Methods for Aiding Decision Makers

There are a number of methods which have been developed to provide a rational model for making decisions. The purpose of these techniques is to provide a decision maker with a rational perspective for selecting the "best" path.  These techniques help a decision maker frame the known criteria and alternatives and deal with uncertainty where it may be present. The term for the body of these techniques is Decision Analysis (DA). These techniques are higher level of analysis than those oriented exclusively toward finance such as return on investment (ROI) or payback period. This digital paper provides a general introduction to the elements, provides a brief example, gives a single paragraph description of many of the techniques, and gives pointers to specific commercial products for implementing them.

Introduction to the Elements of Decision Analysis

A decision analysis technique may contain some or all of the following elements.

Element Purpose is to:
Goal / Challenge succintly state the ultimate end point of the challenge
Alternatives / Options / Objectives help in eliciting and describing the list of alternative measures or objectives to be met in attacking the challenge
Criteria / Objectives / Attributes 
(may include sub-criteria)
list such items as cost, technical, social, and political factors to be considered in the decision
Uncertainty / Preference provide a method for attaching information relating to the probability or expected value of an occurrance
Measurement Scales specifically value a criteria or alternative. Examples of scales include $, points, yards, horsepower,yes/no
Synthesis Technique  provide for combining all the elicited and evaluated data to produce a specific answer or ranking in the alternatives
Decision Makers poll and apply values from multiple participants

A Brief Example

The goal is to select a new automobile.
Alternatives might include a Volvo 740, a Mercedes 190e, a Thunderbird, a Maxima, and a Grand Am.
Criteria would include such common characteristics as cost, performance, obsolescence period, and styling.
Uncertainty would relate to a criteria such as family size - which may currently be four but may expand or contract depending on a variety of conditions.
Preference would relate to a criteria such as styling - which is obviously subjective measure.
Measurement scales would differ depending on the criteria such as dollars for costs, a scale such as great/good/fair/poor for styling, and a scale such as years for obsolescence.
A synthesis technique would dictate how all the above would be "combined" to rank or distance the alternatives. Methods here include additive, multiplicative, geometric mean, and vector processing.
Multiple decision makers must be provided for by weighing the value of each decision maker.
The simple diagram below shows the results of an analysis where a decision maker has evaluated the autos on the criteria.
An excellent in-depth description of this and other examples may be found in An Exposition on the Analytic Hierarchy Process .

Description of Some Techniques

Researchers have developed a number of macro level techniques for organizing, controlling and effecting these elements. Nine of these techniques and a brief description of each are listed and discussed below.

Analytic Hierarchy Process (AHP) provides selection and ranking of alternatives using criteria and pairwise relative comparison. That is the BMW would be compared to the Oldsmobile on the different criteria such as cost, speed, etc. The synthesis technique utilizes a mathematical techniques called eigenvector/eigenvalue processing. It also has a consistency check to insure you are not making inconsistent judgements when evaluating large problems. Inherent in AHP is a cognitive short term memory aide and a 1 to 9 numeric scale for evaluation. This scale was developed using human cognitive experiments.

Bayesian Updating is a "a posteriori" technique postulated in the 18th Century by Rev. Thomas Bayes. It combines a users beliefs with evidence and hypotheses. It follows the basic tenets of mathematical probability to help a user evaluate network paths for subsequent action. It was partially developed because humans tend to understate changes in position based upon new information.

Cost Benefit Analysis (CBA) is a relatively simple technique where a dollar assignment is made to a list of benefits and costs. Final evaluation is made through an additive or ratio comparison of costs and benefits. A major complaint of this method is the difficulty in determining benefits.

