Title: An optimal information gathering algorithm

Authors: Debora Di Caprio, Francisco J. Santos-Arteaga

Addresses: Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON, M3J 1P3 Canada. ' GRINEI, Universidad Complutense de Madrid, Campus de Somosaguas, 28223 Madrid, Spain

Abstract: The current paper defines the optimal sequential information gathering structure of a rational utility maximiser decision maker in the simplest non-trivial theoretical scenario, where the decision maker is allowed to acquire only two pieces of information from a set of multidimensional goods. We show how this problem, hardly ever considered in the literature, does not admit a simple or intuitive solution. Indeed, while the standard sequential search and information gathering algorithms presented in the literature are identified with optimal stopping rules, we analyse explicitly the behaviour of the decision maker when choosing which piece of information to acquire. We show that the decision of how to optimally allocate the second available piece of information depends on two well-defined real-valued expected utility functions. The crossing points between the graphs of both functions correspond to optimal thresholds for the information gathering process that define the dynamic behaviour of the algorithmic search structure. We characterise explicitly the behaviour and the value of these thresholds through the properties of the utility functions and probability densities inherent to the decision maker. The results are illustrated numerically for a variety of utility functions commonly used in decision theory.

Keywords: multiple criteria decision making; MCDM; rational behaviour; expected utility; choice theory; decision support; information gathering; knowledge management; information dashboards; risk aversion.

DOI: 10.1504/IJADS.2009.026549

International Journal of Applied Decision Sciences, 2009 Vol.2 No.2, pp.105 - 150

Published online: 19 Jun 2009 *

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