24 the evolution of decision theory consider first

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Unformatted text preview: e in 1812, could represent an optimistic view of decision analysis today (Howard, 1988 p679): “By this theory, we learn to appreciate precisely what a sound mind feels through a kind of intuition often without realising it. The theory leaves nothing arbitrary in choosing opinions or in making decisions, and we can always select, with the help of this theory, the most advantageous choice on our own. It is a refreshing supplement to the ignorance and feebleness of the human mind. If we consider the analytic methods brought out by this theory, the truth of its basic principles, the fine and delicate logic called for in solving problems, the establishments of public utility that rest on this theory, and its extension in the past and future by its application to the most important problems of natural philosophy and moral science, and if we observe that even when dealing with 20 things that cannot be subjected to this calculus, the theory gives the surest insight that can guide us in our judgement and teaches us to keep ourselves from the illusions that often mislead us, we will then realise that there is no other science that is more worthy of our meditation.” The possibility of effective, systematic reasoning about human action has been appreciated for over two hundred years. Laplace’s predecessor, Bayes, showed in 1763 that probability had epistemological power that transcended its aleatory uses (Howard, 1988). In the early 1700s, Bernoulli captured attitudes towards risk taking in mathematical form. In his Ars Conjectandi (1713), Jacob Bernoulli proposed an alternative to the objectivist view that probability is a physical concept such as a limiting frequency or a ratio of physically described possibilities. He suggested that probability is a “degree of confidence” - later writers use degree of belief - that an individual attaches to an uncertain event, and that this degree depends on the individual’s knowledge and can vary from individual to individual. Similarly, Laplace himself stated in A Philosophical Essay of Probabilities (1812), that probability is but the “expression of man’s ignorance” and probability calculus is relevant to “the most important questions of life” and not just to repetitive games of chance as previously thought. In addition, Augustus De Morgan in his Formal Logic (1847) argued that: “By degree of probability we really mean, or ought to mean, degree of belief…” (Raiffa, 1968 p275) The resurgence of the field in modern times began with statistical decision theory and a new appreciation of the Bayesian perspective (Howard, 1988) which seeks to introduce intuitive judgements and feelings directly into the formal analysis (Raiffa, 1968). In his A Treatise on Probability (1921) Keynes took the position that a probability expresses the rational degree of belief that should hold logically between a set of propositions (taken as given hypotheses) and another proposition (taken as the conclusion) (Raiffa, 1968). Jeffreys (1939) and Jaynes (1956), who worked in the field of physics rather than in mathematics and statistics, provided an...
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