Computational decision analysis (CDA) as a subject has so far not received that much attention. This is bound to change in the near future, since the demand for software to act more independently can only be met realistically by computational methods that are possible to realise in a consistent and perspicious manner. Apart from CDA, not many formalisms and methods are understood by humans and computable by machines at the same time. Even though software agents have been slower than expected to permeate the Web, in the long run distributed computing without decision power in the distributed elements will not be a powerful enough mechanism. Once we stop looking at software objects as entities created to execute in a well-defined ambience, general methods for selecting courses of action at pivotal points in the combined executional state of the object and its environment will become important building blocks if provided with tools for their usage.

Each of the three words in CDA is a key word. Decision means that it deals with selection problems, i.e. situations in which there are more than one alternative course of action. Analysis means that there are not only advises given, not only a single best alternative pointed out by a mechanised procedure, but rather also an aid in understanding the decision problem and how the solutions relate to each other. Computational means that there exist efficiently computable algorithms that perform the analysis in a reasonably short time, to admit interactive analysis. This is equally important for interfaces to man and machine.

Unlike many other formalisms, CDA coexists happily with most of statistics, operations research, and utility theory to the extent of relying on key results in these areas and introducing computationality where needed. CDA has begun to enter into textbooks on AI. Not that AI is the success story it set out to become, but for CDA it is a road into the core of computational CS in general. A view that seems to become more widespread as the years go by is that AI has largely failed, except as a branch of operations research, concerned with ill-defined problems and as a branch of statistics, dealing with less rigoruosly defined problems. This does not mean that spendings on AI have been wasted. The US military claims that all their accumulated spendings on AI research can be justified solely by the savings made using AI scheduling for operation Desert Storm (the Iraq/Kuwait war).

Below, you will find the summary of my thesis (which feels a bit old by now).


Ph.D. Thesis
Royal Institute of Technology
Stockholm, Sweden
Author: Mats Danielson
Title: Computational Decision Analysis
ISBN: 91-7153-613-2
Submitted: March 17, 1997
Defended: May 26, 1997



The thesis deals with Computational Decision Analysis. The thesis presents the DELTA method for decision-making using imprecise information. The objective is to present a method for evaluating choices under uncertainty. The nature of most information available to decision-makers is imprecise, be it information for human managers in organisations or for process agents in a distributed computer environment. In spite of this, most traditional models for decisions disregard this state of affairs. Some more modern approaches, like fuzzy decision analysis and Dempster-Shafer theory address the problem of vagueness. Many of these modern approaches concentrate more on representation and less on evaluation. The emphasis in this thesis is more on evaluation, and even though the representation used is that of standard probability theory, there is nothing to prevent the use of any of the other well-established formalisms. Below you will find a short summary of the thesis.


The first part introduces decision analysis in general and the DELTA method in particular. Chapter 1 begins by surveying a number of traditional decision models and discussing some of their properties. The models are divided into three categories: risk-free, strictly uncertain, and risk models. Following that, some approaches to imprecision in input data are discussed.

Chapter 2 presents a suggested decision method for human decision-makers in work cycle form based on the DELTA method. It attempts to convey some feeling for how a decision-maker can utilise the method in analysing a decision situation. It also tries to demonstrate that the suggested method is realistic to work with.

Chapter 3 presents the DELTA Decision Tool (DDT), an interactive graphical software implementation of the DELTA method intended for aiding human decision-makers in understanding and analysing real-life decision situation. It contains a description of the DDT software and its architecture. The rest of the chapter is devoted to an industrial example, which is used in presenting the features of DDT and the user interaction.


The core of the thesis is the presentation of the DELTA method. Chapter 4 starts with the structure of a decision problem and the required representation of user statements. A model of the situation is created with relevant courses of action and their consequences, should certain events occur. The model is represented by a decision frame. The courses of action will be called alternatives in the model, and they are represented by consequence sets in the decision frame. Following the establishment of a frame, the probabilities of the events and the values of the consequences are filled in. The requirement is emphasised that all statements have an interval form to reflect the imprecise nature of the input data. Next, properties particular to bases (collections of statements) of probability statements and then the value base counterparts are discussed. Finally, the chapter also presents general properties of bases, i.e. collections of constraints and estimates - properties that apply to probability as well as to value bases. Further, the section on translations shows the representation of numerical and qualitative statements of both probability and value.


