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Journal articles on the topic 'Probability discounting'

Author: Grafiati

Published: 4 June 2021

Last updated: 21 February 2023

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1

Weatherly, Jeffrey N., Thomas V. Petros, Harpa L. Jόnsdόttir, Adam Derenne, and Joseph C. Miller. "Probability Alters Delay Discounting, but Delay Does Not Alter Probability Discounting." Psychological Record 65, no. 2 (November 8, 2014): 267–75. http://dx.doi.org/10.1007/s40732-014-0102-3.

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2

YOSHINO, Toshihiko, Tetsuo YAMAGUCHI, Yuriko JIKKO, and Hirota OKOUCHI. "Probability discounting of food reward." Proceedings of the Annual Convention of the Japanese Psychological Association 74 (September 20, 2010): 3PM106. http://dx.doi.org/10.4992/pacjpa.74.0_3pm106.

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3

Thomas, Katie B., Adam Derenne, and Jeffrey N. Weatherly. "Delay and probability discounting in the context of gambling function and expectancies." Journal of Gambling Issues, no. 30 (May 1, 2015): 35. http://dx.doi.org/10.4309/jgi.2015.30.6.

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The current study investigated the relationship between two forms of discounting (delay and probability) and two measures of factors that may maintain gambling behavior (behavioral contingencies and expectancies). Participants (272 undergraduates) completed discounting questions for scenarios of gaining or losing $1,000 or $100,000 with uncertain or delayed outcomes. They also filled out the South Oaks Gambling Screen, the Gambling Functional Assessment -Revised, and the Gambling Expectancies Questionnaire. Results showed that gambling for positive reinforcement was consistently the best predictor of discounting, suggesting that the function of gambling behavior may be a better predictor of discounting than are the emotional expectancies of gambling. However, the direction of the relationship was inconsistent, with function negatively predicting discounting of both uncertain gains and losses. No consistent relationship was found between discounting and gambling for negative reinforcement or emotional expectancies. Results were generally the same when non-gamblers were excluded from the analyses. The results suggest that studying gambling function may be an informative pursuit.

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4

Yamashita, Hiroshi, and Toshihiko Yoshino. "Probability discounting in a game situation." Proceedings of the Annual Convention of the Japanese Psychological Association 79 (September 22, 2015): 2AM—108–2AM—108. http://dx.doi.org/10.4992/pacjpa.79.0_2am-108.

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5

Weitzman, Martin L. "Gamma Discounting." American Economic Review 91, no. 1 (March 1, 2001): 260–71. http://dx.doi.org/10.1257/aer.91.1.260.

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By incorporating the probability distribution directly into the analysis, this paper proposes a new theoretical approach to resolving the perennial dilemma of being uncertain about what discount rate to use in cost-benefit analysis. A numerical example is constructed from the results of a survey based on the opinions of 2,160 economists. The main finding is that even if every individual believes in a constant discount rate, the wide spread of opinion on what it should be makes the effective social discount rate decline significantly over time. Implications and ramifications of this proposed “gamma-discounting” approach are discussed. (JEL H43)

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6

Jikko, Yuriko, and Hiroto Okouchi. "Real and hypothetical rewards in probability discounting." Japanese journal of psychology 78, no. 3 (2007): 269–76. http://dx.doi.org/10.4992/jjpsy.78.269.

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7

Dai, Zhijie, Randolph C. Grace, and Simon Kemp. "Reward contrast in delay and probability discounting." Learning & Behavior 37, no. 3 (August 2009): 281–88. http://dx.doi.org/10.3758/lb.37.3.281.

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8

Lawyer, Steven R. "Probability and delay discounting of erotic stimuli." Behavioural Processes 79, no. 1 (September 2008): 36–42. http://dx.doi.org/10.1016/j.beproc.2008.04.009.

