A hyperbolic decay of subjective probability of obtaining delayed rewards
Background Hyperbolic discounting of delayed and probabilistic outcomes has drawn attention in psychopharmacology and neuroeconomics. Sozou's evolutionary theory proposed that hyperbolic delay discounting may be totally attributable to aversion to a decrease in subjective probability of obtaini...
Ausführliche Beschreibung
Autor*in: |
Takahashi, Taiki [verfasserIn] |
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E-Artikel |
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Sprache: |
Englisch |
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2007 |
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Anmerkung: |
© Takahashi et al; licensee BioMed Central Ltd. 2007 |
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Übergeordnetes Werk: |
Enthalten in: Behavioral and brain functions - London : BioMed Central, 2005, 3(2007), 1 vom: 25. Sept. |
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Übergeordnetes Werk: |
volume:3 ; year:2007 ; number:1 ; day:25 ; month:09 |
Links: |
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DOI / URN: |
10.1186/1744-9081-3-52 |
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Katalog-ID: |
SPR029339235 |
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520 | |a Background Hyperbolic discounting of delayed and probabilistic outcomes has drawn attention in psychopharmacology and neuroeconomics. Sozou's evolutionary theory proposed that hyperbolic delay discounting may be totally attributable to aversion to a decrease in subjective probability of obtaining delayed rewards (SP) which follows a hyperbolic decay function. However, to date, no empirical study examined the hypothesis, although this investigation is important for elucidating the roles of impatience, precaution, and uncertainty aversion in delay discounting processes. Methods In order to (i) determine the functional form of the relation between delay until receipt and SP, and (ii) examine whether delay discounting is attributable to a decrease in SP, we assessed the subjects' SP and their delay and probability discounting. We examined the fitness of hyperbolic and exponential functions to the assessed SP, and relations between the SP, and delay/probability discounting, and subjective-probability discounting for delayed rewards. Results The results demonstrated (a) SP decayed hyperbolically as delay increases, (b) a decay of SP was associated with delay discounting, and (c) subjective-probability discounting did not significantly correlate with delay discounting. Conclusion Our results demonstrated (i) hyperbolic decay of SP is related to delay discounting, and (ii) delay discounting is, however, not attributable to precautious foresight in intertemporal choice. Further, a novel parameter of pure time preference is proposed. | ||
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700 | 1 | |a Hasegawa, Toshikazu |4 aut | |
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10.1186/1744-9081-3-52 doi (DE-627)SPR029339235 (SPR)1744-9081-3-52-e DE-627 ger DE-627 rakwb eng Takahashi, Taiki verfasserin aut A hyperbolic decay of subjective probability of obtaining delayed rewards 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Takahashi et al; licensee BioMed Central Ltd. 2007 Background Hyperbolic discounting of delayed and probabilistic outcomes has drawn attention in psychopharmacology and neuroeconomics. Sozou's evolutionary theory proposed that hyperbolic delay discounting may be totally attributable to aversion to a decrease in subjective probability of obtaining delayed rewards (SP) which follows a hyperbolic decay function. However, to date, no empirical study examined the hypothesis, although this investigation is important for elucidating the roles of impatience, precaution, and uncertainty aversion in delay discounting processes. Methods In order to (i) determine the functional form of the relation between delay until receipt and SP, and (ii) examine whether delay discounting is attributable to a decrease in SP, we assessed the subjects' SP and their delay and probability discounting. We examined the fitness of hyperbolic and exponential functions to the assessed SP, and relations between the SP, and delay/probability discounting, and subjective-probability discounting for delayed rewards. Results The results demonstrated (a) SP decayed hyperbolically as delay increases, (b) a decay of SP was associated with delay discounting, and (c) subjective-probability discounting did not significantly correlate with delay discounting. Conclusion Our results demonstrated (i) hyperbolic decay of SP is related to delay discounting, and (ii) delay discounting is, however, not attributable to precautious foresight in intertemporal choice. Further, a novel parameter of pure time preference is proposed. Subjective Probability (dpeaa)DE-He213 Delay Discount (dpeaa)DE-He213 Discount Function (dpeaa)DE-He213 Hyperbolic Discount (dpeaa)DE-He213 Indifference Point (dpeaa)DE-He213 Ikeda, Koki aut Hasegawa, Toshikazu aut Enthalten in Behavioral and brain functions London : BioMed Central, 2005 3(2007), 1 vom: 25. Sept. (DE-627)484836994 (DE-600)2185773-8 1744-9081 nnns volume:3 year:2007 number:1 day:25 month:09 https://dx.doi.org/10.1186/1744-9081-3-52 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 3 2007 1 25 09 |