Chapter 5 presents evaluation methods in detail. The DELTA method is presented step by step, beginning with the discussion of the expected value rule for selection amongst a number of available courses of action. Then a number of other evaluation rules to either replace or supplement the expected value are discussed. They are discussed from a choice rather than preference view. One of the conclusions is that there exists no perfect rule, although the expected value seems to be at least as good as many of its contenders. To improve that rule (or any other similar rule), it is suggested that it is supplemented with other, qualitative rules rather than engaging in further modifications in chase of the perfect rule. The common characteristic of all qualitative rules is that they do not rely on multiplying probabilities and values but treat them as separate numeric entities. Once a rule has been agreed upon, it can be applied to all the alternatives, provided there is a computational procedure for evaluating the alternatives under that rule. The DELTA dominance is introduced as a unifying concept for many of the dominance rules in current use. Dominance and threshold methods are discussed and the kinship between them is pointed out.

Dealing with imprecise statements means frequently encountering decision situations where more than one alternative is to prefer in different parts of the consistent solution space. Consequently, dominance selection rules are not enough to indicate preferred choices. Many ideas have emerged in response to the problem arising when the information given is imprecise and overlaps in the sense that parts of the information seems to favour one alternative (consequence set) while other parts favours another one. This thesis conforms to statistical decision theory and introduces some new concepts to aid the selections. The concepts of maximal and minimal differences represent the most and least favourable possibilities respectively. A new set of selection rules are introduced - the concepts of strong, marked, and weak dominance. The selection procedures suggested in this thesis are based on those concepts and on the expansion and contraction principles.


Chapter 6 deals with computational algorithms for DELTA, especially optimisation since they are the most demanding ones. It starts with linear programming (LP) for determining properties of bases. For solving these LP problems computationally, the Simplex method is used. The chapter continues with bilinear programming, necessary to calculate the results of the evaluation rules. First quadratic programming is discussed and then three algorithms are presented that under mild constraints solve a special bilinear programming problem (BLP1) with LP (Simplex) techniques instead. Due to the unusual problem structure (a long sequence of smaller problems rather than the usual single large one), each of the Simplex techniques must be carefully considered in order to select which ones to apply. Furthermore, hardware architectural issues are found to be important for the implementation of the DELTA solver. The conclusion is that a configuration program is necessary, which will measure the relative speeds of different operations and configure the solver's source code accordingly.


There are two appendices, each addressing one application area of computational decision analysis. Appendix A deals with problems of co-ordinating multi-agent systems and the applicability of DELTA to that area. In dealing with rational agents and their ability to make decisions, it is once more emphasised that there is no universal rule with which rationality could be equated. Instead, the conclusion is that a successful agent must be good at analysing results from a set of reasonable decision rules. Such analyses should ideally exploit several decision rules shown appropriate for the particular domain of interest. Different suggestions of decision rules are investigated in the appendix, but it should be noted that these are not the only possible ones and the DELTA method could use other decision rules as well.

Appendix B applies DELTA to the area of risk analysis as the concept is understood within insurance and security by introducing the DEEP (Damage Evaluation and Effective Prevention) method. A risk analysis method is presented that substantially improves the evaluative phases compared with other, earlier approaches. The presentation is focused on the analysis and identification of threats and on the evaluation of the suggested actions, since those are the points where the DEEP method differs the most from other methods. The idea behind DEEP is to offer an analytical framework for risk management in the classic chain identification-valuation-action without aiming at replacing it.


Updated Thesis Chapters

The thesis is published in monographic book form in a limited edition. To reach a wider audience, two of the introductory chapters are available as ftp-able Postscript files, updated to correct typos found after the thesis was printed. Formally, the corrected chapters are not identical to the thesis chapters and should be regarded as separate documents.


  1. Decision Models
  2. Working with DELTA
  3. The DELTA Decision Tool [see below]

    The DELTA Method

  4. Representation
  5. Evaluation
  6. Optimisation


  7. Multi-Agent Systems
  8. Risk Management
  9. References
Hopefully these chapters will give you an overview of the work and possibly satisfy your curiosity. If not, or if you are unable to retrieve the chapters using ftp, please obtain the thesis from the address given below.

There have been problems with printing Chapter 3. It is generated partly from Word 6.0 (pages 54-65) unlike the other chapters which originate entirely from Word 5.1 files. Some viewers seem to have problems displaying it, and not all printers seem to print beyond page 55. The latter problem is due to timeouts in processing the PS file, and if you adjust the timers, you should be able to print it. For example, it takes about 12 minutes on a HP LaserJet 4MV from a Power Mac 7200 on EtherTalk.


Unfortunately, the thesis is out of print. Hopefully, it will be reprinted in 1999. If so, it may be ordered for a nominal fee from:

Dept. of Computer and Systems Sciences
Secretary of Research
Royal Institute of Technology
Electrum 230, SE-164 40 Kista, SWEDEN

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