Delay discounting in dyads and small groups: Group leadership, status information, and actor-partner interdependence

Journal of Experimental Social Psychology 86 (2020) 103902

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Delay discounting in dyads and small groups: Group leadership, status information, and actor-partner interdependence

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Michael T. Bixtera, , Christian C. Luhmannb ⁎

a b

Montclair State University, United States of America Stony Brook University, United States of America

ARTICLE INFO

ABSTRACT

This paper has been recommended for acceptance by Roger Giner-Sorolla

Delay discounting is usually studied at the individual level, though there exist many situations where dyads and small groups have to make intertemporal decisions about delayed rewards. In the current study, we investigated the social dynamics in collective intertemporal decision making by experimentally manipulating group leadership and status differentials among dyad and group members. Participants in all experiments completed three phases of an intertemporal decision-making task: an individual pre-collaboration phase, a collaboration phase in dyads or small groups, and an individual post-collaboration phase. In Experiments 1 and 2, small groups of three made collective decisions during the collaboration phase, with one member of the group being assigned a leadership position. Groups believed that leaders were chosen either randomly (Experiment 1) or systematically based on the normativity of the leader's pre-collaboration decisions (Experiment 2). Leaders exerted a stronger influence on group preferences than non-leaders, but only when participants believed leaders were chosen systematically. Experiment 3 then demonstrated that lower-status dyad members were more affected by a collaborative experience compared to higher-status members, suggesting that social influence on delay discounting depends on the relative status between dyad and group members.

Keywords: Delay discounting Small groups Dyads Social influence Actor-partner interdependence model

1. Introduction Intertemporal tradeoffs between immediate and delayed rewards are pervasive throughout human decision making. A common finding is that humans often have difficulty waiting for delayed rewards, opting instead for immediate consumption (e.g., Mischel, Shoda, & Rodriguez, 1989). This devaluing of delayed rewards is referred to as delay discounting in the research literature. Higher rates of delay discounting relate to a variety of maladaptive outcomes, including reduced savings rates (Finke & Huston, 2013) and addiction (Reynolds, 2006). The vast majority of research on delay discounting has focused on intertemporal decisions made by individuals. As a result, less is known about how small groups of individuals make collective decisions that involve delayed rewards. This gap in the literature is problematic because there exist many circumstances where decisions about delayed rewards must be made by dyads or small groups (e.g., spouses, budgetary committees). To understand decision making in these situations, it is necessary to study how small groups combine and transform the preferences of individual group members into collective decision preferences. Furthermore, studying delay discounting in small group settings affords the ability to measure the extent decision preferences of

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individuals are socially influenced by others. By overly focusing on individual decision-making paradigms, prior research may have overlooked the interdependent nature of intertemporal preference formation and revision. 1.1. Delay discounting in social contexts Delay discounting is affected by social context. For example, individuals make intertemporal decisions differently for themselves versus other people (e.g., Albrecht, Volz, Sutter, Laibson, & von Cramon, 2011; Ziegler & Tunney, 2012; but see Weatherly & Ruthig, 2013). Another social context investigated recently is the extent individuals make intertemporal decisions differently when alone or in the presence of others. Late adolescents are more likely to prefer immediate rewards over delayed rewards when in the presence of peers than when making decisions alone (O'Brien, Albert, Chein, & Steinberg, 2011). However, this difference is eliminated when late adolescents make decisions in front of a group that includes a slightly older adult (Silva, Chein, & Steinberg, 2016). The above research demonstrates that individuals' intertemporal decisions are affected by social context, but it does not shed light on the processes involved in collective intertemporal

Corresponding author at: Department of Psychology, Montclair State University, Montclair, NJ 07043, United States of America. E-mail address: [email protected] (M.T. Bixter).

https://doi.org/10.1016/j.jesp.2019.103902 Received 2 May 2019; Received in revised form 18 September 2019; Accepted 19 September 2019 0022-1031/ © 2019 Elsevier Inc. All rights reserved.

Journal of Experimental Social Psychology 86 (2020) 103902

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decisions making. Gaining a better understanding of how intertemporal decisions are made by small groups motivated a recent study by Bixter, Trimber, and Luhmann (2017). Participants completed three phases of an intertemporal decision-making task: an individual pre-collaboration phase, a collaboration phase in dyads or small groups, and an individual postcollaboration phase. This collaborative decision-making paradigm allows one to explore how intertemporal decisions are made by dyads and small groups, as well as how collaboration subsequently influences the preferences of individual group members during the post-collaboration phase. Two group effects were of note. First, group preferences during the collaboration phase were strongly related to the mean of group members' pre-collaboration preferences (an averaging effect). Second, group members' individual preferences were more similar post-collaboratively compared to pre-collaboratively (a convergence effect). These results demonstrate that socially interacting with others in smallgroup settings can lead to revisions in delay discounting, with these revisions being driven by the decision preferences observed in other group members during collaboration. Bixter and Rogers (2019) replicated and extended these findings by observing the averaging and convergence effects in an older adult sample, suggesting that social influences on delay discounting extend into older adulthood.

