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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

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The Local Geometry of Multiattribute Tradeoff Preferences.

Michael McGeachie¹, Jon Doyle

¹Computer Science and ArtificialIntelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139 USA MMCGEACH@CSAIL.MIT.EDU.

Artificial Intelligence

|April 30, 2011

Summary

This study introduces a novel geometric approach to understand quantitative tradeoffs in multiattribute preferences. It extends economic concepts to better represent complex choices involving multiple factors.

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Area of Science:

Decision Sciences
Economics
Mathematical Modeling

Background:

Existing preference representations lack clarity for quantitative tradeoffs.
Qualitative comparisons are well-defined, but quantitative aspects remain ambiguous.

Purpose of the Study:

To develop clear semantics for multiattribute preference statements involving quantitative tradeoffs.
To extend economic notions of marginal rate of substitution to multiple attributes.

Main Methods:

Utilizing directional derivatives from differential geometry.
Applying geometric concepts to interpret preference comparisons with bounded tradeoff ratios.

Main Results:

Established a geometric framework for quantitative tradeoff analysis in preferences.
Extended the marginal rate of substitution concept to multiattribute scenarios.
Provided methods for interpreting attribute importance.

Conclusions:

Differential geometry offers a robust method for analyzing complex preferences.
The new semantics enhance understanding of quantitative tradeoffs and attribute weighting.