In statistics and related subfields of philosophy, the theory and method of formulating and solving general decision problems. Such a problem is specified by a set of possible states of the environment or possible initial conditions; a set of available experiments and a set of possible outcomes for each experiment, giving information about the state of affairs preparatory to making a decision; a set of available acts depending on the experiments made and their consequences; and a set of possible consequences of the acts, in which each possible act assigns to each possible initial state some particular consequence. The problem is dealt with by assessing probabilities of consequences conditional on different choices of experiments and acts and by assigning a utility function to the set of consequences according to some scheme of value or preference of the decision maker. An optimal solution consists of an optimal decision function, which assigns to each possible experiment an optimal act that maximizes the utility, or value, and a choice of an optimal experiment. See also cost-benefit analysis, game theory.

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Multi-Criteria Decision Analysis (MCDA), or Multi Criteria Decision Making (MCDM), is a discipline aimed at supporting decision makers who are faced with making numerous and conflicting evaluations. MCDA aims at highlighting these conflicts and deriving a way to come to a compromise in a transparent process.

For example, the European Parliament may apply MCDA to help assess whether the introduction of software patents in Europe would help or destroy the European software industry. Since MCDA involves a certain element of subjectiveness, the morals and ethics of the researcher implementing MCDA play a significant part in the accuracy and fairness of MCDA's conclusions. The ethical point is very important when one is making a decision that seriously impacts on other people, as opposed to a personal decision. Some of the MCDA methods are:

• Analytic Hierarchy Process (AHP)
• Multi-attribute value theory (MAVT)
• Multi-attribute utility theory (MAUT)
• Multi-Attribute Global Inference of Quality (MAGIQ)
• Goal Programming
• ELECTRE (Outranking)
• PROMETHÉE (Outranking)
• Data Envelopment Analysis
• The Evidential Reasoning Approach
• Dominance-based Rough Set Approach (DRSA)
• Aggregated Indices Randomization Method (AIRM)

The choice of which model is most appropriate depends on the problem at hand and may be to some extent dependent on which model the decision maker is most comfortable with.

The New Approach to Appraisal (NATA), which is a framework used to appraise transport projects and proposals in the United Kingdom, is a major practical application of an MCDA-based approach to support Government decision making. Other applications of MCDA approaches used by the UK Government are set out in its own MCDA manual.

The International Society on Multi-criteria Decision Making is a professional society of researchers and practitioners in the field.

General form

A number of strategies (also called: alternatives / actions) and a number of criteria (also called: aspects / dimensions) by which they are ranked.

	Criterion 1 (f1)	Criterion 2	Criterion 3	Criterion n
Strategy 1 (S1)	f1(S1)
Strategy 2
Strategy 3
Strategy n				fn(Sn)

Classification

A classification is often made, based on the size of the set of strategies:

• MADM (Multi-Attribute Decision Making), concerned with choosing from small, finite, or countable number of strategies.

and

• MODM (Multi-Objective Decision Making), concerned with choosing from a large, infinite, or uncountable number of alternatives.

MCDA's are also often classified based upon the type of aggregation or the nature of the input data.

References

• Andrew, J. H., Stefan, H., & Elisabeth, B. (2008). A multi-objective model for environmental investment decision making. Comput. Oper. Res., 35(1), 253-266.
• Scholz, R.W. & Tietje, O. (2002). Embedded Case Study Methods. Integrating Quantitative and Qualitative Knowledge. Sage Publications. Thousand Oaks, Sage. ISBN 0761919465