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9

Kyonka, Elizabeth G. E., and Nicola S. Schutte. "Probability discounting and gambling: a meta-analysis." Addiction 113, no. 12 (August 31, 2018): 2173–81. http://dx.doi.org/10.1111/add.14397.

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10

Asgarova, Rana, Anne C. Macaskill, and Maree J. Hunt. "Gain–Loss Asymmetry in Experiential Probability Discounting." Psychological Record 70, no. 3 (February 5, 2020): 359–71. http://dx.doi.org/10.1007/s40732-020-00379-1.

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11

Falligant, John Michael, and Sacha T. Pence. "Delay and Probability Discounting of Legal Outcomes." Behavior and Social Issues 28, no. 1 (April 29, 2019): 127–39. http://dx.doi.org/10.1007/s42822-019-00011-0.

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12

Yew-Kwang, NG. "Intergenerational Impartiality: Replacing Discounting by Probability Weighting." Journal of Agricultural and Environmental Ethics 18, no. 3 (May 2005): 237–57. http://dx.doi.org/10.1007/s10806-005-1491-8.

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13

Rachlin, Howard, Jay Brown, and David Cross. "Discounting in judgments of delay and probability." Journal of Behavioral Decision Making 13, no. 2 (April 2000): 145–59. http://dx.doi.org/10.1002/(sici)1099-0771(200004/06)13:2<145::aid-bdm320>3.0.co;2-4.

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14

Reynolds, Brady, Jerry B. Richards, Kimberly Horn, and Katherine Karraker. "Delay discounting and probability discounting as related to cigarette smoking status in adults." Behavioural Processes 65, no. 1 (January 2004): 35–42. http://dx.doi.org/10.1016/s0376-6357(03)00109-8.

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15

Kräplin, Anja, Michael Höfler, Shakoor Pooseh, Max Wolff, Klaus-Martin Krönke, Thomas Goschke, Gerhard Bühringer, and Michael N. Smolka. "Impulsive decision-making predicts the course of substance-related and addictive disorders." Psychopharmacology 237, no. 9 (June 5, 2020): 2709–24. http://dx.doi.org/10.1007/s00213-020-05567-z.

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Abstract Background This study investigated whether patterns of impulsive decision-making (i) differ between individuals with DSM-5 substance use disorders (SUD) or non-substance-related addictive disorders (ND) and healthy controls, and (ii) predict the increase of SUD and ND severity after one year. Methods In a prospective-longitudinal community study, 338 individuals (19–27 years, 59% female) were included in one of three groups: SUD (n = 100), ND (n = 118), or healthy controls (n = 120). Group differences in four impulsive decision-making facets were analyzed with the Bayesian priors: delay discounting (mean = 0.37, variance = 0.02), probability discounting for gains and for losses (each − 0.16, 0.02), and loss aversion (− 0.44, 0.02). SUD and ND severity were assessed at baseline and after 1 year (n = 312, 92%). Predictive associations between decision-making and SUD/ND severity changes were analyzed with the Bayesian prior: mean = 0.25, variance = 0.016. Results Compared with controls, the SUD group displayed steeper delay discounting and lower probability discounting for losses; the ND group displayed lower probability discounting for losses (posterior probabilities > 98%). SUD symptom increase after 1 year was predicted by steeper delay discounting and lower loss aversion; ND symptom increase by lower probability discounting for losses and lower loss aversion (posterior probabilities > 98%). There was low evidence for predictive relations between decision-making and the quantity-frequency of addictive behaviours. Discussion Impulsive decision-making characterizes SUD and ND and predicts the course of SUD and ND symptoms but not the engagement in addictive behaviours. Strength of evidence differed between different facets of impulsive decision-making and was mostly weaker than a priori expected.

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16

Caudle, Kyle A., Gary O. Fowler, Leah R. Jager, and David M. Ruth. "Discounting older data." Wiley Interdisciplinary Reviews: Computational Statistics 3, no. 1 (October 13, 2010): 30–33. http://dx.doi.org/10.1002/wics.134.

