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Introduction: Intertemporal choice refers to a common type of decision in which we need to choose between a relatively small reward that we will receive relatively soon (also called sooner-smaller or SS reward) or a relatively large reward that we will receive later (i.e., later-larger -LL) option. Intertemporal choice has been a focal point in psychological and behavioral economics research for understanding impulsivity (Cohen et al., 2020; Lempert et al., 2019). Traditional discounting models, also called option-wise models, have long dominated the field of intertemporal choice (Laibson, 1997; Loewenstein & Thaler, 1989; Mazur et al., 1987). These models (including exponential and hyperbolic ones) have two basic assumptions. First, they postulate that people compute a single subjective value for each choice option by integrating the reward’s value and its delay time. Second they assume that individuals then base their choices on these subjective values (i.e., choose the option with the higher subjective value). Although discounting models have been successful in explaining intertemporal choices, it has been suggested that discounting models need extra parameters to explain some anomalies, such as magnitude effect and sub-additive effect. Recently another type of model has been proposed that differs in the way options are weighed against each other: The heuristic attribute-wise model posits that —when decision makers are making an intertemporal choice— they first compare the two option's attribute values within each attribute (Busemeyer et al., 2019; Dai & Busemeyer, 2014; Scholten & Read, 2010). In a second step, the value difference within each attribute would compete to generate the response. Accordingly, impatient behavior is assumed to be reflected in the ratio between the two attributes’ weights. For example, if someone has a larger ratio between the weights of the reward attribute versus the delay attribute (i.e., the reward magnitudes have a larger impact on choice than the delay times), individuals are more likely to choose the LL option. In comparison to the discounting model, the attribute-wise model is grounded in several psychological principles and has the potential to explain several anomalies (Dai et al., 2018; Ericson et al., 2015). The empirical battle between discounting and attribute-wise models has led to interesting insights. Both can account for various phenomena in intertemporal choice, including dynamic preference reversals (adding a front-end delay to SS and LL option would increase the chance of picking the LL option) and the magnitude effect (people become more patient if the reward magnitude increases). However, studies that compared model fits of discounting models and attribute-wise models showed mixed results, with some studies showing better performance for attribute-wise models and others - at least in certain conditions- better performance of discounting models (Ericson et al., 2015; Wulff & van den Bos, 2018). Recent studies have shown that eye-tracking data can be helpful to empirically distinguish between these two strategies. For example, Reeck et al. (2017) showed that people use a mixed visual search strategy of attribute-wise and option-wise fixation patterns. Namely participants with LL options in intertemporal choice are more likely to be chosen when using an attribute-wise strategy in visual search, whereas SS options have more chance to be preferred when adopting the discounting strategy. Additionally, experimentally inducing an attribute-wise search strategy can increase patience. Accordingly, a study by Fisher (2021) revealed that there is a higher likelihood of picking the LL options in trials where participants employed a more attribute-wise visual search strategy. While a mixture of decision strategies has been observed in the intertemporal choice task, the relationship between these strategies remains unclear. Self-reported confidence ratings, as a measure of self-performance, could potentially serve as a tool for understanding which decision strategy that participant would like to use. Previous research on confidence ratings in the context of intertemporal choice tasks has suggested that confidence primarily reflects the subjective value difference or choice difficulty between options. For example, Bulley et al. (2022) propose that confidence indicates the subjective value difference between two options and that higher levels of confidence arise when the subjective value of the SS option remarkably exceeds or is exceeded by the LL option. However, research in the risky choice task has indicated that confidence reports tend to be significantly higher when individuals select a certain option in comparison to a risky one (da Silva Castanheira et al., 2021). This finding underscores the possibility that, in the intertemporal choice task, the chosen option (LL or SS option) might similarly affect the reported confidence levels. Based on the previous eye-tracking studies, we expect that if reported confidence rating do have a relationship between the chosen option (LL or SS option), they also have a connection with the decision strategy (attribute-wise or discounting strategy). If people report higher confidence when choosing LL option, they might also use a more attribute-wise decision strategy. To test this hypothesis, we designed an intertemporal binary choice task with varying reward amount levels. Previous studies have shown that people’s probability of choosing the LL option as a function of increase in reward amount level (i.e., the magnitude effect). Our design enables us to influence participants' expressed preferences systematically, such that they are expected to make more patient choices with increasing reward levels. We have tested 60 participants online and this preregistration precedes the data analyses. To assess confidence and decision difficulty, following each choice, participants were instructed to indicate (a) their confidence regarding the choice they just made and (b) the difficulty they experienced making this choice. In addition, we used eye-tracking to record the gaze location to identify participants' decision strategies. In our analyses we will identify participants' decision strategies by quantitatively fitting different types of computational models (attribute-wise/option-wise) to their choice and RT data. We hypothesize that at higher reward levels, we will observe increased patience (the often-replicated magnitude effect), together with an increase in participants’ confidence and increased use of an attribute-wise decision-making strategy.

