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Thresholds and Transitivity in Stochastic Consumer Choice: A Multinomial Logit Analysis

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  • S. K. Lioukas

    (Public Power Corporation, Athens, Greece)

Abstract

In previous work, thresholds have been introduced to describe situations where the consumer is indifferent between any two alternatives. Krishnan (Krishnan, K. S. 1977. Incorporating thresholds of indifference in probabilistic choice models. Management Sci. 23 (July) 1224--1233.) formalised thresholds as minimum perceivable differences between the utilities of the alternatives compared and incorporated such thresholds into the binary logit model. The present paper provides an extension and application of the theory to situations where the decision maker is confronted with more than two alternatives. In such situations thresholds can lead to systematic and predictable intransitivity of indifference, violating a basic postulate of utility theory. Explicit probabilities of transitive and intransitive choices are derived within the framework of the multinomial logit model and the stochastic consumer theory associated with this model. The empirical applicability and managerial usefulness of the proposed theory is illustrated using a transportation example with three alternatives. The data employed reflect actual travellers' use of interurban transport modes in Greece. Parameters are estimated by a maximum-likelihood technique, based on a gradient search method. The results support the existence of thresholds. The application has important policy implications.

Suggested Citation

  • S. K. Lioukas, 1984. "Thresholds and Transitivity in Stochastic Consumer Choice: A Multinomial Logit Analysis," Management Science, INFORMS, vol. 30(1), pages 110-122, January.
  • Handle: RePEc:inm:ormnsc:v:30:y:1984:i:1:p:110-122
    DOI: 10.1287/mnsc.30.1.110
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    Cited by:

    1. Haghani, Milad & Bliemer, Michiel C.J. & Hensher, David A., 2021. "The landscape of econometric discrete choice modelling research," Journal of choice modelling, Elsevier, vol. 40(C).
    2. Di, Xuan & Liu, Henry X., 2016. "Boundedly rational route choice behavior: A review of models and methodologies," Transportation Research Part B: Methodological, Elsevier, vol. 85(C), pages 142-179.
    3. Watling, David Paul & Rasmussen, Thomas Kjær & Prato, Carlo Giacomo & Nielsen, Otto Anker, 2018. "Stochastic user equilibrium with a bounded choice model," Transportation Research Part B: Methodological, Elsevier, vol. 114(C), pages 254-280.
    4. Obermeyer, Andy & Treiber, Martin & Evangelinos, Christos, 2015. "On the identification of thresholds in travel choice modelling," Journal of choice modelling, Elsevier, vol. 17(C), pages 1-9.
    5. Wayne DeSarbo & Kamel Jedidi & Joel Steckel, 1991. "A stochastic multidimensional scaling procedure for the empirical determination of convex indifference curves for preference/choice analysis," Psychometrika, Springer;The Psychometric Society, vol. 56(2), pages 279-307, June.
    6. Cantillo, Víctor & Amaya, Johanna & Ortúzar, J. de D., 2010. "Thresholds and indifference in stated choice surveys," Transportation Research Part B: Methodological, Elsevier, vol. 44(6), pages 753-763, July.
    7. Obermeyer Andy & Wieland Bernhard & Evangelinos Christos, 2014. "Die ökonomische Bewertung kleiner Reisezeiteinsparungen / The Economic Valuation of Small Travel Time Savings," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 234(1), pages 44-69, February.
    8. Xuan Di & Henry X. Liu & Shanjiang Zhu & David M. Levinson, 2017. "Indifference bands for boundedly rational route switching," Transportation, Springer, vol. 44(5), pages 1169-1194, September.
    9. Xinjie Zhang & Hongzhi Guan & Haiyan Zhu & Junze Zhu, 2019. "Analysis of Travel Mode Choice Behavior Considering the Indifference Threshold," Sustainability, MDPI, vol. 11(19), pages 1-23, October.
    10. Desheng Wu, 2017. "Pass-through decision analysis in a supply chain," Annals of Operations Research, Springer, vol. 257(1), pages 297-316, October.

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