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10.1186/1744-9081-3-52 doi (DE-627)SPR029339235 (SPR)1744-9081-3-52-e DE-627 ger DE-627 rakwb eng Takahashi, Taiki verfasserin aut A hyperbolic decay of subjective probability of obtaining delayed rewards 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Takahashi et al; licensee BioMed Central Ltd. 2007 Background Hyperbolic discounting of delayed and probabilistic outcomes has drawn attention in psychopharmacology and neuroeconomics. Sozou's evolutionary theory proposed that hyperbolic delay discounting may be totally attributable to aversion to a decrease in subjective probability of obtaining delayed rewards (SP) which follows a hyperbolic decay function. However, to date, no empirical study examined the hypothesis, although this investigation is important for elucidating the roles of impatience, precaution, and uncertainty aversion in delay discounting processes. Methods In order to (i) determine the functional form of the relation between delay until receipt and SP, and (ii) examine whether delay discounting is attributable to a decrease in SP, we assessed the subjects' SP and their delay and probability discounting. We examined the fitness of hyperbolic and exponential functions to the assessed SP, and relations between the SP, and delay/probability discounting, and subjective-probability discounting for delayed rewards. Results The results demonstrated (a) SP decayed hyperbolically as delay increases, (b) a decay of SP was associated with delay discounting, and (c) subjective-probability discounting did not significantly correlate with delay discounting. Conclusion Our results demonstrated (i) hyperbolic decay of SP is related to delay discounting, and (ii) delay discounting is, however, not attributable to precautious foresight in intertemporal choice. Further, a novel parameter of pure time preference is proposed. Subjective Probability (dpeaa)DE-He213 Delay Discount (dpeaa)DE-He213 Discount Function (dpeaa)DE-He213 Hyperbolic Discount (dpeaa)DE-He213 Indifference Point (dpeaa)DE-He213 Ikeda, Koki aut Hasegawa, Toshikazu aut Enthalten in Behavioral and brain functions London : BioMed Central, 2005 3(2007), 1 vom: 25. Sept. (DE-627)484836994 (DE-600)2185773-8 1744-9081 nnns volume:3 year:2007 number:1 day:25 month:09 https://dx.doi.org/10.1186/1744-9081-3-52 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 3 2007 1 25 09 |
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10.1186/1744-9081-3-52 doi (DE-627)SPR029339235 (SPR)1744-9081-3-52-e DE-627 ger DE-627 rakwb eng Takahashi, Taiki verfasserin aut A hyperbolic decay of subjective probability of obtaining delayed rewards 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Takahashi et al; licensee BioMed Central Ltd. 2007 Background Hyperbolic discounting of delayed and probabilistic outcomes has drawn attention in psychopharmacology and neuroeconomics. Sozou's evolutionary theory proposed that hyperbolic delay discounting may be totally attributable to aversion to a decrease in subjective probability of obtaining delayed rewards (SP) which follows a hyperbolic decay function. However, to date, no empirical study examined the hypothesis, although this investigation is important for elucidating the roles of impatience, precaution, and uncertainty aversion in delay discounting processes. Methods In order to (i) determine the functional form of the relation between delay until receipt and SP, and (ii) examine whether delay discounting is attributable to a decrease in SP, we assessed the subjects' SP and their delay and probability discounting. We examined the fitness of hyperbolic and exponential functions to the assessed SP, and relations between the SP, and delay/probability discounting, and subjective-probability discounting for delayed rewards. Results The results demonstrated (a) SP decayed hyperbolically as delay increases, (b) a decay of SP was associated with delay discounting, and (c) subjective-probability discounting did not significantly correlate with delay discounting. Conclusion Our results demonstrated (i) hyperbolic decay of SP is related to delay discounting, and (ii) delay discounting is, however, not attributable to precautious foresight in intertemporal choice. Further, a novel parameter of pure time preference is proposed. Subjective Probability (dpeaa)DE-He213 Delay Discount (dpeaa)DE-He213 Discount Function (dpeaa)DE-He213 Hyperbolic Discount (dpeaa)DE-He213 Indifference Point (dpeaa)DE-He213 Ikeda, Koki aut Hasegawa, Toshikazu aut Enthalten in Behavioral and brain functions London : BioMed Central, 2005 3(2007), 1 vom: 25. Sept. (DE-627)484836994 (DE-600)2185773-8 1744-9081 nnns volume:3 year:2007 number:1 day:25 month:09 https://dx.doi.org/10.1186/1744-9081-3-52 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 3 2007 1 25 09 |