experiences. As mentioned above, Bixter et al. (2017) found that individuals revised their delay discounting following collaboration to be more aligned with their respective group's preferences. If leaders disproportionally influence group intertemporal decision making during collaboration, there would likely be less of a discrepancy between their preferences and their respective group's preferences. This might then result in leaders revising their post-collaborative preferences less than non-leaders. 1.3. Actor-partner interdependence Studying decision making in dyadic and small-group designs presents certain statistical problems, due to the dependency of the data. However, statistical methods have been developed that quantify social influence while taking into account the interdependency of group data. This is most easily seen in research on dyadic relationships, with the actor-partner interdependence model (APIM; Cook & Kenny, 2005; Kenny, 1996) being one commonly used method. The APIM most often uses a structural equation modeling framework to estimate both actor and partner effects simultaneously. Actor effects refer to the influence of an individual's score on an independent variable on his or her score on a dependent variable. Partner effects refer to the influence of a partner's score on the independent variable on the actor's dependent variable score. By estimating actor and partner effects simultaneously, the APIM allows social influence to be directly estimated. The APIM can be applied to the collaborative decision-making paradigm used by Bixter et al. (2017) to quantify social influence in intertemporal decision making. Specifically, individuals' post-collaboration preferences can be simultaneously predicted by the individual's own pre-collaboration preferences (the actor effect) and the pre-collaboration preferences of his or her dyadic partner (the partner effect). One critical distinction in dyadic research is whether members of dyads are distinguishable or indistinguishable on a particular variable. Using the variable sex as an example, husbands and wives would be considered distinguishable whereas pairs of same-sex friends would be considered indistinguishable. Manipulating group leadership leads to members of a dyad or small group to be distinguishable (i.e., leaders vs. non-leaders) with regards to status, which allows the differential influences of the group members to be estimated. That is, the partner effects of leaders on non-leaders can be compared to the partner effects of non-leaders on leaders. The degree of social influence on delay discounting can then be measured for both the leaders and non-leaders of decision-making dyads.

1.2. Group leadership The social dynamics and processes involved in collective intertemporal decision making remain largely unknown. This is problematic because hierarchies in power and status often exist among group members. As a result, there is a long tradition in social psychology of studying the role of leaders in shaping small-group preferences and behavior (Berkowitz, 1953; Burke, 1974). A major focus is the extent leadership qualities and status differentials among group members influence group outcomes and performance (Dubrovsky, Kiesler, & Sethna, 1991; Lucas & Lovaglia, 1998). Hierarchies within a group can exert both positive and negative impacts on group/team effectiveness (for meta-analytic evidence, see Greer, de Jong, Schouten, & Dannals, 2018). For instance, interpersonal conflicts can stem from status inequality among group members, especially in situations where status differentials are paired with power differentials (Anicich, Fast, Halevy, & Galinsky, 2016). However, certain leadership qualities can help mitigate group conflict and promote prosocial behavior, such as the prototypicality of a leader (Hogg & van Knippenberg, 2003; Rast, Gaffney, Hogg, & Crisp, 2012; van Knippenberg & van Knippenberg, 2000) and the social identification by the leader with a group (Scholl, Sassenberg, Ellemers, Scheepers, & de Wit, 2018; Tost & Johnson, 2019). One important leadership distinction is whether leaders are chosen randomly or selected systematically based on some personal characteristic (Haslam et al., 1998; Henningsen, Henningsen, Jakobsen, & Borton, 2004). Randomly-chosen leaders are given leadership responsibilities over groups (e.g., leading group discussions, authority in resolving disagreements), but members of the group are made aware that the leader is being assigned these responsibilities through a random process. Systematically-selected leaders, on the other hand, are chosen because some personal characteristic of theirs is believed to make them better suited to represent the group as a leader. In these latter situations, status information can be either shared or unshared among group members (e.g., Bonner, Baumann, & Dalal, 2002). In shared information conditions, all members of the group are made aware of the relative standing of all group members. In unshared information conditions, status information is only made available to a possible subset of group members. Bixter et al. (2017) did not manipulate or control for group leadership in their study, so it remains unclear if leadership status (whether based on random or systematic selection) influences collective intertemporal decisions. Moreover, it is unknown the extent that leaders and non-leaders are differently influenced by collaborative

1.4. Overview of current study The current study sought to address a gap in the literature by exerting experimental control over the social dynamics during collaborative intertemporal decision making. Specifically, we manipulated leadership positions and status differentials among collaborators. Participants completed three phases of an intertemporal decisionmaking task. In both the pre-collaboration and post-collaboration phases, participants completed the task individually. However, in the intervening collaboration phase, participants completed the task in small groups of three (Experiments 1 and 2) or dyads (Experiment 3). We were interested in two types of collaborative decision-making effects. The first refers to the influence of group members' pre-collaboration preferences on group delay discounting during collaboration. That is, how do the delay-discounting preferences of individual group members shape the delay-discounting preferences of groups during collaboration? The second type of effect deals with the extent a collaborative experience subsequently influences the post-collaboration preferences of the individual group members. Specifically, to what extent do individuals' delay-discounting preferences change from pre- to post-collaboration due to the intervening collaborative experience? Leadership was assigned to a member of a group prior to 2

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collaboration. Groups were either instructed that leaders were chosen randomly (Experiment 1) or systematically (Experiment 2). Systematic selection was believed to be based on the normativity of the leader's decisions during the pre-collaboration phase. Experiment 3 then further investigated how status information is used by dyads making collective intertemporal decisions. Status was directly manipulated by having one member of the dyad being designated the higher-status member (believed to be based on pre-collaboration decisions). To see how status information is used by the dyad members, three information conditions were used in Experiment 3: (1) a shared information condition where both dyad members were provided the status information before collaboration, (2) an unshared information condition where only the higher-status dyad member was provided the status information before collaboration, and (3) an unshared information condition where only the lower-status dyad member was provided the status information before collaboration. Using dyadic data analytic techniques such as the APIM, we were then able to measure actor and partner effects for higher- and lower-status participants in the various information conditions. These results help shed light on the social processes that underlie group intertemporal decision making.

$50 today

$____ 3 months

Fig. 1. An example trial from the intertemporal decision-making task. In this trial, participants would have to provide an amount of money to be received in 3 months that would be valued the same as $50 to be received today. Participants in all three experiments completed three phases of the task: an individual pre-collaboration phase, a collaboration phase in dyads (Experiment 3) or small groups (Experiments 1 and 2), and an individual post-collaboration phase.

sample consisted of 20 groups of three. The mean age of the sample was 19.4 (SD = 1.66) and 70% were female. Participants received course credit for completing the study.

