Decision Strategies in a Sequential Decision Making
Paradigm
Internship Paper Sofieke Kevenaar
31-08-2017
Student
Name : Sofieke Kevenaar
Student ID number : 10537732
Address : Hacquartstraat 28-II
Postal code and residence : 1071 SJ Amsterdam
Telephone number : +31 6 27463494
Email address : Sofieke.k@hotmail.com
Supervisor(s)
Within ResMas (obligatory) : Hilde Huizenga, Helen Steingröver, Laura Dekkers
Specialisation : Developmental Psychology
Research center / location : Psychology department, University of Amsterdam Number of credits (1 ec = 28 hrs) :
20
Word count Abstract : 137
Abstract
Decision-making is often a sequential process; more information about the choice options is gained over time. Previous research in simultaneous contexts found evidence for three different decision-making strategies in choice options, namely an integrative, a lexicographic and an adaptive strategy. The current study investigates which of the three strategies people use in a sequential, rather than simultaneous, gambling task. In this task, a choice between two gambling machines had to be made. First, gain value of the machine was presented and then gain
probability. The machines differed on the attribute (informative) or not (uninformative) and the attributes can be conflicting or non-conflicting, resulting in five trial conditions. To differentiate between the strategies, parameters of the drift diffusion model were estimated and then
compared across relevant trial conditions. Results indicate the use of a possibility biased adaptive strategy.
Introduction
When making a decision in daily life, oftentimes more information about the things you’re choosing between comes up over time. Imagine a person who wants to go to the movies in the evening. Based on watching trailers, the options are reduced to two movies. Then, the person looks up the reviews for both movies and the reviews favor movie A over movie B. Next, the person looks up the possibility of obtaining a good seat for both movies in her favorite theater. She finds out that for movie B there are plenty of good seats left, but for movie A, probably only poor seats are left.
According to expectation models, like the Prospect Theory of Kahneman and Tversky (1979), people use an integrative strategy when making decisions. This entails that people integrate all information by weighing it according to the attribute values and then assessing the most beneficial option. However, according to heuristic models, people use simple heuristics to make decisions and do not attend to all information equally. According to some of these models, people use a lexicographic strategy in decision making, which means that people first focus on the most dominant attribute (Luce, 1956; 1978). If this first attribute differs between choice options, people choose the most beneficial option according to this first attribute. Only if there is not enough difference between the options on this first, dominant attribute, the second most important attribute will be assessed. This process continues until a choice can be made. Prior research often found support for lexicographic strategies as well as integrative strategies. When tasks got more difficult (e.g. when the difference between the choice options was small), people often switched from an integrative strategy to a lexicographic one (Brandstätter, Gigerenzer & Hertwig, 2006; Payne Bettman & Johnson, 1988). Due to these findings, a third possible decision strategy arose, namely the adaptive strategy. This strategy entails anticipation of conflict between attributes. If no conflict between options is anticipated, people use a lexicographic strategy, but if conflict is anticipated, they switch to an integrative strategy (Gigerenzer & Selten, 2001).
To sum up, current research indicated integrative, lexicographic and adaptive strategies as decision strategies when attributes are simultaneously presented. However, these strategies are impossible to distinguish if all information about the decision options is presented
simultaneously because the use of different strategies can result in the same outcomes. In addition, in the real world, attributes about the decision options are often not all simultaneously available, as in the movies example. A possibility to improve distinction between the strategies is to present the relevant attributes of the decision options sequentially.
To gain more insight about processes underlying decision-making, models can be used. A model that is often used for two choice decision problems is the drift diffusion model (DDM;
Ratcliff, 1978). ( Vandekerckhove, Tuerlinckx, & Lee, 2011; Voss, Nagler & Lerche, 2013;
Wiecki, Sofer & Frank, 2013). This model assumes that people accumulate information about the attributes of the choice options that sum up until enough information is gathered that favors one choice option over the other, and then people choose that option. How information is
accumulated exactly, depends on the four parameters of the model.
