Abstract
In this chapter, the fundamentals of decisions are presented. Basic terminology (alternatives, states, events, outcomes, etc.) is introduced and the different typologies of decisions are analyzed. After a very brief review of the history of Decision Theory, the decision process is analyzed, from the point of view of several authors. Finally, it is shown that all methodologies can be aligned with Herbert A. Simon’s model of decision process. Based on that model, the three major steps in decision management are studied: intelligence, design, and choice. Afterwards, the fundamental choice step is analyzed according to the different possible scenarios: single decision scenario and multiple decision scenario. In the single decision scenario, the different situations are described: decision-making under certainty, decision-making under risk, decision-making under uncertainty, and decision-making under hybrid scenarios. In the multiple decision scenario, two formalisms of decision modelling are explained: decision trees and influence diagrams. Finally, group decision-making is described, and general procedures are outlined.
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Notes
- 1.
A lottery is a probabilistic mixture of outcomes, according to von Neumann and Morgenstern.
- 2.
Herbert Simon borrowed the military meaning of intelligence for naming the first phase, as he wrote in his book (Simon, 1960).
- 3.
p(A ∩ B) = p(A) ∗ p(B| A), but if A and B are independent, then p(A ∩ B) = p(A) ∗ p(B), because p(B| A) = p(B).
- 4.
An event is a random variable, which have as possible values the different states. It is formed by the union of all its constituent states. The sum of all probabilities of the states of an event sum one.
- 5.
The operator div provides the quotient of the integer division and the operator mod provides the remainder of the integer division.
- 6.
An event can be assimilated to the statistical concept of random variable, and its states or possible results are the possible values of the random variable.
- 7.
an inference rule is a rule with this format: if <conditions> then <conclusions>
- 8.
According to Arrow (1951), who was awarded the Nobel prize in economics in 1972, a social welfare function maps a set of individual orderings (ordinal utility functions) for everyone in the society to a social ordering, i.e. a rule for ranking alternative social states.
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Further Reading
Fidora, A. and Sierra, C. (Eds.) (2011). Ramon Llull: From the Ars Magna to Artificial Intelligence. Institut d’Investigació en Intel·ligència Artificial (IIIA-CSIC). Available at http://www.iiia.csic.es/library
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Luce, R. D., & Raiffa, H. (1957). Games and decisions: Introduction and critical survey. Wiley.
The Augsburg Web Edition of Llull’s Electoral Writings. (2016). Available at www.uni-augsburg.de/llull/
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Sànchez-Marrè, M. (2022). Decisions. In: Intelligent Decision Support Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-87790-3_2
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