2. Experiment 1: randomly chosen group leaders Prior to the collaboration phase in Experiment 1, groups were instructed that one group member would be randomly selected to lead the group discussion on each trial. The responsibility of the leader was to be the first member of the group on each trial to propose a response. During the collaboration phase, groups needed to reach agreement and provide a single decision on each trial. Because group leaders proposed a response first on each trial, group leaders' preferences may act as anchors for the group. Primacy effects do exist in multiple-anchor environments (Ariely, Loewenstein, & Prelec, 2003). If leaders' preferences act as first anchors, group decisions during the collaboration phase would then be biased towards the preferences of the leader. Another way that leaders could disproportionally influence group decision making in the current paradigm stems from the fact that collaboration is an effortful process. If groups do not want to initiate an aggregation process that more fully incorporates the preferences of all group members, group decisions would align more closely with the preferences of the leaders than the non-leaders. On the other hand, if leaders and non-leaders are found to exert similar influences on group decision making, it would be evidence that small groups use more of an equal-weighting scheme when making collective intertemporal decisions.

2.1.2. Materials 2.1.2.1. Decision-making task. The delay-discounting task involved participants making judgments regarding smaller-sooner and largerlater hypothetical monetary rewards (see Fig. 1 for an example trial). Rewards consisted of a magnitude (in dollars) and a delay (in months). However, each trial omitted one of the two reward magnitudes. Participants' task was to supply this missing reward magnitude with a value that would render them indifferent between the two reward items. These so-called matching tasks are a common method of eliciting discount rates in the intertemporal decision-making literature (e.g., Chapman, 1996; Thaler, 1981). Both the pre-collaboration and post-collaboration phases consisted of 48 trials. This was based on the trial manipulation of reward magnitude size ($30, $75, $150, $275), reward delay (3 months, 6 months, 12 months), whether it was the smaller-sooner or larger-later reward that had the missing magnitude value that needed to be supplied, and whether the smaller-sooner reward was to be received immediately (today) or in the future. The collaboration phase consisted of 36 trials. The only difference between the collaboration phase and the other two phases were the reward magnitude sizes ($40, $125, $250). Different reward magnitudes were included in the collaboration phase to prevent individuals in the post-collaboration phase from simply reiterating the exact responses their group made during the collaboration phase.

2.1. Method All measures and manipulations are presented below. No participants were excluded from any of the analyses, and statistical analyses were not performed until all data collection occurred. Sample size was based on the earlier Bixter et al. (2017) study that investigated intertemporal decision making in dyads and small groups. In Experiment 1 of that study, participants consisted of 20 small groups of three; in Experiment 2 of that study, 30 dyads were used in each condition. The two social influence effects observed in that study were the averaging and convergence effects. The averaging effect consisted of a group level correlation of 0.77 and the convergence effect consisted of a Cohen's D of 0.62. These effect sizes were entered into power analyses using G*Power software (alpha = 0.05, power = 0.80), which produced a total number of groups of 10 and 23, respectively. Because the current study focused on the social dynamics involved in these two effects, 20 small groups (in Experiments 1 and 2) and 30 dyads per condition (in Experiment 3) were deemed to be appropriate sample sizes.

2.1.2.2. Discount rates. Participants' responses on each trial were converted to annual discount rates using Eq. (1) (Zauberman, Kim, Malkoc, & Bettman, 2009):

ln r=

( ) Xt + h Xt

h 12

(1)

where Xt is the magnitude of the smaller-sooner reward, Xt + h is the magnitude of the larger-later reward, t is the delay associated with the smaller-sooner reward, and h is the additional delay associated with the larger-later reward. Higher discount rates imply greater devaluing of delayed rewards. Overall discount rates were calculated for each individual participant and group by computing the discount rates implied by each response and then averaging the resulting set of discount rates across trials.

2.1.1. Participants Sixty undergraduate students participated in the experiment. The

2.1.3. Procedure Once all three group members arrived to the lab, participants 3

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p = .044) or the mean of the two non-leaders discount rates (r = 0.51, p = .021) were used instead of the group average. This pattern of correlations suggests that groups incorporated the preferences of all group members during the collaboration phase.

received instructions regarding the decision-making task. Participants were not alerted to the fact that they would subsequently be collaborating with other participants. Participants completed the decisionmaking task during the pre-collaboration phase at individual computer workstations. Upon completion of the pre-collaboration phase, all three participants were gathered together and informed that they would be completing a similar task but as a group. Participants were also provided with the following instructions:

2.2.1.1. Group leaders vs. non-leaders. To directly measure whether leaders had more of an influence on group discounting during the collaboration phase, absolute deviation scores were calculated between individual group members' pre-collaboration discount rates and their respective group's discount rate during the collaboration phase. Lower deviation scores for leaders would imply that group discount rates were closer to their preferences compared to non-leaders' preferences. These deviation scores were not significantly different between leaders (M = 0.66, SD = 0.70) and non-leaders (M = 0.73, SD = 0.73), t (58) = 0.33, p = .747, d = 0.09. These results suggest that leaders did not exert a disproportionate influence on group decision making.1

As a group, you will only provide one answer on each trial. So you will have to come to a consensus for the reward amount that would lead to equal liking of the two items on the screen. Now, you may disagree about the amount that makes the two items on the screen liked equally, but in these situations we would like you to discuss it as a group so that your answer is an amount that the group is satisfied with. Also, even though you are making judgments as a group, imagine that the rewards would be received individually. That is, if one of the reward items is $60 to be received in 4 months, that $60 would not be divided among the group, but would be received individually. Finally, one of you three will be randomly chosen to be the proposer. The role of the proposer on each trial is to be the first one of the group who voices a response. So on each trial, after the rewards have been presented on the screen, the proposer voices his/her response first. Once the proposer has voiced his/her response, the other two group members can voice their responses and then the group can begin to reach consensus.