Introduction: Intertemporal choice refers to a common type of decision in which we need to choose between a relatively small reward that we will receive relatively soon (also called sooner-smaller or SS reward) or a relatively large reward that we will receive later (i.e., later-larger -LL) option. Intertemporal choice has been a focal point in psychological and behavioral economics research for understanding impulsivity (Cohen et al., 2020; Lempert et al., 2019). Traditional discounting models, also called option-wise models, have long dominated the field of intertemporal choice (Laibson, 1997; Loewenstein & Thaler, 1989; Mazur et al., 1987). These models (including exponential and hyperbolic ones) have two basic assumptions. First, they postulate that people compute a single subjective value for each choice option by integrating the reward’s value and its delay time. Second they assume that individuals then base their choices on these subjective values (i.e., choose the option with the higher subjective value). Although discounting models have been successful in explaining intertemporal choices, it has been suggested that discounting models need extra parameters to explain some anomalies, such as magnitude effect and sub-additive effect. Recently another type of model has been proposed that differs in the way options are weighed against each other: The heuristic attribute-wise model posits that —when decision makers are making an intertemporal choice— they first compare the two option's attribute values within each attribute (Busemeyer et al., 2019; Dai & Busemeyer, 2014; Scholten & Read, 2010). In a second step, the value difference within each attribute would compete to generate the response. Accordingly, impatient behavior is assumed to be reflected in the ratio between the two attributes’ weights. For example, if someone has a larger ratio between the weights of the reward attribute versus the delay attribute (i.e., the reward magnitudes have a larger impact on choice than the delay times), individuals are more likely to choose the LL option. In comparison to the discounting model, the attribute-wise model is grounded in several psychological principles and has the potential to explain several anomalies (Dai et al., 2018; Ericson et al., 2015). The empirical battle between discounting and attribute-wise models has led to interesting insights. Both can account for various phenomena in intertemporal choice, including dynamic preference reversals (adding a front-end delay to SS and LL option would increase the chance of picking the LL option) and the magnitude effect (people become more patient if the reward magnitude increases). However, studies that compared model fits of discounting models and attribute-wise models showed mixed results, with some studies showing better performance for attribute-wise models and others - at least in certain conditions- better performance of discounting models (Ericson et al., 2015; Wulff & van den Bos, 2018). Recent studies have shown that eye-tracking data can be helpful to empirically distinguish between these two strategies. For example, Reeck et al. (2017) showed that people use a mixed visual search strategy of attribute-wise and option-wise fixation patterns. Namely participants with LL options in intertemporal choice are more likely to be chosen when using an attribute-wise strategy in visual search, whereas SS options have more chance to be preferred when adopting the discounting strategy. Additionally, experimentally inducing an attribute-wise search strategy can increase patience. Accordingly, a study by Fisher (2021) revealed that there is a higher likelihood of picking the LL options in trials where participants employed a more attribute-wise visual search strategy. While a mixture of decision strategies has been observed in the intertemporal choice task, the relationship between these strategies remains unclear. Self-reported confidence ratings, as a measure of self-performance, could potentially serve as a tool for understanding which decision strategy that participant would like to use. Previous research on confidence ratings in the context of intertemporal choice tasks has suggested that confidence primarily reflects the subjective value difference or choice difficulty between options. For example, Bulley et al. (2022) propose that confidence indicates the subjective value difference between two options and that higher levels of confidence arise when the subjective value of the SS option remarkably exceeds or is exceeded by the LL option. However, research in the risky choice task has indicated that confidence reports tend to be significantly higher when individuals select a certain option in comparison to a risky one (da Silva Castanheira et al., 2021). This finding underscores the possibility that, in the intertemporal choice task, the chosen option (LL or SS option) might similarly affect the reported confidence levels. Based on the previous eye-tracking studies, we expect that if reported confidence rating do have a relationship between the chosen option (LL or SS option), they also have a connection with the decision strategy (attribute-wise or discounting strategy). If people report higher confidence when choosing LL option, they might also use a more attribute-wise decision strategy. To test this hypothesis, we designed an intertemporal binary choice task with varying reward amount levels. Previous studies have shown that people’s probability of choosing the LL option as a function of increase in reward amount level (i.e., the magnitude effect). Our design enables us to influence participants' expressed preferences systematically, such that they are expected to make more patient choices with increasing reward levels. We have tested 60 participants online and this preregistration precedes the data analyses. To assess confidence and decision difficulty, following each choice, participants were instructed to indicate (a) their confidence regarding the choice they just made and (b) the difficulty they experienced making this choice. In addition, we used eye-tracking to record the gaze location to identify participants' decision strategies. In our analyses we will identify participants' decision strategies by quantitatively fitting different types of computational models (attribute-wise/option-wise) to their choice and RT data. We hypothesize that at higher reward levels, we will observe increased patience (the often-replicated magnitude effect), together with an increase in participants’ confidence and increased use of an attribute-wise decision-making strategy.