Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases.

In recent years, there has appeared high interest to the possibility of formulating decision theory in the language of quantum mechanics. Numerous references on this topic can be found in the books [1-4] and review articles [5-8]. This interest is caused by the inability of classical decision theory [9] to comply with the behaviour of real decision makers, which requires to develop other approaches. Resorting to the techniques of quantum theory gives hopes for a better representation of behavioral decision making. There are several variants of using quantum mechanics for interpreting conscious effects.

In the light of ongoing progresses of research on artificial intelligent systems exhibiting a steadily increasing problem-solving ability, the identification of practicable solutions to the value alignment problem in AGI Safety is becoming a matter of urgency. In this context, one preeminent challenge that has been addressed by multiple researchers is the adequate formulation of utility functions or equivalents reliably capturing human ethical conceptions. However, the specification of suitable utility functions harbors the risk of "perverse instantiation" for which no final consensus on responsible proactive countermeasures has been achieved so far. Amidst this background, we propose a novel socio-technological ethical framework denoted Augmented Utilitarianism which directly alleviates the perverse instantiation problem. We elaborate on how augmented by AI and more generally science and technology, it might allow a society to craft and update ethical utility functions while jointly undergoing a dynamical ethical enhancement. Further, we elucidate the need to consider embodied simulations in the design of utility functions for AGIs aligned with human values. Finally, we discuss future prospects regarding the usage of the presented scientifically grounded ethical framework and mention possible challenges.

Approaches to decision-making under uncertainty in the belief function framework are reviewed. Most methods are shown to blend criteria for decision under ignorance with the maximum expected utility principle of Bayesian decision theory. A distinction is made between methods that construct a complete preference relation among acts, and those that allow incomparability of some acts due to lack of information. Methods developed in the imprecise probability framework are applicable in the Dempster-Shafer context and are also reviewed. Shafer's constructive decision theory, which substitutes the notion of goal for that of utility, is described and contrasted with other approaches. The paper ends by pointing out the need to carry out deeper investigation of fundamental issues related to decision-making with belief functions and to assess the descriptive, normative and prescriptive values of the different approaches.

Statistical decision theory axiomatically assumes that the relative desirability of different options that humans perceive is well described by assigning them option-specific scalar utility functions. However, this assumption is refuted by observed human behavior, including studies wherein preferences have been shown to change systematically simply through variation in the set of choice options presented. In this paper, we show that interpreting desirability as a relative comparison between available options at any particular decision instance results in a rational theory of value-inference that explains heretofore intractable violations of rational choice behavior in human subjects. Complementarily, we also characterize the conditions under which a rational agent selecting optimal options indicated by dynamic value inference in our framework will behave identically to one whose preferences are encoded using a static ordinal utility function.

The effective tailoring of decisions to the needs and desires of specific users requires automated mechanisms for preference assessment. We provide a brief overview of recent direct preference elicitation methods: these methods ask users to answer (ideally, a small number of) queries regarding their preferences and use this information to recommend a feasible decision that would be (approximately) optimal given those preferences. We argue for the importance of assessing numerical utilities rather than qualitative preferences, and survey several utility elicitation techniques from artificial intelligence, operations research, and conjoint analysis.

This article provides an overview of the field of qualitative decision theory: its motivating tasks and issues, its antecedents, and its prospects. Qualitative decision theory studies qualitative approaches to problems of decision making and their sound and effective reconciliation and integration with quantitative approaches. Although it inherits from a long tradition, the field offers a new focus on a number of important unanswered questions of common concern to AI, economics, law, psychology, and management.

Annals of Operations Research, 28 (1-4), 47-66.

This review examines two important works in decision analysis: Howard and Matheson's The Principles and Applications of Decision Analysis, and Winterfeldt and Edwards's "Decision Analysis and Behavioral Research.