2.2.2. Predicting changes in delay discounting 2.2.2.1. Group convergence. Convergence was measured in the current experiment by comparing the average standard deviation of group members' pre-collaboration discount rates to the average standard deviation of group members' post-collaboration discount rates. This measure of within-group variability was higher pre-collaboratively (M = 0.93, SD = 0.67) compared to post-collaboratively (M = 0.44, SD = 0.32), t(19) = 3.54, p = .002, d = 1.62, demonstrating that group members' discount rates were more similar following a collaborative experience. Another way to quantify within-group variability is to look at the intraclass correlation coefficient (ICC) for group members' discount rates both during the pre-collaboration phase and the post-collaboration phase. The coefficient value from a one-way random effects model was non-significant for pre-collaboration discount rates (ICC = −0.21, p > .05), which is to be expected due to groups being chosen by random assignment. However, the coefficient value became positive and significant for post-collaboration discount rates (ICC = 0.45, p = .001).

After receiving these instructions, the group was escorted to a single computer workstation where the collaboration phase of the study was completed. Upon finishing the collaboration phase, participants were instructed that they would be completing a similar decision-making task but once again individually. Participants were then escorted back to the same individual computer workstations and completed the postcollaboration phase of the study. The entire study took less than 1 h to complete. 2.2. Results The Results section is organized in two sections. In the first section, we report results dealing with how group members' pre-collaboration discount rates predicted group discount rates during the collaboration phase. In the second section, we report results dealing with the extent group members' discount rates changed from the pre-collaboration phase to the post-collaboration phase.

2.2.2.2. Group leaders vs. non-leaders. The group convergence effects above demonstrated that collaboration led to changes in group members' individual discount rates. In order to see if group leaders and non-leaders changed at similar or different rates, the absolute difference between individual group members' pre-collaboration and post-collaboration discount rates were used as change scores. That is, a score of zero would imply no change in an individual's discount rates from pre- to post-collaboration. As Fig. 2 shows, group leaders' discount rates changed (M = 0.45, SD = 0.40) at a comparable level compared to non-leaders (M = 0.60, SD = 0.64), t(58) = 0.95, p = .34, d = 0.25.2

2.2.1. Predicting group delay discounting A group averaging effect was observed, with group discount rates during the collaboration phase being strongly related to the mean of all three group members' discount rates during the pre-collaboration phase, r = 0.71, p < .001 (see Table 1). The correlations were lower when group leaders' pre-collaboration discount rates (r = 0.46,

1

The preceding analysis contrasting leaders vs. non-leaders' influence on group decision making did not take the dependency of the group data into account. In order to account for the non-independence of the group data, a multilevel regression model was constructed with the above deviation scores as the dependent variable and leadership status (0 = Non-leader, 1 = Leader) as a fixed predictor. A random intercept was included in the model with group affiliation as the clustering variable. The fixed effect of leadership status (b = −0.06, SE = 0.17) was not significant, t = −0.36, p = .718. 2 A multilevel regression model was constructed with the above change scores as the dependent variable, leadership status (0 = Non-leader, 1 = Leader) as a fixed predictor, and a random intercept with group affiliation as the clustering variable. The fixed effect of leadership status (b = −0.15, SE = 0.14) was not significant, t = −1.068, p = .292. The non-significant coefficient demonstrates that leaders and non-leaders revised their discount rates at comparable magnitudes.

Table 1 Correlations between pre-collaboration metrics of delay discounting and group delay discounting during collaboration. Pre-collaboration metric of delay discounting

Collaboration delay discounting Experiment 1

Experiment 2

Mean (all 3 group members) Leader Non-leaders

0.71⁎⁎⁎ 0.46⁎ 0.51⁎⁎

0.44 0.87⁎⁎⁎ −0.05

p < .05. p < .01. ⁎⁎⁎ p < .001. ⁎

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4

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Absolute Change in Discount Rates

1

3.1.2. Materials and procedure The decision-making task and procedure where the same as Experiment 1 with the following exception. The final paragraph of the instructions that were provided to groups prior to the collaboration phase of the experiment stated:

Leaders Non-leaders

0.8

Finally, one of you three will be assigned to be the proposer. The role of the proposer on each trial is to be the first one of the group who voices a response. So on each trial, after the rewards have been presented on the screen, the proposer voices his/her response first. Once the proposer has voiced his/her response, the other two group members can voice their responses and then the group can begin to reach consensus. The assigning of the role of the proposer will be based on the individual who made decisions in the previous phase of the study that most closely aligned with the normative strategy prescribed by financial experts. That is, the proposer will be the participant who made decisions that were closest to how financial experts advise time and money should be traded off.

0.6

0.4

0.2

0 Experiment 1

Experiment 2

Fig. 2. Change in discount rates for leaders and non-leaders in Experiments 1 and 2. Change scores were constructed by taking the absolute difference between discount rates during the pre-collaboration phase and the post-collaboration phase. Groups believed that leadership positions were determined either randomly (Experiment 1) or systematically (Experiment 2).

Though participants were instructed that the leadership position during the collaboration phase was based on some normative decision criterion during the pre-collaboration phase, the proposer/leadership position was actually determined randomly (same as in Experiment 1). As a result, the only difference between Experiments 1 and 2 were the brief sentences towards the end of the collaboration phase instructions that mentioned the normative assigning of the leadership position. This normative criterion was intentionally left vague so that groups did not have specific decision qualities to look for that might differentiate leaders' and non-leaders' decision preferences.

