Confidence-based Representation in Decision Making

ion (derived from Latin abstrahere “to strip off, remove forcibly”) is “the process which allows people to consider what is relevant and to forget a lot of irrelevant details which would get in the way of what they are trying to do” [Giunchiglia and Walsh, 1992]. Abstractionbased processes are pervasive in human reasoning. The earliest and most common use of abstraction was in problem solving. Abstraction maps a “ground” representation of the problem onto a new “abstract” representation, which preserves certain desirable properties and is simpler to handle, since it is built by “throwing away details” of the ground representation [Holte and Choueiry, 2003]. Management science is concerned with modelling and solving managerial decision problems. Problems investigated in the literature are generally abstracted from real world cases. This process of abstraction is necessarily non-deductive: it is led by inductive and/or abductive reasoning and cannot represent nor preserve all (potentially infinite) properties of the real problem faced by a manager [Popper, 1934]. Unfortunately, non-deductive reasoning is often representation dependent: representing the same situation in two different ways may lead to different answers. For instance, Ptolemy’s epicyclic solar system was more accurate predicting the positions of planets than Copernicus’ view, until Kepler introduced the possibility that orbits are ellipses. Interestingly, the authors in Halpern and Koller [2004] remark that representation independence is too much to expect if one aims for nontrivial conclusions and that researchers in machine learning and statistics have long realised that representation bias is an inevitable component of effective inductive reasoning. A management science model, like any other scientific model, is essentially a hypothesis. This perspective finds its origins in the scientific method pioneered by Galileo and Bacon and reinforced by Karl Popper’s explication of the hypothetico-deductive model [Popper, 1963] in which the hypothesis is considered to be just “a guess.” As such, one may say that there is no single “correct” or “true” model. There are instead models that reflect, to a greater or lesser extent, certain aspects of reality that are of interest to the decision maker. This perspective on the nature of decision support models is often lost in management science, because researchers tend to mainly focus on the analytical part of the scientific method, heavily influenced by the strong tradition of Platonic realism found in mathematics [Tait, 1986], while disregarding the importance of the inductive and/or abductive aspects of modelling. In short, classical management science models focus on providing a single optimal or near-optimal solution, obtained analytically, to an abstracted problem. ∗29 Buccleuch place, EH8 9JS, Edinburgh, UK