First, Boundary Separation (a) indicates how big the difference is between the boundaries for the two choice options. If a is big, the boundaries are far away from each other and more information is needed to reach one of the boundaries to make a final decision (Voss et al., 2013). Second, Starting Point (z) is the point in between the two boundaries where the evidence
accumulation starts. If this point is not exactly in the middle of the two boundaries, there is an a priori bias towards one of the choice options (Voss et al., 2013). Third, Drift Rate (v) indicates the speed the information accumulation process (Voss et al., 2013). Lastly, Non-Decision Time (Terr) indicates the time that is needed for processes that are not related to the decision making
process, such as pressing the button (Voss et al., 2013). In Figure 1, two information
accumulation processes according to the drift diffusion model are visually represented for a trial, as well as the two corresponding reaction time distributions over trials.
A previous study already used the drift diffusion model to investigate decision-making in a sequential paradigm (Dekkers, Seijdel, Weeda, Jansen & Huizenga; in prep.). This study found that when Gain Probability was presented first and both Gain Probability and Gain Value were presented numerically, people appeared to use a forth strategy, namely a biased adaptive strategy. People were biased by the first attribute in their adaptive strategy, so they assigned a higher relative importance to Gain Probability. However, there was a confound in this study; an anticipation effect that could have had influenced the results. In the current study, this confound is intended to be resolved by adaptation of the research design. This study aims to gain insight about which decision strategy, lexicographic, integrative or adaptive, people use in two choice decisions when multiple attributes of the options are presented sequentially. To answer this question, this study investigates if the Drift Diffusion Model parameters indicate the use of a lexicographic, an integrative or an adaptive strategy in a sequential gambling task.
Figure 1. In this figure, the drift diffusion for a trial is visually represented, with parameters
boundary separation a, starting point z, drift rate v and non-‐decision time Ter. On the edges of this figure, the reaction time distributions over trials are shown.
Reprinted from “Dissociable mechanisms of speed-‐accuracy tradeoff during visual perceptual learning are revealed by a hierarchical drift-‐diffusion model” by Zhang, J., & Rowe, J. B. (2016). Toward a Unified View of the Speed-‐Accuracy Trade-‐Off: Behaviour, Neurophysiology and Modelling, 71.
To answer the question of which decision strategy people use in a sequential gambling task, the hypotheses about the Drift Diffusion Model Parameters are elaborated below. All of the hypotheses below were based on the hypotheses of Dekkers et al. (in prep.).
The Δ indicates if there’s a difference between the machines on attribute 1. 1) Boundary Separation (a)
HINT: a(ΔAttribute1 = 0) = a(ΔAttribute1 ≠ 0)
HLEX: a(ΔAttribute1 = 0) > a(ΔAttribute1 ≠ 0)
HADAPT: a(ΔAttribute1 = 0) < a(ΔAttribute1 ≠ 0)
For the integrative strategy, it doesn’t matter if the options differ on attribute 1, because all information will be considered anyway. For the lexicographic strategy, the Boundary Separation is expected to be bigger for trials in which attribute 1 does not differ between the options than for trials in which there is difference. Hence, if there is a difference between the machines on the first attribute, the choice would be made based on this difference so the boundaries are then close. For the adaptive strategy, the Boundary Separation is expected to be smaller for Uninformative first attributes than for Informative first attributes, because when the first attribute is Informative, conflict is expected. When conflict is expected, people will continue in an integrative manner and uncertainty is high. In Uninformative first attributes, people will continue in a simpler lexicographic manner because no conflict is anticipated, so uncertainty is low. This results in wider Boundary Separation for Informative first attributes than for
Uninformative first attributes. As Boundary Separation a is determined a priori, the actual detection of whether or not there is Conflict cannot have influence on this parameter.