2.3. Discussion Two different group effects of note were observed in Experiment 1. First, group discount rates during collaboration were strongly related to the mean of the three group members' pre-collaboration discount rates (an averaging effect). Leaders and non-leaders exerted comparable influences on group discount rates during collaboration, further evidence that groups adopt more of an equal weighting scheme when making collective intertemporal decisions. The second group effect was a convergence effect (e.g., Bixter et al., 2017; Sherif, 1936), with group members' discount rates being more similar post-collaboratively compared to pre-collaboratively. Similar to the averaging effect, group leaders and non-leaders changed in delay discounting at comparable magnitudes.

3.2. Results The Results section of Experiment 2 is organized similarly as Experiment 1. 3.2.1. Predicting group delay discounting In contrast to the results of Experiment 1, group discount rates during the collaboration phase correlated the strongest with group leaders' discount rates during the pre-collaboration phase, r = 0.87, p < .001 (see Table 1). The correlations were lower when either the mean of all three group members' pre-collaboration discount rates (r = 0.44, p = .053) or the mean of the two non-leaders' pre-collaboration discount rates (r = −0.05, p = .829) were used. This pattern of correlations suggest that groups largely relied on the preferences of leaders while making decisions during the collaboration phase.

3. Experiment 2: normative group leaders In naturalistic settings, leadership positions are usually chosen nonrandomly. Leaders often gain or are assigned their position because of status or some other personal characteristic, with agreement among group members regarding leadership positions being common (Livi, Kenny, Albright, & Pierro, 2008). Example characteristics include experience, domain-general expertise, and task-related knowledge. According to expectation states theory (Berger, Wagner, & Zelditch, 1985; Correll & Ridgeway, 2003), small groups form hierarchies based on the expectations the group has about the ability of the various members to help achieve goals. These expectations are formed based on either taskrelated skills (specific status characteristics) or relevant general traits (diffuse status characteristics; Barreto & Hogg, 2018). In Experiment 2, instead of participants being instructed that leaders were being chosen randomly, groups were instructed that leaders were being chosen systematically. Specifically, participants were led to believe that leaders were chosen based on the group member who made decisions during the pre-collaboration phase that were most aligned with a normative strategy prescribed by financial experts.

3.2.1.1. Group leaders vs. non-leaders. Absolute deviation scores between group discount rates during the collaboration phase and precollaboration discount rates were significantly lower for leaders (M = 0.30, SD = 0.30) compared to non-leaders (M = 0.83, SD = 0.83), t(58) = 2.72, p = .009, d = 0.71.3 3.2.2. Predicting changes in delay discounting 3.2.2.1. Group convergence. Within-group variability in discount rates was higher pre-collaboratively (M = 0.73, SD = 0.53) compared to post-collaboratively (M = 0.33, SD = 0.31), t(19) = 4.55, p < .001, d = 2.09. Comparing intraclass correlation coefficients (ICC) for group members' discount rates between the pre-collaboration and post-

3.1. Method

3 A multilevel regression model was constructed with the above deviation scores as the dependent variable, leadership status (0 = Non-leader, 1 = Leader) as a fixed predictor, and a random intercept with group affiliation as the clustering variable. The fixed effect of leadership status (b = −0.52, SE = 0.15) was significant, t = −3.49, p < .01. The significant coefficient here demonstrates that leaders influenced group decision making during the collaboration phase to a greater extent than non-leaders.

3.1.1. Participants Sixty undergraduate students participated in the experiment. The sample consisted of 20 small groups of three. The mean age of the sample was 19.5 (SD = 1.70) and 62% were female. Participants received course credit for completing the study. 5

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collaboration phases demonstrated a similar convergence effect. The coefficient value from a one-way random effects model was nonsignificant for pre-collaboration discount rates (ICC = −0.01, p > .05) but became positive and significant for post-collaboration discount rates (ICC = 0.70, p < .001).

with the normative standard. By investigating how dyad members utilize status information during collaboration, this experiment will help clarify the social dynamics and processes involved in dyadic and small-group intertemporal choice. 4.1. Method

3.2.2.2. Group leaders vs. non-leaders. To see if group leaders and nonleaders changed at similar or different rates, the absolute difference between individual group members' pre-collaboration and postcollaboration discount rates were used as change scores. As Fig. 2 shows, group leaders' discount rates changed (M = 0.28, SD = 0.31) significantly less than non-leaders' (M = 0.72, SD = 0.84), t (58) = 2.22, p = .03, d = 0.58.4

4.1.1. Participants Participants were 180 undergraduate students. The sample consisted of 90 dyads (30 dyads per information condition). The mean age of the sample was 20.7 (SD = 1.70) and 63% were female. Participants received course credit for completing the study. We also report unpublished APIM analyses of data from Bixter et al. (2017; Experiment 2). Dyads in that study performed a similar task as in the current experiment, but no status information was given to participants prior to collaboration. As a result, these indistinguishable dyads were used as a reference for estimations of actor and partner effects when no status information was given to dyads. Participants were 60 undergraduate students. The mean age of the sample was 19.8 (SD = 1.43) and 55% were female.

3.3. Discussion In contrast to the results of Experiment 1, an averaging effect was not observed in group intertemporal decision making in Experiment 2. Instead, group discount rates were more strongly related to the precollaboration discount rates of group leaders. This is evidence of an unequal weighting scheme, with the preferences of group leaders being given additional weight compared to the preferences of the two nonleaders. These results suggest flexibility in the social decision schemes used during collective intertemporal decision making, with the availability of status information being necessary for leaders to exert a disproportionate influence on group preferences. We also found that group leaders revised their preferences following collaboration to a lesser extent than non-leaders. This result also contrasts with Experiment 1. If leadership positions are believed to be determined systematically, collaborative experiences appear to affect leaders and non-leaders differently.