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17

Mobekk, Hilde, Asle Fagerstrøm, and Donald A. Hantula. "The Influence of Probability Discounting on Escalation in Information Technology Projects." International Journal of Information Technology Project Management 9, no. 1 (January 2018): 23–39. http://dx.doi.org/10.4018/ijitpm.2018010102.

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An experimental study was conducted with 17 experienced information technology (IT) project decision-makers. Each participated in a computer based simulation where they had to choose whether to continue an ongoing IT project despite negative feedback, (called escalation of commitment), or abandon it and sell the project as is. A titration procedure for sales price was manipulated over seven probability conditions for success of the project. The switching points where each participant would choose to sell the project instead of continuing development was determined, and probability discounting factors were calculated. The median switching point of the participant's subjective values of the project fit a hyperbolic discounting function well. An escalation factor was calculated and the results indicate that several participants in the study showed signs of escalation. These data demonstrate that the discounting framework may be a viable approach to understand the phenomenon of escalation in IT projects.

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18

Mintz-Woo, Kian. "Principled Utility Discounting Under Risk." Moral Philosophy and Politics 6, no. 1 (May 27, 2019): 89–112. http://dx.doi.org/10.1515/mopp-2018-0060.

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Abstract Utility discounting in intertemporal economic modelling has been viewed as problematic, both for descriptive and normative reasons. However, positive utility discount rates can be defended normatively; in particular, it is rational for future utility to be discounted to take into account model-independent outcomes when decision-making under risk. The resultant values will tend to be smaller than descriptive rates under most probability assignments. This also allows us to address some objections that intertemporal considerations will be overdemanding. A principle for utility discount rates is suggested which is rooted in probability discounting. Utility discounting is defended against objections from Parfit (1984) and Broome (2005); Broome (2012). A sample utility discount rate is estimated.

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19

Tian, Moqian, Ran Tao, Ya Zheng, Huimin Zhang, Guochun Yang, Qi Li, and Xun Liu. "Internet gaming disorder in adolescents is linked to delay discounting but not probability discounting." Computers in Human Behavior 80 (March 2018): 59–66. http://dx.doi.org/10.1016/j.chb.2017.10.018.

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20

Ostaszewski, Pawel. "Temperament and the Discounting of Delayed and Probabilistic Rewards." European Psychologist 2, no. 1 (January 1997): 35–43. http://dx.doi.org/10.1027/1016-9040.2.1.35.

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The present study attempts to combine the more European tradition of studying temperament and individual differences with the more North American tradition of functionalism and behavior analysis by examining the relationship between several temperamental traits (sensation seeking, extraversion, and impulsivity) and discounting of delayed and probabilistic rewards. To evaluate discounting of delayed rewards, participants chose between hypothetical immediate monetary rewards and larger amounts that could be obtained after a specified delay. To evaluate discounting of probabilistic rewards, participants chose between monetary rewards that were certain and larger amounts that could be obtained with a specified probability. Hyperbolic functions described well the discounting of both delayed and probabilistic rewards for all groups of participants. The rate at which delayed rewards were discounted was related to extraversion and impulsivity, but not to the sensation-seeking dimension. Both extraverts and high impulsive individuals showed higher temporal discounting rates than introverts and low impulsive individuals. Differences in their subjective perception of time might account for the different rates of discounting between these groups. On the other hand, the rate at which probabilistic rewards were discounted did not differ between high and law impulsive participants, nor between introverts and extraverts. That temperament was related to differences in discounting of delayed but not probabilistic rewards in extraverts versus introverts and high versus low impulsive participants suggests that, although the same mathematical function describes both forms of discounting in all groups, delay and probability might not be functionally equivalent.

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21

Weatherly, Jeffrey N., Richard A. Wise, and Adam Derenne. "Probability Discounting of Legal and Non-Legal Outcomes." Behavior and Social Issues 21, no. 1 (May 2012): 165–87. http://dx.doi.org/10.5210/bsi.v2110.4183.