2) Starting point (z)
HINT: z(ΔAttribute1 = 0) = z(ΔAttribute1 ≠ 0)
HLEX: z(ΔAttribute1 = 0) > z(ΔAttribute1 ≠ 0)
HADAPT: z(ΔAttribute1 = 0) = z(ΔAttribute1 ≠ 0)
For the integrative strategy, it doesn’t matter if the options differ on attribute 1, because all information will be considered anyway. The same applies for the adaptive strategy, because initially, this strategy is the same as the integrative strategy. For the lexicographic strategy however, the starting point is expected to be biased, because the choice is based on the first attribute only if this attribute is Informative.
3) Drift rate (v)
a. HINT: v(ΔAttribute1 = 0) = v(ΔAttribute1 ≠ 0)
HLEX: v(ΔAttribute1 = 0) < v(ΔAttribute1 ≠ 0)
HADAPT: v(ΔAttribute1 = 0) > v(ΔAttribute1 ≠ 0)
b. HINT: vNON-CONFLICT = vCONFLICT
HLEX: vNON-CONFLICT = vCONFLICT
HADAPT: vNON-CONFLICT > vCONFLICT
For the hypotheses about Drift Rate, it is important to attend to whether or not the first attribute is Informative or not, as well as to whether or not there is Conflict between first and second attribute in order to make a distinction between all three decision strategies.
For the integrative strategy, it doesn’t matter if the options differ on attribute 1, because all information will be weighted anyway. For the lexicographical strategy, choices are always based on attribute 1 if the machines differ on this attribute. So, if the first attribute is informative, a choice is immediately made based on this attribute, whether or not attribute 1 and 2 are conflicting, making Drift Rate high. Drift Rate will be lower for cases with Uninformative first attributes, because in that case, people using a lexicographic strategy have to wait for the second attribute to make a choice, resulting in lower Drift Rates in cases with an Uninformative first attribute compared to cases with an Informative first attribute. For the adaptive strategy, Conflict is anticipated when attribute 1 is Informative. If there appears to be no Conflict between the attributes, a lexicographic strategy will be used and drift rate will be higher than if there is Conflict. If there is Conflict, an integrative strategy will be used and Drift Rate will be smaller. Hence, Drift Rate will be larger for Uninformative first attributes, because then, people will go on in a lexicographic manner and make a decision fast. In case of Informative first attributes, people will continue in an integrative manner. This takes longer, so Drift Rate will be smaller for Informative first attributes.
4) Non-Decision Time (Terr) H1: Terr CONFLICT = Terr NON-CONFLICT H2: Terr CONFLICT > Terr NON-CONFLICT
H3: Terr CONFLICT > Terr NON-CONFLICT | Adaptive strategy use
For the time needed for other processes than making the decision, three behaviors are
this detection doesn’t influence Non-Decision Time (H1). Second, Conflict may be detected, and this detection results in longer Non-Decision Time compared to cases when there is no Conflict detected, no matter the used strategy (H2). Third, Conflict may be detected, and this detection results in longer Non-Decision Time compared to cases when there is no Conflict detected, but only when people use an adaptive strategy, in which they search for conflicting information to make their decision (H3). Note that hypotheses about this parameter will not result in clear differentiation between decision strategies.
Methods Operationalization
Participants engaged in a Sequential Gambling Task (SGT) on a computer. They were instructed to choose the most beneficial gambling machine out of two machines; one machine displayed on the left side of the screen, the other machine on the right side. On each trial of the task, two machines were shown with their numerical Gain Values. After 1000 ms, the Gain Values disappeared and the Gain Probabilities (as fractions) of the two machines were presented for 1000 ms instead. During the presentation of the second attribute, Gain Probability, the participants had to choose which of the machines they would pick by pressing the ‘z’ or ‘/’ keyboard button, corresponding to respectively the left and the right machine. Each trial began with a fixation cross and after each trial, a mask was presented.
Each trial belonged to one of five conditions. The order of the trials within each block was random, with the restriction that the same trial could not be presented twice in a row. So, the Sequential Gambling Task has a within subjects design with five conditions.
