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A comparison of intertemporal choices for oneself versus someone else based on Tsallis’ statistics

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  • Takahashi, Taiki

Abstract

Impulsivity and inconsistency in intertemporal choice (discounting) have drawn attention in econophysics and neuroeconomics. Although it is well established that most people often show irrational discounting (e.g., hyperbolic discounting), little is known regarding whether the irrationality is mitigated or not, when the choice was performed by someone else instead of subject herself. This point is important for economic policy-making. In order to compare consistency and impulsivity in choices for oneself versus someone else, we experimentally estimated the consistency parameter q in Tsallis’ statistics-based discount function for oneself and someone else, by assessing the points of subjective equality (indifference points) at 7 delays (1 week to 25 years) in humans. We observed that (i) most people are more inconsistent when the outcomes of intertemporal choice are only relevant to someone else (q=−8.89) than when relevant to oneself (q=−2.63), and (ii) impulsivity, distinguished from inconsistency by utilizing the Tsallis statistics-based q-exponential discount function, is also larger in the choice for someone else than for oneself. Our results indicate that (i) leaving decision-making processes with some others may neither reduce impulsivity nor correct inconsistency and (ii) when q-exponential discounting is utilized, the definition range of q-parameter should be extended to q<0, and smaller (q<1) and larger (q>1) values indicate more inconsistent discounting. Together, the usefulness of the q-exponential discounting for analyzing the dynamic consistency of economic policy was demonstrated in the present study.

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  • Takahashi, Taiki, 2007. "A comparison of intertemporal choices for oneself versus someone else based on Tsallis’ statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 637-644.
  • Handle: RePEc:eee:phsmap:v:385:y:2007:i:2:p:637-644
    DOI: 10.1016/j.physa.2007.07.020
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    Cited by:

    1. Salvador Cruz Rambaud & Ana María Sánchez Pérez, 2020. "Discounted and Expected Utility from the Probability and Time Trade-Off Model," Mathematics, MDPI, vol. 8(4), pages 1-17, April.
    2. Zhao, Pan & Xiao, Qingxian, 2016. "Portfolio selection problem with liquidity constraints under non-extensive statistical mechanics," Chaos, Solitons & Fractals, Elsevier, vol. 82(C), pages 5-10.
    3. Takahashi, Taiki & Oono, Hidemi & Radford, Mark H.B., 2008. "Psychophysics of time perception and intertemporal choice models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2066-2074.
    4. Lu, Yang & Zhuang, Xintian, 2014. "The impact of gender and working experience on intertemporal choices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 146-153.
    5. West, B.J. & Grigolini, P., 2010. "A psychophysical model of decision making," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3580-3587.
    6. Cruz Rambaud, Salvador & Muñoz Torrecillas, María José, 2013. "A generalization of the q-exponential discounting function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(14), pages 3045-3050.
    7. Cruz Rambaud, Salvador & Parra Oller, Isabel María & Valls Martínez, María del Carmen, 2018. "The amount-based deformation of the q-exponential discount function: A joint analysis of delay and magnitude effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 788-796.
    8. Destefano, Natália & Martinez, Alexandre Souto, 2011. "The additive property of the inconsistency degree in intertemporal decision making through the generalization of psychophysical laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(10), pages 1763-1772.
    9. Lu, Yang & Wu, Dongmei & Zhuang, Xintian, 2016. "Part-whole bias in intertemporal choice: An empirical study of additive assumption," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 231-235.
    10. Kirsten I. M. Rohde, 2019. "Measuring Decreasing and Increasing Impatience," Management Science, INFORMS, vol. 65(4), pages 1700-1716, April.
    11. Martinez, Alexandre Souto & González, Rodrigo Silva & Terçariol, César Augusto Sangaletti, 2008. "Continuous growth models in terms of generalized logarithm and exponential functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5679-5687.
    12. Han, Ruokang & Takahashi, Taiki, 2012. "Psychophysics of time perception and valuation in temporal discounting of gain and loss," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6568-6576.
    13. dos Santos, Lindomar Soares & Destefano, Natália & Martinez, Alexandre Souto, 2018. "Decision making generalized by a cumulative probability weighting function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 250-259.
    14. Yang, Xiaojun & Carlsson, Fredrik, 2021. "Are People More Patient with Their Spouse's Money? An Experimental Study," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 94(C).
    15. Salvador Cruz Rambaud & María José Muñoz Torrecillas, 2016. "Measuring Impatience in Intertemporal Choice," PLOS ONE, Public Library of Science, vol. 11(2), pages 1-17, February.
    16. Takahashi, Taiki, 2009. "Tsallis’ non-extensive free energy as a subjective value of an uncertain reward," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(5), pages 715-719.
    17. Meredith S Berry & Mary M Sweeney & Justice Morath & Amy L Odum & Kerry E Jordan, 2014. "The Nature of Impulsivity: Visual Exposure to Natural Environments Decreases Impulsive Decision-Making in a Delay Discounting Task," PLOS ONE, Public Library of Science, vol. 9(5), pages 1-7, May.
    18. Salvador Cruz Rambaud & Isabel González Fernández & Viviana Ventre, 2018. "Modeling the inconsistency in intertemporal choice: the generalized Weibull discount function and its extension," Annals of Finance, Springer, vol. 14(3), pages 415-426, August.
    19. Bhattacharyya, Trambak & Shukla, Shanu & Pandey, Ranu, 2022. "A Tsallis-like effective exponential delay discounting model and its implications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    20. Alexandre Souto Martinez & Rodrigo Silva Gonzalez & Cesar Augusto Sangaletti Tercariol, 2008. "Continuous growth models in terms of generalized logarithm and exponential functions," Papers 0803.2635, arXiv.org, revised May 2008.
    21. Natalia Destefano & Alexandre Souto Martinez, 2010. "The additive property of the inconsistency degree in intertemporal decision making through the generalization of psychophysical laws," Papers 1010.5648, arXiv.org, revised May 2011.
    22. Ausloos, M., 2012. "Measuring complexity with multifractals in texts. Translation effects," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1349-1357.
    23. Takahashi, Taiki, 2010. "A social discounting model based on Tsallis’ statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3600-3603.

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