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22

Lawyer, Steven R., Sonja A. Williams, Tereza Prihodova, Jason D. Rollins, and Anita C. Lester. "Probability and delay discounting of hypothetical sexual outcomes." Behavioural Processes 84, no. 3 (July 2010): 687–92. http://dx.doi.org/10.1016/j.beproc.2010.04.002.

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23

McKerchar, Todd L., and C. Renee Renda. "Delay and Probability Discounting in Humans: An Overview." Psychological Record 62, no. 4 (October 2012): 817–34. http://dx.doi.org/10.1007/bf03395837.

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24

Palenik, Marcin. "The effect of uncertainty on negative discounting." International Journal of Management and Economics 57, no. 4 (December 1, 2021): 287–98. http://dx.doi.org/10.2478/ijme-2021-0023.

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Abstract The preference to receive benefits as early as possible and delay costs as much as possible is natural for people. That means a positive discount rate in the intertemporal choice, which is a common assumption in economics. However, as research in behavioral economics proves, in certain situations a negative discount rate occurs. The purpose of this paper is to show that the assumption of positive discounting is not always true. The presented experimental study shows how a decrease in probability increases the chances of negative discounting. According to the results, the expected large, uncertain profit is more likely to be deferred over time than a certain profit of the same value. On the other hand, the expected large, uncertain loss is more willingly experienced earlier than a certain loss of the same value. In both cases, it means an increase in the frequency of negative discounting due to increased uncertainty. The results of the study broaden the existing knowledge about the impact of probability on discounting in a situation of expected losses and the area of negative discounting.

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25

Isomura, Mieko, and Kenjiro Aoyama. "Subjective probability of reward receipt and the magnitude effect in probability discounting." Japanese journal of psychology 79, no. 2 (2008): 172–78. http://dx.doi.org/10.4992/jjpsy.79.172.

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26

Mahalingam, Vaishali, Michael Palkovics, Michal Kosinski, Iva Cek, and David Stillwell. "A Computer Adaptive Measure of Delay Discounting." Assessment 25, no. 8 (November 24, 2016): 1036–55. http://dx.doi.org/10.1177/1073191116680448.

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Delay discounting has been linked to important behavioral, health, and social outcomes, including academic achievement, social functioning and substance use, but thoroughly measuring delay discounting is tedious and time consuming. We develop and consistently validate an efficient and psychometrically sound computer adaptive measure of discounting. First, we develop a binary search–type algorithm to measure discounting using a large international data set of 4,190 participants. Using six independent samples ( N = 1,550), we then present evidence of concurrent validity with two standard measures of discounting and a measure of discounting real rewards, convergent validity with addictive behavior, impulsivity, personality, survival probability; and divergent validity with time perspective, life satisfaction, age and gender. The new measure is considerably shorter than standard questionnaires, includes a range of time delays, can be applied to multiple reward magnitudes, shows excellent concurrent, convergent, divergent, and discriminant validity—by showing more sensitivity to effects of smoking behavior on discounting.

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27

Calluso, Cinzia, Maria Giovanna Devetag, and Carmela Donato. "“I Feel Therefore I Decide”: Effect of Negative Emotions on Temporal Discounting and Probability Discounting." Brain Sciences 11, no. 11 (October 25, 2021): 1407. http://dx.doi.org/10.3390/brainsci11111407.