In the original study, four conditions were used. In the original study, in the First Attribute Uninformative, Second Attribute Informative (1U-2I) condition, the machines did not differ on the first attribute but did differ on the second attribute. In the First Attribute Informative, Second Attribute Uninformative (1I-2U) condition, the machines only differed on the second attribute. In the First Attribute Informative, Second Attribute Informative, First Attribute Correct (1I-2I-1) condition, the machines differed on both attributes, but the correct decision could have been made if one only attended to the first attribute. In the First Attribute
Informative, Second Attribute Informative, Second Attribute Correct (1I-2I-2) condition, the machines differed on both attributes, idem but a correct decision is made when attending to the second attribute.
In the initial study, if a participant picked a machine by only attending to the first attribute (if this first attribute is Informative), this would result in a correct choice (picking the machine with the highest Expected Value) in 2/3 of the trials. This is a problem, because it could lead to an anticipation effect. To resolve the possible anticipation confound, the proportion of trials in which the participant would make a correct if (s)he would only attend to the first attribute should be (close to) 1/2 instead of 2/3. To accomplish this, a new condition with two Informative attributes was included and the proportion of items per condition was changed. The new First Attribute Informative, Second Attribute Informative, Both Attributes Correct (1I-2I) condition was developed, in which the machines differed on both attributes, and both attributes favored the same machine. An additional advantage of this new 1I-2I condition is that it provides a fairer baseline for Non-Conflict trials. In the original study, the 1I-2U condition was used as a baseline. In the current study, the Non-Conflict trials differ from the Conflict trials only on the Conflict factor and not in whether or not the attributes are Informative. This is a benefit over using the 1I-2U condition as a Non-Conflict baseline, because the latter condition differs on both the Conflict factor and the Informative factor, so possible effects will non-distinguishable.
Furthermore, the proportion of the amount of trials for each condition was adapted. In the original study, 504 trials of each trial condition were presented, resulting in a total of 2016
trials. These trials were presented in 14 blocks of 144 trials. In order to keep the current study as similar to the original study as possible, the total amount of trials was kept nearly equal.
Consequently, the duration of the task was about as long as the original task. However, the amount of trials per condition differed, as did the number of blocks. The new total amount of trials for the conditions became 156 for 1U-2I, 312 for 1I-2U, 312 for the new 1I-2I condition, 312 for the 1I-2I-1 and 936 for the 1I-2I-2 conditions. This change of design solved the anticipation confound, because now for trials that have an Informative first attribute, the proportion in which the correct decision can be made based on the first attribute is nearly equal to the proportion in which the correct decision can be made based on the second attribute (46.2% vs. 53.8%). The total amount of trials became 2028 in total, divided into 13 blocks, resulting in 156 trials in each block. The distribution of trials within and across blocks is displayed for each condition separately in Table 1. All the presented value and probability pairs are displayed in Table 2. Note that the different pairs were presented multiple times in each block and that each pair was mirrored in half of the cases, so that machine 1 became machine 2 and vice versa.
All five conditions consist of either three or six items, and the item characteristics didn’t significantly differ between the five conditions. This means that the ranges, means and standard deviations of the values used for Gain Probability and Gain Value and the expected value were similar across conditions.
Table 1: Proportions of Trials within each of the 13 Blocks and Total Amount of Trials per
condition
Condition Trials within each block Total amount of trials
1U-‐2I 12 156 1I-‐2U 24 312 1I-‐2I 24 312 1I-‐2I-‐1 24 312 1I-‐2I-‐2 72 936 Total 156 2028
Table 2: Characteristics of Pairs of Gambling Machines in the Different Conditions of the
Sequential Gambling Task (SGT).
