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

• Autorzy: Nikolova N. , Tenekedjiev K. , Dong F. , Hirota K.
• Języki publikacji: EN

Abstrakty

EN

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) arctan-approximation 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.

Słowa kluczowe

EN

utility function; interpolation; approximation; weighted least square; goodness-of-fit; statistical tests

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2009
• Tom: Vol. 38, no 3
• Strony: 835--861
• Opis fizyczny: Bibliogr. 19 poz., wykr.

Twórcy

autor

Nikolova N.

autor

Tenekedjiev K.

autor

Dong F.

autor

Hirota K.

• Technical University - Varna 1, Studentska Str., 9010 Varna, Bulgaria,

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