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Eliciting the just-noticeable difference

Author

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  • Pawel Dziewulski

Abstract

Abstract The evidence from psychophysics suggest that people are unable to discriminate between alternatives unless the options are significantly different. Since this assumption implies non-transitive indifferences, it can not be reconciled with utility maximisation. We provide a method of eliciting consumer preference from observable choices when the agent is incapable of discerning between similar bundles. It is well-known that the issue of noticeable differences can be modelled with semiorder maximisation. We introduce a necessary and sufficient condition under which a finite dataset of consumption bundles and corresponding budget sets can be rationalised with such a relation. The result can be thought of as an extension of Afriat's (1967) theorem to semiorders, rather than utility optimisation. Our approach is constructive and allows us to infer the just-noticeable difference that is sufficient for the agent to differentiate between bundles as well as the "true" preferences of the consumer (i.e., as if perfect discrimination were possible). Furthermore, we argue that the former constitutes a natural measure of how well the preference revealed in the data could be approximated by a weak order. We conclude by applying our test to household-level scanner panel data of food expenditures. Revised June 2017.

Suggested Citation

  • Pawel Dziewulski, 2016. "Eliciting the just-noticeable difference," Economics Series Working Papers 798, University of Oxford, Department of Economics.
  • Handle: RePEc:oxf:wpaper:798
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    File URL: http://www.economics.ox.ac.uk/materials/papers/14548/798-revised-june-17-dziewulski.pdf
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    References listed on IDEAS

    as
    1. Federico Echenique & Sangmok Lee & Matthew Shum, 2011. "The Money Pump as a Measure of Revealed Preference Violations," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1201-1223.
    2. Avraham Beja & Itzhak Gilboa, 1989. "Numerical Representations of Imperfectly Ordered Preferences (A Unified Geometric Exposition," Discussion Papers 836, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
    4. Chambers,Christopher P. & Echenique,Federico, 2016. "Revealed Preference Theory," Cambridge Books, Cambridge University Press, number 9781107087804, December.
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    Cited by:

    1. Anthony Heyes & Sandeep Kapur & Peter W. Kennedy & Steve Martin & John W. Maxwell, 2018. "But What Does it Mean? Competition between Products Carrying Alternative Green Labels when Consumers are Active Acquirers of Information," Birkbeck Working Papers in Economics and Finance 1812, Birkbeck, Department of Economics, Mathematics & Statistics.
    2. Echenique, Federico & Imai, Taisuke & Saito, Kota, 2018. "Approximate Expected Utility Rationalization," Rationality and Competition Discussion Paper Series 103, CRC TRR 190 Rationality and Competition.
    3. Pawel Dziewulski, 2018. "Just-noticeable difference as a behavioural foundation of the critical cost-efficiency," Economics Series Working Papers 848, University of Oxford, Department of Economics.

    More about this item

    Keywords

    Revealed preference; testable restrictions; semiorder; just-noticeable difference; GARP; Afriat's efficiency index; money-pump index;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis

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