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From Von Neumann to Morgenstern: How to use mathematics to solve the puzzle of uncertainty?
Decision Analysis (DA) is a profession that addresses the philosophy, methodology, and practice of critical decision-making in a formal manner. This discipline includes a variety of procedures, methods, and tools for identifying, articulating, and formally evaluating important aspects of decisions and recommending courses of action through the application of the axiom of maximum expected utility. As uncertainty deepens, how can decision analysis play a key role in business and public policy decisions?
Historical background
In 1931, mathematical philosopher Frank Ramsay proposed the concept of subjective probability, which became an expression of personal belief and uncertainty. Later, in the 1940s, mathematician John von Neumann and economist Oscar Morgenstern jointly developed the axiomatic basis of utility theory to express individual preferences for uncertain outcomes.
The expected utility theory of decision analysis provides a complete axiomatic basis for making decisions under uncertainty.
In the early 1950s, statistician Leonard Jimmy Savage further advanced the application of decision analysis by developing an alternative axiomatic framework. As these basic theories gradually mature, decision analysis methods continue to be standardized and popularized, and are widely offered in business schools and industrial engineering departments. In 1968, Howard Reiffa, a decision theorist at Harvard Business School, published a concise and easy-to-understand introduction.
Methodology and its significance
"Framework building" in decision analysis is core content, emphasizing key steps such as developing opportunity statements, boundary conditions, and success indicators. Many people mistakenly believe that decision analysis must rely on quantitative methods, but in fact, many decisions can rely solely on qualitative tool understanding, such as value-oriented thinking. This process may lead to the development of impact diagrams or decision trees, graphical tools that help visualize decision options and their uncertainty.
Risk attitude is represented by a utility function, and when faced with conflicting goals, it can be expressed using a multi-attribute value function.
Application scope of decision analysis
Decision analysis is widely used in various fields such as business, management, environmental governance, medical care, energy, and law. For example, in the 1970s, the Stanford Research Institute conducted a major study on the pros and cons of hurricane vaccination. Today, many large companies make billions of dollars in capital investments every year, all of which are inseparable from the support of decision analysis.
"Decision analysis is part of how Chevan operates because it works."
Decision Analysis as a Normative Method
Normative decision research focuses on how to make the "best" decisions, while descriptive research attempts to explain how people actually make decisions. When time is tight, formal methods of decision analysis often appear inflexible, and intuition and experience often dominate decision-making at this time. Furthermore, research shows that, given time, decision-making outcomes from quantitative algorithms often outperform pure intuition.
Applications in specific fields
Decision analysis methods are applicable to many specific fields, such as medical decision-making, military planning and diplomatic security. Its applications began in environmental science and have even gained traction in areas such as insurance and litigation. By assessing trade-offs and managing risks, decision analytics can guide companies to make smarter choices.
Conclusion
Decision analysis provides a structural methodology when dealing with complex decisions, but in some cases it may also help decision makers overcome choice difficulties. As the industry advances and technology develops, decision analysis tools and software continue to evolve, and they are widely used in university research and professional practice. In the face of an increasingly complex decision-making environment, can decision analysis truly guide us towards a better future?