Condition Gain Value Machine 1 Gain Probability Machine 1 Gain Value Machine 2 Gain Probability Machine 2 Δ Gain Value Δ Gain Probability Δ Expected Value 1U-‐2I 5.0 0.3 5.0 0.5 0.0 0.2 1.0 1U-‐2I 8.0 0.3 8.0 0.5 0.0 0.2 1.6 1U-‐2I 3.0 0.4 3.0 0.6 0.0 0.2 0.6 1U-‐2I 7.0 0.4 7.0 0.6 0.0 0.2 1.4 1U-‐2I 2.0 0.5 2.0 0.7 0.0 0.2 0.4 1U-‐2I 5.0 0.5 5.0 0.7 0.0 0.2 1.0 1I-‐2U 4.0 0.3 6.0 0.3 2.0 0.0 0.6 1I-‐2U 5.0 0.4 7.0 0.4 2.0 0.0 0.8 1I-‐2U 2.0 0.5 4.0 0.5 2.0 0.0 1.0 1I-‐2U 6.0 0.5 8.0 0.5 2.0 0.0 1.0 1I-‐2U 3.0 0.6 5.0 0.6 2.0 0.0 1.2 1I-‐2U 4.0 0.7 6.0 0.7 2.0 0.0 1.4 1I-‐2I 5.0 0.3 7.0 0.5 2.0 0.2 2.0 1I-‐2I 4.0 0.4 6.0 0.6 2.0 0.2 2.0 1I-‐2I 3.0 0.5 5.0 0.7 2.0 0.2 2.0 1I-‐2I-‐1 4.0 0.3 2.0 0.5 2.0 0.2 0.2 1I-‐2I-‐1 5.0 0.4 3.0 0.6 2.0 0.2 0.2 1I-‐2I-‐1 6.0 0.5 4.0 0.7 2.0 0.2 0.2 1I-‐2I-‐2 6.0 0.3 4.0 0.5 2.0 0.2 0.2 1I-‐2I-‐2 7.0 0.4 5.0 0.6 2.0 0.2 0.2 1I-‐2I-‐2 8.0 0.5 6.0 0.7 2.0 0.2 0.2 Procedure
The participants first read the information letter and signed the informed consent form. Then, the participants read a detailed instruction of the task on the computer screen by themselves. The researcher was present during this to answer questions. After the instructions, a practice block of 60 trials was presented. After completion of this practice block, the researcher came in to answer any questions left and started the experimental SGT trials. These SGT trials consisted of 13 blocks of 156 trials. After each block, a game in which the participants had to pick a square is presented. Every square corresponded to a trial that was performed on. The expected values of the 13 gambles matching the picked squares were summed up to determine the additional earned monetary reward of ten euros at most. After seven blocks, the participants could take a longer break, in which they were offered a drink and a snack.
After the SGT, another task, the non-sequential gambling task (NSGT) was administered. The participants read the instruction on the computer screen while the researcher was present to answer questions. Contrary to the SGT, the NSGT had no practice block. Hereafter, the
participants filled in a questionnaire about their demographics and about the tasks. Lastly, the participants were paid and debriefed. The total experiment took around 2.5 hours per participant.
Participants
A total of nineteen undergraduate students participated in this study. The participants (78.9% female) had a mean age of 21.76 with a standard deviation of 1.52. All participants were between 20 and 25 years old and mastered Dutch, as all of the instructions we in Dutch. Participants were selected on not having (uncorrected) visual or hearing disabilities, and self-reported psychiatric, neurological, or systemic illness.
Materials
Sequential Gambling Task.
The participants performed on a Sequential Gambling Task (SGT), in which they were presented with two gambling machines on each trial. First, the amount that could be won (Gain Value) was visible for each machine. Second, the proportion of winning (Gain Probability) was presented for each machine. During the presentation of the Gain Probability, the participants had to indicate which of the gambling machines they would pick.
Non-Sequential Gambling Task.
After the SGT, a similar task was conducted in which the attributes were presented
simultaneously instead of sequentially. Participants are required to indicate whether the left or right machine is optimal, or whether the machines were equivalent. The Non-Sequential Gambling Task (NSG) consisted of one experimental block, containing 6 trials of the five conditions. So, there were no trials in which the machines didn’t differ in Expected Value. Contrary to the SGT, the NSGT had no response time limit.
Questionnaire.
Finally, a questionnaire about demographic variables and experiment thoughts and strategies was administered.
