5.1. Formal definition

5.1. Formal definition#

Formally decisions are made based on preference, or, to quote Barzilai 1:

Choice is synonymous to preference as we choose those objects that we prefer.

If a decision maker has to choose between alternatives A and B and prefers A over B then the formal notation is:

\(A \succ B\)

If the decision maker is indifferent between both options the formal notation is:

\(A \sim B\)

Finally, if the decision maker prefers B over A then the formal notation is:

\(A \prec B\)

When decision making problems become more complex different properties, characteristics or aspects of the alternatives to choose from need to be taken into account and are called decision criteria.

Decision theory articulates the three key elements of decision-making processes as:

  1. Identification of options or choices

  2. Development of expectations on the outcomes of each choice

  3. Formulation of a system of values for rating the outcomes to provide an effective ranking and thereby obtaining the preferred choice.

1

Barzilai, J. (2001). Preference Function Modeling: The Mathematical Foundations of Decision Theory.