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Temporal and probability discounting are considered two fundamental constructs in economic science, as they are associated with phenomena with major societal impact and a variety of sub-optimal behaviors and clinical conditions. Although it is well known that positive and negative affective states bear important cognitive/behavioral consequences, the effect of emotional experiences on decision-making remains unclear due to the existence of many conflicting results. Inspired by the need to understand if and to what extent the current COVID-19 pandemic has determined changes in our decision-making processes by means of the unusual, prolonged experience of negative feelings, in this study we investigate the effect of anger, fear, sadness, physical and moral disgust on intertemporal and risky choices. Results show that all emotions significantly increase subjects’ preferences for immediate rewards over delayed ones, and for risky rewards over certain ones, in comparison to a “neutral emotion” condition, although the magnitude of the effect differs across emotions. In particular, we observed a more pronounced effect in the case of sadness and moral disgust. These findings contribute to the literature on emotions and decision-making by offering an alternative explanation to the traditional motivational appraisal theories. Specifically, we propose that the increased preference for immediate gratification and risky outcomes serves as a mechanism of self-reward aimed at down-regulating negative feelings and restore the individual’s “emotional balance”.

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28

Gray, Joshua C., Michael T. Amlung, Abraham A. Palmer, and James MacKillop. "Syntax for calculation of discounting indices from the monetary choice questionnaire and probability discounting questionnaire." Journal of the Experimental Analysis of Behavior 106, no. 2 (September 2016): 156–63. http://dx.doi.org/10.1002/jeab.221.

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29

Marcowski, Przemysław, Wojciech Białaszek, Joanna Dudek, and Paweł Ostaszewski. "Higher Behavioral Profile of Mindfulness and Psychological Flexibility is Related to Reduced Impulsivity in Smokers, and Reduced Risk Aversion Regardless of Smoking Status." Polish Psychological Bulletin 48, no. 4 (December 20, 2017): 445–55. http://dx.doi.org/10.1515/ppb-2017-0051.

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Abstract Empirical evidence suggests that mindfulness, psychological flexibility, and addiction are interrelated in decision making. In our study, we investigated the relationship of the behavioral profile, composed of mindfulness and psychological flexibility, and smoking status on delay and probability discounting. We demonstrated the interaction of the behavioral profile of mindfulness and psychological flexibility (lower or higher) and smoking status on delay discounting. We found that individuals who smoked and displayed higher mindfulness and psychological flexibility devalued rewards at a slower rate, compared to smokers with a lower profile. Importantly, in those with a higher profile, smokers discounted rewards no differently than nonsmokers. Smokers with a lower profile did display, however, increased impulsivity, compared to nonsmokers. These results suggest that behavioral interventions aiming to modify the behavioral profile with regard to mindfulness and psychological flexibility can indeed support the regulation of elevated impulsivity in smokers to equate with that of nonsmokers. In probability discounting, we observed that individuals with a higher profile displayed lower discounting rates, i.e., were less risk-averse, with no other significant main effect or interaction.

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30

Mishima, Daiki, Yuki Iwamoto, and Koji Hori. "Effects of deprivation level on probability discounting in pigeons." Proceedings of the Annual Convention of the Japanese Psychological Association 78 (September 10, 2014): 2AM—2–019–2AM—2–019. http://dx.doi.org/10.4992/pacjpa.78.0_2am-2-019.

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31

Myerson, Joel, Leonard Green, and Joshua Morris. "MODELING THE EFFECT OF REWARD AMOUNT ON PROBABILITY DISCOUNTING." Journal of the Experimental Analysis of Behavior 95, no. 2 (March 2011): 175–87. http://dx.doi.org/10.1901/jeab.2011.95-175.

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32

Ohmura, Yu, Taiki Takahashi, Nozomi Kitamura, and Paul Wehr. "Three-month stability of delay and probability discounting measures." Experimental and Clinical Psychopharmacology 14, no. 3 (2006): 318–28. http://dx.doi.org/10.1037/1064-1297.14.3.318.

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33

Bidwell, L. Cinnamon, James MacKillop, James G. Murphy, Andrea Grenga, Robert M. Swift, and John E. McGeary. "Biphasic effects of alcohol on delay and probability discounting." Experimental and Clinical Psychopharmacology 21, no. 3 (2013): 214–21. http://dx.doi.org/10.1037/a0032284.