Detailed analyses of the NSGT and the Questionnaire are beyond the scope of this paper. The main focus of this paper will be on the results of the SGT.
Data analysis Data pre-processing
First, for each participant, in each condition, the DDM parameters were freely estimated with fast-dm (Voss & Voss, 2007; Voss et al., 2013) using the Kolmogorov- Smirnov statistic,
implemented in C. DDM parameters are not informative if there is no variance in accuracy (Voss et al., 2013). So, if there is no correct or no incorrect response by a participant in a condition, the scores of this participant in this condition was coded as missing. As result of this, the DDM parameters of one participant in the 1U-2I condition were not estimated. After estimation in fast-dm, the Starting Points zr were linearly transformed to Starting Points z, which is centered around 0 instead of 0.5, to improve interpretability. Similarly, Drift Rates were transformed to absolute Drift Rates to make interpretation easier. Consequently, there is no difference between transformed Drift Rates towards optimal choices and non-optimal choices.
Data Analysis
For the main analyses, a General Linear Mixed Model (GLMM) was used to test if the dependent variables (DDM parameters) of different conditions differ. The model was fit in IBM SPSS Statistics (version 22, IBM, 1989-2013) and R (3.3.2 GUI 1.68 Mavericks build, 2016) was used for data pre-processing and development of figures and tables. To test the hypotheses about the between-condition effects, post-hoc comparisons were conducted. The 1U-2I condition is used as a baseline for Non-Informative first attributes, versus the Informative 1I-2U, 1I-2I, 1I-2I-1 and 1I-2I-2 informative conditions. Furthermore, for the hypotheses about Conflicting versus Non-Conflicting attributes, the 1I-2I condition is used as a baseline condition for Non-Conflict, versus the 1I-2I-1 and 1I-2I-2 Conflict conditions. The 1I-2I condition was chosen as the baseline for Non-Conflict, rather than the 1U-2I or the 1I-2U condition, because it only differs from the Conflict conditions on the factor or interest – whether or not the attributes are Conflicting – while all three conditions have Informative first and second attributes.
Hypothesis 1 was tested by comparing the following conditions: a1I-2U vs. a1U-2I
a1I-2I vs. a1U-2I
a1I-2I-1 vs. a1U-2I
a1I-2I-2 vs. a 1U-2I
Hypothesis 2 was tested by comparing the following conditions: z1I-2U vs. 0
z1I-2I vs. 0
z1I-2I-1 vs. 0
z1I-2I-2 vs. 0
Hypothesis 3 was tested by comparing the following conditions: a. vabs 1I-2U vs. vabs 1U-2I
vabs 1I-2I vs. vabs 1U-2I vabs 1I-2I-1 vs. vabs 1U-2I vabs 1I-2I-2 vs. vabs 1U-2I b. vabs 1I-2I vs. vabs 1I-2I-1
vabs 1I-2I vs. vabs 1I-2I-2
Hypothesis 4 was tested by comparing the following conditions:
Terr 1I-‐2I vs. Terr 1I-‐2I-‐1
Terr 1I-‐2I vs. Terr 1I-‐2I-‐2
Results
Firstly, the proportion missing and correct responses, as well as the mean response times for both correct responses and incorrect responses are displayed in Table 3. Figure 2 displays the proportion correct, incorrect and missing responses for each condition. The Drift Diffusion Model parameters were estimated in fast-dm. The parameter estimates are displayed in Table 4.
Table 3: Proportion of Missing Responses and Means (Standard Deviations) of
Accuracy and Response Time Measures.
Condition Proportion Missing Responses (* 10-2)
Proportion Correct Mean Correct RT (s) Mean Incorrect RT (s) 1U-2I 0.810 (0.090) 0.887 (0.316) 0.459 (0.107) 0.338 (0.143) 1I-2U 1.175 (0.131) 0.735 (0.442) 0.517 (0.184) 0.460 (0.183) 1I-2I 0.860 (0.092) 0.874 (0.331) 0.469 (0.147) 0.370 (0.170) 1I-2I-1 0.843 (0.091) 0.210 (0.407) 0.357 (0.186) 0.493 (0.137) 1I-2I-2 0.776 (0.088) 0.776 (0.417) 0.489 (0.133) 0.356 (0.183)
Figure 2: Proportion correct, incorrect and missing for each condition.
