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Comparison of linear interpolation and arctan approximation of one-dimensional monotonic utility functions based on experimental data

Citation

Nikolova, N and Tenekedjiev, K and Dong, F and Hirota, K, Comparison of linear interpolation and arctan approximation of one-dimensional monotonic utility functions based on experimental data, Control and Cybernetics, 38, (3) pp. 835-861. ISSN 0324-8569 (2009) [Refereed Article]


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Abstract

Elicitation of utilities is among the most time consuming tasks in decision analysis. We search for ways to shorten this phase without compromising the quality of results. We use the results from an empirical experiment with 104 participants. They elicited 9 inner nodes from their one-dimensional utility function over monetary gains and losses using three elicitation techniques. A specific feature of the results is their interval character, as the elicitators are fuzzy rational individuals. The data is used to construct arctan-approximated and linearly interpolated utilities and to compare the results. We form partial samples with 3, 4 and 5 nodes for each participant and each elicitation method, and again interpolate/approximate the utilities. We introduce goodness-of-fit and deterioration measures to analyze the decrease in quality of the utility function due to reduced data nodes. The analysis, using paired-sample tests, leads to the following conclusions: 1) arctanapproximation is more adequate than linear interpolation over the whole samples; 2) 5 inner nodes are sufficient to construct a satisfactory arctan-approximation; 3) arctan-approximation and linear interpolation are almost equal in quality over the partial samples, but the local risk aversion of the linearly interpolated utility function is of poor quality unlike that of the arctan-approximated utility function.

Item Details

Item Type:Refereed Article
Keywords:utility function, interpolation
Research Division:Information and Computing Sciences
Research Group:Information Systems
Research Field:Decision Support and Group Support Systems
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Information and Computing Sciences
UTAS Author:Nikolova, N (Professor Nataliya Nikolova)
UTAS Author:Tenekedjiev, K (Professor Kiril Tenekedjiev)
ID Code:127966
Year Published:2009
Web of Science® Times Cited:1
Deposited By:AMC Governance Office
Deposited On:2018-08-26
Last Modified:2018-09-10
Downloads:0

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