4.1.2. Materials and procedure The decision-making task and procedure were the same as in Experiments 1 and 2 with the following exceptions. There were three information conditions (Shared, Unshared Higher-Status, Unshared Lower-Status). Each condition received slightly different instructions prior to the collaboration phase. For the Shared information condition, dyads were provided with the following instruction: Finally, we would like to inform you that one of you two made decisions in the previous phase of the study that more closely aligned with the normative strategy prescribed by financial experts. That is, one of you two made decisions that were closest to how financial experts advise time and money should be traded off.

4. Experiment 3: status information and actor-partner interdependence

Both members of the dyad received the above instruction while in the same room. One member of the dyad was then assigned the HigherStatus position, so that both members of the dyad were made aware of the status information. For the Unshared Higher-Status information condition, one member of the dyad was provided with the following instruction:

It remains unclear how status information is used by group members during collaboration. For instance, it could be that higher-status leaders adopt a more dominant position in the group by exerting greater influence over group preferences. However, lower-status group members may reduce their influence in the group and choose to surrender more decision-making responsibilities to the higher-status member. Of course, these two social processes are not mutually exclusive, both could operate in affecting group decision making. In Experiment 3, we tested how status information is used by dyads in collective intertemporal decision making. Three information conditions were included in the experiment. In the Shared information condition, both members of the dyad were instructed which member was the Higher-Status member prior to the collaboration phase. This condition is similar to the instructions that small groups received in Experiment 2. The two other conditions in Experiment 3 were unshared information conditions, with only one member of the dyad receiving the status information in private prior to the collaboration phase. In the Unshared Higher-Status condition, the Higher-Status member of the dyad was told prior to collaboration that he or she made decisions during the pre-collaboration phase that were more aligned with the normative standard. In the Unshared Lower-Status condition, the Lower-Status member of the dyad was told prior to collaboration that the other member of the dyad made decisions during the pre-collaboration phase that were more aligned

We would like to inform you that you made decisions in the previous phase of the study that more closely aligned with the normative strategy prescribed by financial experts compared to the decisions your partner made. That is, out of you two, you made decisions that were closest to how financial experts advise time and money should be traded off. However, during the next phase of the study, when you will be making decisions as a pair, we ask that you do not share this fact with your partner. The Higher-Status member of the dyad received the above information in private. As a result, the Lower-Status member of the dyad did not receive any information about any asymmetry in decision quality between the two dyad members. For the Unshared Lower-Status information condition, one member of the dyad was provided with the following instruction: We would like to inform you that your partner made decisions in the previous phase of the study that more closely aligned with the normative strategy prescribed by financial experts compared to the decisions you made. That is, out of you two, your partner made decisions that were closest to how financial experts advise time and money should be traded off. However, during the next phase of the study, when you will be making decisions as a pair, we ask that you do not share this fact with your partner.

4 A multilevel regression model was constructed with the above change scores as the dependent variable, leadership status (0 = Non-leader, 1 = Leader) as a fixed predictor, and a random intercept with group affiliation as the clustering variable. The fixed effect of leadership status (b = −0.43, SE = 0.18) was significant, t = −2.37, p = .02. The significant coefficient demonstrates that non-leaders revised their discount rates to a greater extent than the leaders.

The Lower-Status member of the dyad received the above 6

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Fig. 3. (A) The actor-partner interdependence model used in Experiment 3. X1 and X2 refer to the pre-collaboration discount rates of the two dyad members. Y1 and Y2 refer to postcollaboration discount rates. (B) The actor-partner interdependence model with phantom variables (pv1 and pv2) added to estimate the k parameters (k1 and k2).

no leadership position or asymmetry in status was manipulated. A few constraints had to be added to the APIM to account for this indistinguishability. As a result, a single actor and a single partner effect is produced by the APIM for indistinguishable dyads.

information in private. As a result, the Higher-Status member of the dyad did not receive any information about any asymmetry in decision quality between the two dyad members. Similar to Experiment 2, though participants in the various information conditions were instructed that status was based on some normative decision criterion, status positions were actually determined randomly. This means that the only difference between the three conditions in Experiment 3 was the type of status information given to participants prior to collaboration. Because the unshared information conditions only involved instructing one member of the dyad about status, we did not assign the group leadership responsibilities of Experiments 1 and 2 to the Higher-Status member (which would reveal the status information to both members). This is why we do not refer to Higher- and Lower-Status dyad members as leaders and non-leaders, respectively, in Experiment 3; no member of the dyad was required to provide a response first on each trial during the collaboration phase.

4.1.3.2. APIM with k parameters. A modified APIM has been developed that directly estimates the ratio of a partner effect to an actor effect (see Fig. 3B). The model utilizes phantom variables (Rindskopf, 1984) to directly estimate the k parameters.5 Kenny and Ledermann (2010) describe the different types of effects implied by various k values. A k of 1 implies a couple pattern; a k of 0 implies an actor-only pattern; and a k of −1 implies a contrast pattern. Whether a confidence interval includes one of the above three values (−1, 0, or 1) determines what pattern of effect is being observed for a particular dyad member. For indistinguishable dyads, k1 and k2 are constrained to be equal so that a single k estimate is produced. 4.2. Results