Table 4: Means (Standard Deviations) of Drift Diffusion Model (DDM) Parameter
Estimates for all Five Conditions.
Condition Boundary
Separation a Starting Point z Drift Rate v Non-Decision Time Terr
1U-2I 0.92 (0.26) fixed 3.73 (1.44) 0.34 (0.08) 1I-2U 0.84 (0.16) -0.07 (0.12) 2.12 (1.05) 0.37 (0.13) 1I-2I 0.95 (0.31) -0.02 (0.12) 3.35 (1.18) 0.34 (0.10) 1I-2I-1 0.89 (0.27) -0.02 (0.16) 2.51 (0.93) 0.36 (0.10) 1I-2I-2 0.91 (0.24) -0.06 (0.16) 2.74 (1.02) 0.34 (0.10)
In Figure 3, the means of the four parameter estimates are shown for each condition separately, with their corresponding standard errors. Each panel represents a different parameter.
This figure provides a clear visual representation of the parameters per condition. However, in order to test the hypotheses, analyses with planned contrasts are needed. Figure 3 does not take this into account. So, in order to determine whether conditions differ or not, the planned contrasts analyses predominate.
Figure 3. In this figure, the means of Boundary Separation, Starting Point, Drift Rate and Non-‐
Decision Time are displayed with their standard errors, for each condition separately. Note: Error bars indicate Standard Errors of Mean (not 95% confidence intervals) and bars represent means, therefore not all differences between conditions show like they do in the statistics in the written results section.
The results of the analyses about the hypotheses of the Drift Diffusion Modeling parameter estimates are discussed below for each parameter individually.
Boundary Separation a. Trials with Uninformative first vs. Informative first attributes appeared not to differ in Boundary Separation (1U-2I vs. 1I-2U, t(7.91) = 1.44, p = 0.190; 1U-2I vs. 1I-2I, t(8.25) = -0.69, p = 0.515; 1U-2I vs. 1, t(12.72) = 0.45, p = 0.662; 1U-2I vs. 1I-2I-2, t(14.28) = 0.13, p = 0.895). This indicates that people don’t adjust their decision strategy depending on whether or not de first attribute was Informative. This result indicates the use of an integrative strategy.
1U−2I 1I−2U 1I−2I 1I−2I−1 1I−2I−2
Boundary Separation a Condition a 0.0 0.2 0.4 0.6 0.8 1.0 1.2
1U−2I 1I−2U 1I−2I 1I−2I−1 1I−2I−2
Starting Point z Condition z −0.10 −0.05 0.00 0.05 0.10
1U−2I 1I−2U 1I−2I 1I−2I−1 1I−2I−2
Drift Rate v Condition v 0 1 2 3 4
1U−2I 1I−2U 1I−2I 1I−2I−1 1I−2I−2
Non−Decision Time t Condition t 0.0 0.1 0.2 0.3 0.4 0.5
Starting Point z. When an Informative first attribute was followed by an Uninformative second attribute, Starting Point z was biased towards the opposite of the optimal choice according to the first attribute (1I-2U vs. 0, t(18.00) = -2.53, p = 0.021). However, in the other condition in which there was no conflict, Starting Point z appeared not to be biased (1I-2I vs. 0, t(18.00) = -0.56, p = 0.584). Likewise, no bias was found in the Conflict conditions (1I-2I-1 vs. 0, t(18.00) = -0.42, p = 0.678; 1I-2I-2 vs. 0, t(18.00) = -1.57, p = 0.133). So, although most results indicate no difference in Starting Point z, a result which is congruent with either an integrative or adaptive strategy, there is an unexpected result for the condition in which an Informative first attribute is followed by an Uninformative attribute. This result is not consistent with the integrative, lexicographic or adaptive strategy.