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34

Yi, Richard, Xochitl de la Piedad, and Warren K. Bickel. "The combined effects of delay and probability in discounting." Behavioural Processes 73, no. 2 (September 2006): 149–55. http://dx.doi.org/10.1016/j.beproc.2006.05.001.

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35

Green, Leonard, and Joel Myerson. "Hyperbola-like discounting, impulsivity, and the analysis of will." Behavioral and Brain Sciences 28, no. 5 (October 2005): 655–56. http://dx.doi.org/10.1017/s0140525x05270115.

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Ainslie's insightful treatment of dynamically inconsistent choice stands in contrast to traditional views in psychology, economics, and philosophy. We comment on the form of the discounting function and on new findings regarding choice between delayed rewards. Finally, we argue that the positive correlation between temporal and probability discounting is inconsistent with the view that impulsivity represents a unitary trait.

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36

Dolan, Sean B., Matthew W. Johnson, Kelly E. Dunn, and Andrew S. Huhn. "The discounting of death: Probability discounting of heroin use by fatal overdose likelihood and drug purity." Experimental and Clinical Psychopharmacology 29, no. 3 (June 2021): 219–28. http://dx.doi.org/10.1037/pha0000486.

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37

Clatch, Lauren, and Eugene Borgida. "Behavioral Economics in Plea-Bargain Decision-Making: Beyond the Shadow-of-Trial Model." Review of Law & Economics 17, no. 2 (July 1, 2021): 349–83. http://dx.doi.org/10.1515/rle-2021-0069.

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Abstract Legal scholars have long assumed that plea bargains are contracts negotiated between rational actors who adhere to the dictates of the normative shadow-of-trial model. The two key features that rational actors presumably haggle over in the shadow of trial are the criminal charge (and associated sentence) and the probability of trial conviction. The behavioral economics theory of discounting, however, offers a theoretical foundation for testing the shadow-of-trial model. This article summarizes findings from experimental discounting studies in behavioral economics and psychological science – showing that these paradigms can be successfully applied to the plea-bargaining decision context wherein the likelihood of trial is uncertain and delayed, and the plea bargain is relatively certain and immediate. We suggest that the implications of applying discounting to plea bargaining are three-fold: (1) empirical evidence suggests that the shadow-of-trial model is too narrow; (2) the discounting of non-monetary losses may involve slightly different psychological processes than contexts involving monetary outcomes; and (3) probability of conviction and delay until trial constitute situational features that elicit guilty pleas despite a defendant’s factual innocence.

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38

Mejía Cruz, Diana, Laura Hernández, and Laurent Ávila-Chauvet. "Discounting and Executive functions as indicators of methamphetamine use in adolescents and adults." Revista Argentina de Ciencias del Comportamiento 14, no. 3 (December 30, 2022): 139–47. http://dx.doi.org/10.32348/1852.4206.v14.n3.32190.

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Abstract Meth-users have shown low performance in some executive functions tasks. This low performance can entail problems of control behavior, and increased impulsivity such as preference the small reward over the large delayed one. The current study was aimed to evaluate the performance in three executive tasks (shifting, updating and inhibition), and four discounting tasks (delay and probability) of gains and losses by meth-users and non-users. We worked with 40 male adults (20 meth-users and 20 non-users), and 32 male adolescents (20 meth-users and 12 non-users). We found with CART algorithm that inhibition, updating and probability discounting tasks were the good predictors to identify non users and meth-users. Our general conclusion is the executive functions: Inhibition and Updating are related with cognitive issues due to drug use in a developing brain, and the discounting tasks do not reflect a general impulsivity trait.

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39

Chattopadhyay, Manas K. "Two-Armed Dirichlet Bandits with Discounting." Annals of Statistics 22, no. 3 (September 1994): 1212–21. http://dx.doi.org/10.1214/aos/1176325626.

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40

Goudie, Andrew James, Matt Field, and Jon Cole. "Different vulnerabilities for addiction may contribute to the same phenomena and some additional interactions." Behavioral and Brain Sciences 31, no. 4 (July 29, 2008): 445–46. http://dx.doi.org/10.1017/s0140525x08004810.