4.1.3. Statistical analyses 4.1.3.1. Actor-partner interdependence model (APIM). By focusing on dyads in Experiment 3, we were able to utilize the APIM (Cook & Kenny, 2005; Kenny, 1996) to directly estimate actor and partner effects. The standard APIM is presented in Fig. 3A. In the current experiment, X1 and X2 are the pre-collaboration discount rates of the two dyad members, and Y1 and Y2 are the post-collaboration discount rates, respectively. There are two actor effects in the APIM (a1 and a2). These effects measure the influence of dyad members' pre-collaboration discount rates on their post-collaboration discount rates. The two partner effects (p1 and p2) reflect the influence of a dyad partner's pre-collaboration discount rates on an actor's post-collaboration discount rates. In the three information conditions, X1 and Y1 refer to the discount rates of the Higher-Status dyad member and X2 and Y2 refer to the discount rates for the Lower-Status dyad member. For the dyadic data from Bixter et al. (2017), the dyads were indistinguishable;

4.2.1. APIM results The APIM results are included in Table 2. We first focus on the actor effects. The path coefficients were positive and significant for both Higher-Status and Lower-Status members in all information conditions. The standardized6 actor effect was 0.759 for the indistinguishable dyad 5 The k parameter in the APIM should not be confused with the commonly used k discount rate parameter used in various models of intertemporal choice. 6 Standardized estimates for actor and partner effects were calculated according to the recommendations of Ledermann and Kenny (2017). Specifically, scores were standardized across all participants in a condition for both the precollaboration discount rates (i.e., pooled means and standard deviations for X1 and X2 in Fig. 3A) and post-collaboration discount rates (i.e., pooled means and standard deviations for Y1 and Y2 in Fig. 3A). These standard scores were then entered into an APIM SEM to calculate the standardized estimates.

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Table 2 Actor-partner interdependence model results for Experiment 3.⁎

Actor effects Shared Information Higher-Status (a1) Lower-Status (a2) Unshared Higher-Status Higher-Status (a1) Lower-Status (a2) Unshared Lower-Status Higher-Status (a1) Lower-Status (a2) Indistinguishable Dyads Partner effects Shared Information Higher-Status (p1) Lower-Status (p2) Unshared Higher-Status Higher-Status (p1) Lower-Status (p2) Unshared Lower-Status Higher-Status (p1) Lower-Status (p2) Indistinguishable Dyads

Estimate

SE

CI

Standardized estimate

0.988⁎⁎⁎ 0.684⁎⁎⁎

0.078 0.092

[0.807, 1.193] [0.438, 0.861]

1.019 0.705

0.978⁎⁎⁎ 0.504⁎⁎⁎

0.068 0.128

[0.847, 1.285] [0.243, 0.753]

0.937 0.482

0.884⁎⁎⁎ 0.423⁎⁎⁎ 0.758⁎⁎⁎

0.067 0.086 0.063

[0.742, 0.983] [0.207, 0.608] [0.614, 0.900]

0.944 0.452 0.759

0.158⁎⁎ 0.469⁎⁎⁎

0.055 0.131

[0.051, 0.250] [0.209, 0.719]

0.163 0.483

0.143 0.320⁎⁎⁎

0.116 0.075

[0.017, 0.353] [0.133, 0.598]

0.137 0.307

0.148 0.508⁎⁎⁎ 0.336⁎⁎⁎

0.082 0.071 0.063

[−0.030, 0.392] [0.370, 0.607] [0.154, 0.523]

0.158 0.542 0.336

Notes. Confidence intervals are 95% bias-corrected confidence intervals based on 5000 bootstrap samples. The parameter labeling included in parentheses (a1, a2, p1, and p2) can be found in Fig. 3A. In the Shared Information condition, both dyad members received the status information prior to collaboration; in the Unshared Higher-Status and Unshared Lower-Status conditions, only the higher- or lower-status member, respectively, received the status information prior to collaboration. ⁎ p < .05. ⁎⁎ p < .01. ⁎⁎⁎ p < .001.

condition, which provided an estimation of actor effects when no status information was given to participants prior to collaboration. For all three status information conditions, the standardized actor effects were stronger for Higher-Status members (0.937 to 1.019) compared to Lower-Status members (0.452 to 0.705). We next focus on the partner effects. The path coefficients were positive and significant for Lower-Status members in all conditions, but only reached significance for Higher-Status members in the Shared information condition. The standardized partner effect was 0.336 for the indistinguishable dyads. For all three status information conditions, the standardized partner effects were stronger for Lower-Status members (0.307 to 0.542) compared to Higher-Status members (0.137 to 0.163).

Table 3 Actor-partner interdependence model k parameter estimates.

4.2.2. k estimates The k estimate for the indistinguishable dyads was 0.443, with a 95% bootstrapped confidence interval ranging from 0.196 to 0.750 (see Table 3). This suggests an effect between an actor-only pattern (k = 0) and a couple pattern (k = 1). For the status information conditions, the k estimates for the Lower-Status dyad members (0.636 to 1.201) were higher than for the Higher-Status members (0.146 to 0.167). Moreover, the confidence intervals for the Lower-Status members in all three status information conditions included 1 but not 0, suggesting a couple pattern. For the Higher-Status members, the lower end of the confidence intervals either contained 0 (the Unshared Lower-Status condition) or nearly contained 0 (the Shared Information and Unshared Higher-Status conditions). These latter results suggest an actor-only pattern for the Higher-Status dyad members.

Notes. Confidence intervals are 95% bias-corrected confidence intervals based on 5000 bootstrap samples. The parameter labeling included in parentheses (k1 and k2) can be found in Fig. 3B. In the Shared Information condition, both dyad members received the status information prior to collaboration; in the Unshared Higher-Status and Unshared Lower-Status conditions, only the higher- or lowerstatus member, respectively, received the status information prior to collaboration.

