## The Science Of Decision Making

Scientists have studied decision making for centuries. In the 16th century, the Italian Gerolamo Cardano (1501-1576) studied betting strategies for gambling. Before his time, the outcomes of gambling were viewed as the will of the gods. His book The Book on Games of Chance, written in the 1560s but published only in 1663 after his death, contains the first systematic treatment of probability. In the 17th and 18th centuries, Pierre Fermat (1601-1665), Blaise Pascal (1623-1662), and Pierre Laplace (1749-1827) developed probability theory (Laplace, 1812). Daniel Bernoulli (1700-1782), first introduced the subjective (nonfrequentist) view of uncertainty. After this idea,Thomas Bayes (1702-1761) and Laplace introduced a concept, called a subjective probability, defined as the degree of a person's belief in some proposition. This view of probability enabled Bayes to formulate a rule for updating subjective probabilities in the light of new evidence. Bayes' view of probability theory was published posthumously in 1763 (Bayes, 1958). The concept of subjective probability and Bayes' rule greatly expanded the range of decision problems that scientists could analyze. Subjective probability and Bayes rule have become cornerstones of medical diagnosis (Cooper, 1984) and of modern biosurveillance ( Wagner et al., 2001; Cooper et al., 2004).

Daniel Bernoulli introduced an economic theory that accounted for discrepancies between the recommendations of probabilistic models and how people make decisions and choices in every aspect of life (Bernstein, 1996). One well known discrepancy at the time was the St. Petersburg paradox, which Bernoulli addressed. He was the author in 1738 of the Exposition of a New Theory on the Measurement of Risk (Bernoulli, 1954 [1738]; Stanford Encyclopedia of Philosophy, 2005). His solution to the St. Petersburg paradox formed the basis for future economic theories of risk aversion, risk premium, and utility.

Behavioral psychologists study how humans make decisions from an observational perspective. Their research demonstrates that decisions made by experts can be inferior to those made by even the simplest of mathematical models (Dawes, 1979). They have found that humans, when making decisions, use heuristics (rules of thumb) that lead to systematic errors and suboptimal decisions (Tversky and Kahneman, 1974), and they have demonstrated an inverse relationship between time pressure and decision quality (Edland and Svenson, 1993). This long-standing interest of psychologists in human decision making has evolved into a branch of psychology known as behavioral decision theory (Tversky and Kahneman, 1974). Recently, a prominent behavioral psychologist, Daniel Kahneman, received a Nobel Prize for his contribution to our understanding of human judgment under uncertainty.