| Decision theory refers to the analysis, formalization, and prediction, through mathematical models, of optimal and real decision-making; it involves the process of selection of perceived solutions, actions, and outcomes to a given problem from a set of possible alternatives. Depending on the extent of possible quantification, presence of uncertainty, number of decision makers, and number of objectives, decision theory is classified as quantitative or qualitative, deterministic or stochastic, single or multiple party, and single or multiobjective. The management of water resources systems involves unavoidable natural and social conditions of risk and uncertainty and multiple competing or conflicting parties and objectives, which introduce the risks of high economic and social costs due to wrong decisions, necessitating the formulation of models that adequately represent a given situation by incorporating all factors affecting it.; Hence, the adequate modeling of such systems should incorporate risk and uncertainty; decision theory under risk and uncertainty is called decision analysis or risk management. Risk management approaches may be broadly categorized as non-probability and probability based techniques. Non-probability based techniques include sensitivity analysis, decision criteria, analytical hierarchy, and game theory; probability based techniques include scenario analysis, moments, decision trees, expected value, stochastic optimization, Bayesian and fuzzy analysis, and downside risk measures such as Value-at-Risk and Conditional Value-at-Risk metrics. Many of these methods, though very useful, suffer from critical shortcomings: sensitivity and scenario analysis only provide some intuition of risk, expected value fails to highlight extreme-event consequences, decision trees and hierarchical approaches fail to generate robust and efficient solutions in highly uncertain environments, central moments do not account for fat-tailed distributions and penalize positive and negative deviations from the mean equally, recourse does not provide means to control risk, and Value-at-Risk does not provide information about the extent and distribution of the losses that exceed it and is not coherent. Game theory, used in situations of multiple party decision making, suffers from several systematic violations, such as the common consequence, preference reversal, and framing effects. To account for some of these shortcomings, several extensions and alternatives have been suggested such as the conditional-Value-at-Risk and behavioral game theory. |