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AbstractThe framework for addiction offered by the target article can perhaps be simplified into fewer, more basic, vulnerabilities. “Impulsivity” covers a number of vulnerabilities, not just enhanced delay discounting. Real-world drug-use decisions involve both delay and probability discounting. The motivational salience of, and attentional bias for, drug cues may be related to a number of vulnerabilities. Interactions among vulnerabilities are of significance and complicate the application of this framework.

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41

Kurano, Masami, Jinjie Song, Masanori Hosaka, and Youqiang Huang. "Controlled Markov set-chains with discounting." Journal of Applied Probability 35, no. 02 (June 1998): 293–302. http://dx.doi.org/10.1017/s0021900200014959.

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In the framework of discounted Markov decision processes, we consider the case that the transition probability varies in some given domain at each time and its variation is unknown or unobservable. To this end we introduce a new model, named controlled Markov set-chains, based on Markov set-chains, and discuss its optimization under some partial order. Also, a numerical example is given to explain the theoretical results and the computation.

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42

Lawyer, Steven R., and Colin T. Mahoney. "Delay Discounting and Probability Discounting, But Not Response Inhibition, Are Associated With Sexual Risk Taking in Adults." Journal of Sex Research 55, no. 7 (August 10, 2017): 863–70. http://dx.doi.org/10.1080/00224499.2017.1350627.

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43

Donchev, Doncho S. "Random Series with Time-Varying Discounting." Communications in Statistics - Theory and Methods 40, no. 16 (August 15, 2011): 2866–78. http://dx.doi.org/10.1080/03610926.2011.562772.

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44

Jones, Bryan A., and Howard Rachlin. "DELAY, PROBABILITY, AND SOCIAL DISCOUNTING IN A PUBLIC GOODS GAME." Journal of the Experimental Analysis of Behavior 91, no. 1 (January 2009): 61–73. http://dx.doi.org/10.1901/jeab.2009.91-61.

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45

Sugano, Tomoko, and Masahiro Sakamoto. "Relation of Reinforcement Sensitivity Theory and probability discounting of money." Proceedings of the Annual Convention of the Japanese Psychological Association 81 (September 20, 2017): 2C—067–2C—067. http://dx.doi.org/10.4992/pacjpa.81.0_2c-067.

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46

Sugano, Tomoko, and Masahiro Sakamoto. "A study of probability discounting on aggression and gender differences." Proceedings of the Annual Convention of the Japanese Psychological Association 84 (September 8, 2020): PM—041—PM—041. http://dx.doi.org/10.4992/pacjpa.84.0_pm-041.

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47

Anderson, Molly A. B., and Jesse Dallery. "Effects of Amount on Probability Discounting: A Replication and Extension." Behavioural Processes 190 (September 2021): 104448. http://dx.doi.org/10.1016/j.beproc.2021.104448.

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48

Grace, Randolph C., and Anthony P. McLean. "Evidence for a magnitude effect in probability discounting with pigeons." Journal of Experimental Psychology: Animal Learning and Cognition 41, no. 4 (2015): 406–18. http://dx.doi.org/10.1037/xan0000077.

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49

Levy, Hannah C., Benjamin W. Katz, Akanksha Das, Michael C. Stevens, and David F. Tolin. "An investigation of delay and probability discounting in hoarding disorder." Journal of Psychiatric Research 109 (February 2019): 89–95. http://dx.doi.org/10.1016/j.jpsychires.2018.11.019.

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50

Jarmolowicz, David P., Warren K. Bickel, Anne E. Carter, Christopher T. Franck, and E. Terry Mueller. "Using crowdsourcing to examine relations between delay and probability discounting." Behavioural Processes 91, no. 3 (November 2012): 308–12. http://dx.doi.org/10.1016/j.beproc.2012.09.001.

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