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10.1186/1744-9081-3-52 doi (DE-627)SPR029339235 (SPR)1744-9081-3-52-e DE-627 ger DE-627 rakwb eng Takahashi, Taiki verfasserin aut A hyperbolic decay of subjective probability of obtaining delayed rewards 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Takahashi et al; licensee BioMed Central Ltd. 2007 Background Hyperbolic discounting of delayed and probabilistic outcomes has drawn attention in psychopharmacology and neuroeconomics. Sozou's evolutionary theory proposed that hyperbolic delay discounting may be totally attributable to aversion to a decrease in subjective probability of obtaining delayed rewards (SP) which follows a hyperbolic decay function. However, to date, no empirical study examined the hypothesis, although this investigation is important for elucidating the roles of impatience, precaution, and uncertainty aversion in delay discounting processes. Methods In order to (i) determine the functional form of the relation between delay until receipt and SP, and (ii) examine whether delay discounting is attributable to a decrease in SP, we assessed the subjects' SP and their delay and probability discounting. We examined the fitness of hyperbolic and exponential functions to the assessed SP, and relations between the SP, and delay/probability discounting, and subjective-probability discounting for delayed rewards. Results The results demonstrated (a) SP decayed hyperbolically as delay increases, (b) a decay of SP was associated with delay discounting, and (c) subjective-probability discounting did not significantly correlate with delay discounting. Conclusion Our results demonstrated (i) hyperbolic decay of SP is related to delay discounting, and (ii) delay discounting is, however, not attributable to precautious foresight in intertemporal choice. Further, a novel parameter of pure time preference is proposed. Subjective Probability (dpeaa)DE-He213 Delay Discount (dpeaa)DE-He213 Discount Function (dpeaa)DE-He213 Hyperbolic Discount (dpeaa)DE-He213 Indifference Point (dpeaa)DE-He213 Ikeda, Koki aut Hasegawa, Toshikazu aut Enthalten in Behavioral and brain functions London : BioMed Central, 2005 3(2007), 1 vom: 25. Sept. (DE-627)484836994 (DE-600)2185773-8 1744-9081 nnns volume:3 year:2007 number:1 day:25 month:09 https://dx.doi.org/10.1186/1744-9081-3-52 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 3 2007 1 25 09 |
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10.1186/1744-9081-3-52 doi (DE-627)SPR029339235 (SPR)1744-9081-3-52-e DE-627 ger DE-627 rakwb eng Takahashi, Taiki verfasserin aut A hyperbolic decay of subjective probability of obtaining delayed rewards 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Takahashi et al; licensee BioMed Central Ltd. 2007 Background Hyperbolic discounting of delayed and probabilistic outcomes has drawn attention in psychopharmacology and neuroeconomics. Sozou's evolutionary theory proposed that hyperbolic delay discounting may be totally attributable to aversion to a decrease in subjective probability of obtaining delayed rewards (SP) which follows a hyperbolic decay function. However, to date, no empirical study examined the hypothesis, although this investigation is important for elucidating the roles of impatience, precaution, and uncertainty aversion in delay discounting processes. Methods In order to (i) determine the functional form of the relation between delay until receipt and SP, and (ii) examine whether delay discounting is attributable to a decrease in SP, we assessed the subjects' SP and their delay and probability discounting. We examined the fitness of hyperbolic and exponential functions to the assessed SP, and relations between the SP, and delay/probability discounting, and subjective-probability discounting for delayed rewards. Results The results demonstrated (a) SP decayed hyperbolically as delay increases, (b) a decay of SP was associated with delay discounting, and (c) subjective-probability discounting did not significantly correlate with delay discounting. Conclusion Our results demonstrated (i) hyperbolic decay of SP is related to delay discounting, and (ii) delay discounting is, however, not attributable to precautious foresight in intertemporal choice. Further, a novel parameter of pure time preference is proposed. Subjective Probability (dpeaa)DE-He213 Delay Discount (dpeaa)DE-He213 Discount Function (dpeaa)DE-He213 Hyperbolic Discount (dpeaa)DE-He213 Indifference Point (dpeaa)DE-He213 Ikeda, Koki aut Hasegawa, Toshikazu aut Enthalten in Behavioral and brain functions London : BioMed Central, 2005 3(2007), 1 vom: 25. Sept. (DE-627)484836994 (DE-600)2185773-8 1744-9081 nnns volume:3 year:2007 number:1 day:25 month:09 https://dx.doi.org/10.1186/1744-9081-3-52 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 3 2007 1 25 09 |
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hyperbolic decay of subjective probability of obtaining delayed rewards |
