeed A, B and C having passed the filtering stage are only ranked after the takeover bid itself, the decision makers being indifferent about the other objectives. The linear ranking of C P A P B as given in Table 2 is typical for the linear approach. Indeed bid A is more capital intensive and bid C more labor intensive while B is more in between these two situations also what the

364 takeover price is concemeA. In the case of privatization linearity gives never a chance to a midway solution such as solution B. For privatization purposes one may remark that only the first ranked takeover bid is important and in the given example the takeover bid C is chosen first in the nonlinear as well as in" the linear case. Consequently why should we make further complications if a simple linear approach brings the same solution as the nonlinear one? This is not always so however. Let us consider two objectives and three solutions: A a capital intensive one, C a labor intensive one and B an in between solution, while at first the same importance is given to the objectives.

Importance of the objectives A B C Objective1

5

50

100

Objective2

100

50

4

Weighting method A = (5 x 0.5) + (100 × 0.5) = 52.5 B = (50 × 0.5) + (50 x 0.5) = 50 C = (100 x 0.5) + (4 x 0.5) = 52

Conclusion: A P C P B. In the case of a takeover bid solution A is chosen. Referencepoint method A

B

C

Reference point

1st objective 2nd objective

5 100

50 50

I00 4

100 100

Largest deviation from the reference point

95

50

96

Conclusion: as the ranking is made after the smallest size of the deviation: B P A P C. In case of a takeover bid solution B, representing the midway solution, is chosen. Even when the weights allocated to the objectives are different it is possible that with the reference point method the midway solution B is chosen.

365 Suppose higher weights for objective two: 0.4 for objective one 0.6 for objective two

Weighting method A = (5 × 0.4) + (100 × 0.6) = 62 B = ( 5 0 x 0 . 4 ) + ( 5 0 × 0 . 6 ) = 50 C = (100 × 0.4) + (4 x 0.6) = 42.5

Consequently: A P B P C

Reference point method Let us take a simple assumption: the normalization follows the same direction for the scores as in the weighting method for the weights.

A

B

C

Reference point

1st objective 2nd objective

5 x 4 = 20

50 x 4 = 200

100 × 4 = 400

400

100 x 6 = 600

50 x 6 = 300

4 x 6 = 24

600

380

300

576

Largest deviation from the reference point

Conclusion: B P A P C. In case of a takeover bid solution B is chosen. Suppose higher weights for objective one:

0.6 for objective one 0.4 for objective two

Weighting method : CP BP A Reference point method : B P C P A

366 In all the reference point cases midway solution B is chosen before the more extreme positions A and C, a choice which is never proposed with the weighting method. Is a reverse order in ranking possible if a new proposition is introduced? Therefore we return to the main example as given in the previous Tables 1 to 3. Suppose a new takeover bid M with the same co-ordinates as C, with exception of a total employment guaranty of 12,000. Table 3 changes then as follows: Table 4. Changes in Table 3 with another maximal criterion value for employment

d* 5) Total employment Largest deviation

A

12,000 5,500 7,000

B

C

M

6,000 6,000

6,500 6,500

0 5,000

Table 4 produces the following ranking: M P B P C P A instead o f C P B P A The reason of this reverse order is simple: the reference point is changed. Indeed the first reference point was characterized by the following coordinates: (15,000; 9,000; 400; 4,500; 6,500; 10,000; 4,500; 6,000; 3,000) but the second by: (15,000; 9,000; 400; 4,500; 12,000; 10,000; 6,000; 3,000).If we do not change the co-ordinates of the reference point then there is no reverse order in ranking possible. 15 Table 5. Changes in Table 3 with the original maximal criterion value for employment

5) Total employment Largest deviation

d*

A

B

C

M

6,500

0 7,000

500 6,000

1.000 5,000

-5,500 5,500

Result: C P M P B P A. 2.4. Some practical consequences The rigidity in application is one of the objections which could be raised against Privata. In order to answer this remark the several phases of the model will be reconsidered.

367 1. The govemment has to fix its objectives. This phase has always to be present though many governments forget to state clearly their objectives. 2. The private proposals for takeover have to be filed which is also necessary for privatization without a model. 3. The Delphi exercise is the real first new step. Therefore representatives of the agents interested in the issue have to be brought together and working stations of a computer configuration will assist the audience. The meeting is eventually replaced by other devices such as teteconferencing or E-mail. The sending of questionnaires will take more time mostly accompanied with the sending of reminders. 4. The used distance function is a very simple function for which the software is very easy to write even f o r a personal computerJ 6 Output will also be immediately when a new proposition is introduced. In this way it is shown that the model is very flexible with exception perhaps of the Delphi exercise, in fact a one-off operation. It would be nice if the simulation presented here could be tested in reality. 17 2.5. Summary and conclusion If a model for privatization has to be developed it has to take into consideration Social Welfareand even Social Well-Being. At that moment several agents are interested in the issue and even several decision makers who will postulate their several different objectives sometimes expressed in different units of measurement. It is true however that the economic axiom is accepted whereby all objectives are measurable. Moreover the different units of measurement cannot be reduced to a single unit, which is then called the non-transitivity principle. At that m o m e n t traditional methods such as cost-benefit, costeffectiveness, weighting and voting in order to satisfy "as much as possible all agents and all objectives" cannot be applied. Therefore a new model was developed under the name of Privata which, first with a filtering stage, then with a ranking stage and finally with the use of a distance function, will bring a univocal ranking of all the privatization proposals which passed the filtering stage. The model is flexible enough, also due to computerization, to face all peculiar problems of privatizafion.