Shared Information Higher-Status (k1) Lower-Status (k2) Unshared Higher-Status Higher-Status (k1) Lower-Status (k2) Unshared Lower-Status Higher-Status (k1) Lower-Status (k2) Indistinguishable Dyads

k

CI

0.160 0.685

[0.060, 0.288] [0.252, 1.251]

0.146 0.636

[0.007, 0.321] [0.207, 1.492]

0.167 1.201 0.443

[−0.036, 0.460] [0.704, 2.641] [0.196, 0.750]

experience compared to lower-status members. Furthermore, these patterns of results were found even if status information was not communicated to both dyad members prior to collaboration (the unshared information conditions. 5. General discussion The main goal of the present study was to investigate the social processes involved in group intertemporal decision making, processes that prior research has not been able to measure (Bixter et al., 2017; Bixter & Rogers, 2019). Specifically, the current study investigated how social dynamics influence collective intertemporal decision making. Manipulated social dynamics included leadership position assignments and status differentials among dyad/group members. When groups believed that leaders were chosen randomly, leaders did not exert a disproportionate influence on group intertemporal preferences

4.3. Discussion In Experiment 3, actor and partner effects were directly estimated through the use of the APIM. Across the three information conditions, actor effects were higher for Higher-Status members compared to Lower-Status members, with the reversed pattern being observed for partner effects. These results suggest that higher-status members of a group were less likely to be socially influenced by a collaborative 8

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(Experiment 1). However, when groups believed that leaders were chosen because their pre-collaboration decisions aligned more with a normative standard than non-leaders, group intertemporal preferences were strongly determined by the preferences of leaders (Experiment 2). These results demonstrate the flexibility in weighting schemes used by small groups based on status information. If groups have no reason to believe that leaders possess some degree of expertise or relevant knowledge, they are likely to make their intertemporal decisions using a more equal weighting scheme. Conversely, if groups believe that leaders' intertemporal preferences are more aligned with a normative standard, they are more likely to adopt an expert-weighted decision scheme (Bonner et al., 2002).

5.2. Implications and future directions The current results have implications for group decision making more generally. One particularly relevant topic is the role of power in shaping decision-making outcomes (DeWall, Baumeister, Mead, & Vohs, 2011; Duan, Wu, & Sun, 2017; Maner, Gailliot, Butz, & Peruche, 2007). Status inequality within dyads and groups can create power differentials. Feelings of power can then affect a variety of interpersonal and group outcomes (e.g., Maner & Mead, 2010; Mooijman, van Dijk, Ellemers, & van Dijk, 2015; Overall, Hammond, McNulty, & Finkel, 2016; van Bunderen, Greer, & van Knippenberg, 2018). In the present study, it was only in certain situations that leaders exerted dominance over the intertemporal preferences of groups. Specifically, leaders dominated group preferences when groups believed that leaders were chosen based on a normative standard, highlighting the importance of the leadership selection process. Less is known about how leadership and status influence other aspects of collaboration, such as group cohesion, maintenance, and goals. Moreover, future intertemporal decision research needs to investigate social dynamics in group/team performance and not just group preferences. This line of research would then be able to directly test whether individuals or groups make superior decisions in a variety of real-world contexts (organizational settings, budgetary committees, etc.). It would also test the generalizability of the current results into different decision environments, such as choice situations where groups need to select an option from a finite list of outcomes (e.g., binary choice tasks). The present results demonstrate that it will be vital for these future studies to take into account status information when attempting to study group and team decision making.

5.1. Social influence in intertemporal decision making The collaborative decision-making paradigm allowed social influence to be quantitatively measured. This was accomplished by measuring changes in discount rates from the pre-collaboration phase to the post-collaboration phase. Leaders revised their intertemporal preferences to a lesser extent compared to non-leaders. But once again, this effect was only observed when groups believed that leaders were chosen systematically based on a normative standard. When groups believed that leadership positions were determined by a random process, leaders and non-leaders revised their intertemporal preferences at comparable magnitudes. Actor and partner effects in dyads were directly measured in Experiment 3. Both of these effects were influenced by status information. Specifically, actor effects were noticeably larger for higherstatus members compared to lower-status members, with the reverse pattern being observed for partner effects. If individuals believe that their decision making is more aligned with a normative standard, it follows that they may be less socially influenced by an individual believed to be less aligned with this standard. The results of the various information conditions show that there are different ways for these effects to materialize. In the Unshared Higher-Status condition, only the higher-status dyad member received the status information prior to collaboration. In these situations, the higher-status dyad member may take a more dominant position during collaboration, and subsequently revise their own preferences to be aligned with the preferences of their dyad partner to a lesser extent. However, similar patterns of results were observed in the Unshared Lower-Status condition, when only the lower-status dyad member received the status information prior to collaboration. In these circumstances, the lower-status dyad member may reduce his or her standing during collaboration, and subsequently revise their own preferences to be aligned with the preferences of their dyad partner to a greater extent. The ratio of a partner to an actor effect tests theoretically important patterns of dyadic effects (Kenny & Ledermann, 2010). For example, a couple pattern where actor and partner effects are equal in strength; an actor-only pattern where partners do no exert a noticeable strength on the actor's behavior; and a contrast pattern where actor and partner effects are equal in strength but hold different signs. For indistinguishable dyads that did not receive any status information prior to collaboration, we observed an effect that fell in-between an actor-only pattern and a couple pattern. This suggests that post-collaboration delay discounting is influenced by both the actor's and partner's precollaboration delay discounting, but the actor effect is exerting the stronger influence. For the three information conditions included in Experiment 3, the effect patterns were different for Higher- and LowerStatus dyad members. The Lower-Status members in all three conditions demonstrated a couple pattern, where their post-collaboration delay discounting was jointly and equally influenced by their own preferences and the preferences of their collaborative partner. The patterns were starkly different for the Higher-Status members, whose post-collaborative preferences showed little-to-no influence of their collaborative partner, suggesting more of an actor-only pattern.

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