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A hyperbolic decay of subjective probability of obtaining delayed rewards |
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Background Hyperbolic discounting of delayed and probabilistic outcomes has drawn attention in psychopharmacology and neuroeconomics. Sozou's evolutionary theory proposed that hyperbolic delay discounting may be totally attributable to aversion to a decrease in subjective probability of obtaining delayed rewards (SP) which follows a hyperbolic decay function. However, to date, no empirical study examined the hypothesis, although this investigation is important for elucidating the roles of impatience, precaution, and uncertainty aversion in delay discounting processes. Methods In order to (i) determine the functional form of the relation between delay until receipt and SP, and (ii) examine whether delay discounting is attributable to a decrease in SP, we assessed the subjects' SP and their delay and probability discounting. We examined the fitness of hyperbolic and exponential functions to the assessed SP, and relations between the SP, and delay/probability discounting, and subjective-probability discounting for delayed rewards. Results The results demonstrated (a) SP decayed hyperbolically as delay increases, (b) a decay of SP was associated with delay discounting, and (c) subjective-probability discounting did not significantly correlate with delay discounting. Conclusion Our results demonstrated (i) hyperbolic decay of SP is related to delay discounting, and (ii) delay discounting is, however, not attributable to precautious foresight in intertemporal choice. Further, a novel parameter of pure time preference is proposed. © Takahashi et al; licensee BioMed Central Ltd. 2007 |
abstractGer |
Background Hyperbolic discounting of delayed and probabilistic outcomes has drawn attention in psychopharmacology and neuroeconomics. Sozou's evolutionary theory proposed that hyperbolic delay discounting may be totally attributable to aversion to a decrease in subjective probability of obtaining delayed rewards (SP) which follows a hyperbolic decay function. However, to date, no empirical study examined the hypothesis, although this investigation is important for elucidating the roles of impatience, precaution, and uncertainty aversion in delay discounting processes. Methods In order to (i) determine the functional form of the relation between delay until receipt and SP, and (ii) examine whether delay discounting is attributable to a decrease in SP, we assessed the subjects' SP and their delay and probability discounting. We examined the fitness of hyperbolic and exponential functions to the assessed SP, and relations between the SP, and delay/probability discounting, and subjective-probability discounting for delayed rewards. Results The results demonstrated (a) SP decayed hyperbolically as delay increases, (b) a decay of SP was associated with delay discounting, and (c) subjective-probability discounting did not significantly correlate with delay discounting. Conclusion Our results demonstrated (i) hyperbolic decay of SP is related to delay discounting, and (ii) delay discounting is, however, not attributable to precautious foresight in intertemporal choice. Further, a novel parameter of pure time preference is proposed. © Takahashi et al; licensee BioMed Central Ltd. 2007 |
abstract_unstemmed |
Background Hyperbolic discounting of delayed and probabilistic outcomes has drawn attention in psychopharmacology and neuroeconomics. Sozou's evolutionary theory proposed that hyperbolic delay discounting may be totally attributable to aversion to a decrease in subjective probability of obtaining delayed rewards (SP) which follows a hyperbolic decay function. However, to date, no empirical study examined the hypothesis, although this investigation is important for elucidating the roles of impatience, precaution, and uncertainty aversion in delay discounting processes. Methods In order to (i) determine the functional form of the relation between delay until receipt and SP, and (ii) examine whether delay discounting is attributable to a decrease in SP, we assessed the subjects' SP and their delay and probability discounting. We examined the fitness of hyperbolic and exponential functions to the assessed SP, and relations between the SP, and delay/probability discounting, and subjective-probability discounting for delayed rewards. Results The results demonstrated (a) SP decayed hyperbolically as delay increases, (b) a decay of SP was associated with delay discounting, and (c) subjective-probability discounting did not significantly correlate with delay discounting. Conclusion Our results demonstrated (i) hyperbolic decay of SP is related to delay discounting, and (ii) delay discounting is, however, not attributable to precautious foresight in intertemporal choice. Further, a novel parameter of pure time preference is proposed. © Takahashi et al; licensee BioMed Central Ltd. 2007 |
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