Notes 1. Immeasurablenessmakesthe use of economicsimpossible. The sorrowof the widowwho lost her husband and receivedcompassionateallowancehas, e.g., to be localizedoutside the field of economics.

368 2. Weights are then defined as the importance "which a decision maker attaches to each of the events in a set of mutually exclusive and collectively exhaustive events"... "Rule I. The sum of the weights assigned to any set of mutually exclusive and collectively exhaustive events shall be 1"... "Rule 2. The weight assigned to any event shall be a number between 0 and 1 inclusive, 0 representing complete conviction that the event will not occur and I representing complete conviction that it will occur''... "Rule 3. If two or more mutually exclusive events are grouped into a single event, the weight attached to the single event shall be equal to the sum of the weights attached to the original events" (Schlaifer, 1959: 8-11). These rules stress the additivity property of weights. Defined in such a way it means that weights belong to a linear approach. 3. Optimization is rather replaced by a satisficing result as it seems that decision makers are satisfied with it (bounded rationality, Ahituv and Spector, 1990: 5). 4. There is however a limitation in the choice of constraints under the form of thresholds and ceilings. These constraints in the filtering stage have to be hard constraints, which in any case cannot be violated. Indeed one has to be careful not to include soft constraints. Soft constraints are rather considered in the ranking stage. 5. For instance military specialists very often put their aspiration levels too high. Solutions are then mostly far away from their aspiration levels. Consequently they are indifferent about solutions after passing a filtering stage (see Brauers, 1988a and b). 6. For the indifference stage the vector of objectives z of an alternative solution is preferred above the vector of objectives y of another alternative solution iff z~ ~ y~ for all i (with i = 1, 2 ..... n - l ; n as the number of objectives) with one single exception where zn > y~. This just one exception concerns then the cost attribute of the proposed alternatives. 7. For the definition of "the economic value of capital for production", and also for similar notions of capital value, see Braners (1990b). 8. The vector of objectives z strongly dominates the vector of objectives y, iff z > y i.e. zl > yi for all i; i with i = 1, 2, ..,, n; n being the number of objectives (Steuer, 1989a: 147). 9. The vector of objectives z weakly dominates the vector of objectives y, iff z~ _> yi for all i, and z~ > yl for at least one i (Steuer, 1989a). 10. The vectors of objectives z and y are till now incomparable to each other, iff z~ _> yl for some i and zl <_ yi for some other i. 11. The maximal criterion values method is chosen instead of the utopian criterion and the aspiration criterion methods of reference point theory as being more objective. With a utopian criterion vector and an aspiration criterion vector the d% co-ordinates are replaced by d*% and ql respectively. Indeed, the co-ordinates of a utopian criterion vector are formed as follows: d**~ = d*~ + e~ The e~ are moderately small positive values (a subjective element). The co-ordinates ql of an aspiration criterion vector are formed as follows : q~ _< d% ((t% - qi being a subjective element). 12. From mathematics it is known that the most effective distance function in this case runs as follows (Brauers, 1993): Min {max (d*i-yd} with: d*~being the co-ordinates of the reference point yl as the co-ordinates of alternative y, idem for alternatives z, x... i = 1, 2, ...n; n being the number of objectives. Consequently this distance function is a linear function, which strange enough brings a solution to the nonlinearity of the unknown utility function. 13. Of course, most of the time the number of different objectives will be less than the numerous objectives enumerated here. This wide choice of objectives is given however in order to strive to completeness and to show objectives with different units of measurement. 14. The payback period is included as a control on the seriousness of the takeover bid viz. concerning employment, new investments and value added. 15. It has to be remarked that only a reverse order in ranking caused outside the decision maker's opinion has to be condemned. The decision maker himself may however change his priorities with a reverse order in ranking as a result. 16. The author can deliver the software for a personal computer.

369 17. In the previously Centrally Planned Economies of East-Germany and Ukraine the state enterprises were in bad shape with very poor management, low productivity and an urgent need for new investments, being not ready to face competition in a free market economy. Privatization as a solution however presents a problem with several objectives and with several agents interested in the issue. Therefore the Privata-model was presented to <, the official body responsible for privatization in former East-Germany. A member of this important body stated however that privatization was mainly done on pragmatical and political grounds. In fact, Treuhand considered mainly the takeover price and not so much the employment problem creating in that way a huge wave of unemployment and consequently much social unrest in former East-Germany. In an answer on a demand for application in Ukraine it was stated that many preliminary conditions towards a market economy had to be fulfilled before Ukraine could think of privatization (Brauers, 1992).

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