Cost Effectiveness Analysis is a technique in the same genre as CBA. An effectiveness measure is created for each criterion. The ratio of cost to effectiveness then provides a ranking of alternatives. Example: Measure of Effectiveness = time to reach 60mph Measure of Cost = dollars time cost ratio

Alternative A: time to reach 60mph = 5.0 sec cost = $20,000 therefore score = 250
Alternative B: time to reach 60mph = 15.0 sec cost = $5,000 therefore score = 333
One criticism of this method is the lack of consumer "preference" inherent in these ratios. For example in the above, cost may be a significant factor to one consumer but not another. This technique assumes cost "indifference." Another problem is the lack of a specific synthesis technique to combine the scaled criteria.

Decision Trees utilize the application of probabilistic factors and "payoffs" to outcomes (alternatives). A tree is created representing the outcome of all possible states within the stages of a multifaceted decision. One criticism of the tree method is that it uses the "expected value" approach.

Matrix is likely the most commonly used technique. It is a technique which utilizes a simple matrix - e.g criteria along the side and alternatives along the top - for the selection of a "best" alternative. It utilizes a subjective weight assignment for applying weights to the criteria, and for applying scores to each alternative's criteria. While simple, it fails two important criticisms of decision analysis techniques - the accounting for interdependence between criteria, and establishing distance measures among alternatives on every criterion.

Outranking created by B. Roy at the University of Paris. Outranking is less concerned with a method for applying weights to attributes, and more with a holistic comparison of Alternative A to Alternative B. Roy's utilizes both concordance and discordance measures for accomplishing this. The concordance measure is a ratio computed by summing the weights for those attributes for alternative A which are superior to the attributes for Alternative B divided by the weights for Alternative A as a whole. The closer this ratio is to 1.0, the more superior Alternative A is to Alternative B. The discordance measure looks the largest difference for the attribute sets of A over B compared to the largest difference over all alternatives.

Subjective Judgement Theory is a statistically oriented technique which requires the user to evaluate "holistic" hypothetical combinations of criteria. SJT converts these evaluations into weights to be applied to each pre-defined criterion using the least squares method. One criticism is the large number of evaluations which must be performed to elicit these numbers.

Utility Assessment encompasses several known techniques for extracting a decision maker's preferences. These include simple ranking, category methods, direct methods, gamble methods and indifference methods. There is considerable value to establishing what is known as a utility curve for each attribute of a decision. This curve establishes a utility score (e.g. a number from 1 to 10) over the range of values a criterion can assume. For example an automobile's acceleration (from 0 to 60 mph) may take a range of 4.0 to 25.0 seconds, being assigned respectively scores of 10 and 0. A curve would be elicited for values in between these ranges.

Commercial Products

 A short list of some of those vendors follow.
Analytic Hierarchy Process
Expert Choice 2000, $995
Expert Choice, Inc 
5001 Baum Blvd, Suite 650 
Pittsburgh, PA 15213
Influence Diagramming / Decision Tree 
DPL, $995

Syncopation Software Limited
11 West Temple Sheen
London SW14 7RT
United Kingdom

+44 (0) 870 444 2580

See OR/MS Today, June 2002 Decision Analysis Software Survey for a more complete list. Available at 

The publication OR/MS Today from The Institute for Operations Research and Management Science periodically publishes a complete up to date listing of available software in this arena. The latest update may be found in the June 2002 issue. See Decision Analysis: Aiding Insight VI: 'It's Not Your Grandfather's Decision Analysis Software' By Daniel T. Maxwell.


The objective of development in decision analysis  has been to improve the ability of the human decision maker to make more timely and better quality decisions. Toward this end, extensive algorithmic techniques have been developed for  properly framing the decision environment. Practicing University decision science departments have been successful in planting these techniques in daily private and public sector operations. But they are also aware of limitations and shortfalls in their usage.  Research has shown that the more sophisticated techniques tend to produce results that decision makers prefer. But those same techniques require considerable time to understand and to utilize. Therefore they are under utilized.  At the same time education in this area needs to be expanded. Many decision makers continue to rely upon faulty, personal, inductive methods and are unaware of the efficacy of decision science methods. Fortunately packaged software is now available to help in applying these methods and for easily gathering opinion and for weighing alternatives.

(c) 1998 John H. Saunders; updated March 2004.