Multiple objective programming provides a means of aiding decision makers facing complex decisions where trade-offs among conflicting objectives must be reconciled. Interactive multiobjective programming provides a means for decision makers to learn what these trade-offs involve, while the mathematical program generates solutions that seek improvement of the implied utility of the decision maker. A variety of multiobjective programming techniques have been presented in the multicriteria decision-making literature. This study reviews published studies with human subjects where some of these techniques were applied. While all of the techniques have the ability to support decision makers under conditions of multiple objectives, a number of features in applying these systems have been tested by these studies. A general evolution of techniques is traced, starting with methods relying upon linear combinations of value, to more recent methods capable of reflecting nonlinear trade-offs of value. Support of nonlinear utility and enhancing decision-maker learning are considered.

Review of Empirical Studies in Multiobjective Mathematical Programming: Subject Reflection of Nonlinear Utility and Learning

Rissanen's fertile and pioneering minimum description length principle (MDL) has been viewed from the point of view of statistical estimation theory, information theory, as stochastic complexity theory - i.e., a computable approximation of Kolomogorov Complexity - or Solomonoff's recursion theoretic induction principle or as analogous to Kolmogorov's sufficient statistics. All these - and many more - interpretations are valid, interesting and fertile. In this paper I view it from two points of view: those of an algorithmic economist and a dynamical system theorist. From these points of view I suggest, first, a recasting of Jevon's sceptical vision of induction in the light of MDL; and a complexity interpretation of an undecidable question in dynamics

A Stochastic Complexity Perspective of Induction in Economics and Inference in Dynamics

Computing revealed preferences and limits to the validity of quadratic objective functions for policy optimization

In economics, as in other disciplines, there usually is more than one theory purporting to explain any particular phenomena of interest. This has given rise to alternative models of the same economic system. The existence of such rival models has given rise to two different approaches. The first is the general econometric testing and evaluation of rival models (see, e.g., Davidson and Mackinnon, 1981; Hendry, 1983; Hoel, 1947; Mizon, 1984). The second is the simultaneous use of these models in generating pooled forecasts. The latter approach accepts, in the absence of absolute econometric judgement in favour of one of the models, that each model embodies some useful information that is not present in the other models. The forecast of each model is then pooled, for example, to minimize the overall forecast error (see Granger and Newbold, 1977). Both approaches are, nevertheless, interlinked since the former may use the forecast pooling operation as a means to test the hypothesis for the validity of a model against its rivals and the latter approach may use econometric judgement in defining the pooling operation. In this paper we discuss ways in which the latter can be extended to policy optimization.

B. Rustem

Papers

Paper: Respecifying the weighting matrix of a quadratic objective function

On the definition and detection of structural change