Drift Rate v. Absolute Drift Rate v was larger in the Uninformative first attribute
conditions than in Informative first attribute conditions, in three out of four conditions (1U-2I vs. 1I-2U, t(18.26) = 5.97, p < 0.01, d = 1.94; 1U-2I vs. 1I-2I-1, t(18.31) = 3.94, p = 0.010, d = 1.28; 1U-2I vs. 1I-2I-2, t(18.04) = 3.25, p = 0.004, d = 1.05). However, in case of an Uninformative first attribute compared to an Informative first attribute followed by a Non-conflicting Informative second attribute, there was no difference in absolute Drift Rate (1U-2I vs. 1I-2I, t(17.72) = 1.81, p = 0.087 d = 0.59). As in three cases Drift Rates were larger for an
Uninformative compared to Informative first attribute, there is some evidence for the use of an adaptive strategy.In addition, in one case, Non-Conflicting and Conflicting information on the first and second attribute did not differ in absolute Drift Rate (1I-2I vs. 1I-2I-2, t(18.00) = 2.08, p = 0.052,). However, in the other case, Non-Conflicting information on the first and second attribute showed a larger Drift rate compared to Conflicting information (1I-2I vs. 1I-2I-1, t(18.00) = 3.13, p = 0.006, d = 1.01). Together, these results are an indication for the use of an adaptive strategy. The general pattern seems to be that when the machines differ on the first attribute and thus conflict is anticipated, the speed accumulation slows down. However, most of the results, but not all the results, show this pattern, so the lexicographic and integrative strategy cannot be completely discarded based on the results of Drift Rate.
Non-Decision Time T. The Non-Decision Time did, in one case, not differ between Conflicting and Non-conflicting attributes after an informative first attribute (1I-2I vs. 1I-2I-2, t(18.00) = -0.33, p = 0.724), whereas in the other case, Non-Decision Time in cases of
Conflicting attributes was longer than in cases of Non-Conflict (1I-2I vs. 1I-2I-1, t(18.00) = -3.60, p = 0.004, d = -1.17). This last result indicates that conflict detection delays the decision by prolonging the Non-Decision Time. This provides some evidence for the use of an adaptive strategy, although it is also not impossible to find these results under the integrative or lexicographic strategy.
Discussion
The current paper aimed to answer the question which decision strategy people use when making sequential, multi-attribute choices, by investigating if the Drift Diffusion Model parameters indicate the use of a lexicographic, an integrative or an adaptive strategy in a sequential gambling task. This study made use of a sequential gambling task with five conditions of numerically presented Gain Values followed by numerical proportions of Gain Probability and these
attributes differed across conditions on an Information and on a Conflict factor. DDM analyses were performed on the reaction time distributions of correct and incorrect choices. This study aimed to nullify the anticipation confound in the original study of Dekkers et al. (in prep.) by adding the 1I-2I condition, with two Non-Conflicting Informative attributes, and by changing the proportions of trial distributions across conditions.
The hypotheses for these analyses were the same as the original hypotheses in the Dekkers et al. (in prep.) paper and can be summarized as follows. For the integrative strategy, people were expected to calculate the Expected Values of both the machines. Consequently, no differences between DDM parameters of the conditions were expected. For the lexicographic strategy, people were expected to assess if the machines differed on the first attribute. If the first attribute was judged to differ, only this first attribute would be attended to. Only if the first attribute were assessed not to be Informative the second attribute would be attended to. Thus, differences on DDM parameters between Informative first attribute conditions and
Non-Informative first attribute conditions were expected under the lexicographic strategy. Finally, for the adaptive strategy, the choice of the ultimate strategy was expected to depend on whether or not Conflict was anticipated. A lexicographic continuation was expected for Uninformative first attribute conditions, were no Conflict was anticipated. An integrative continuation was expected for Informative first attribute conditions, were Conflict was anticipated.
Results mainly correspond to the use of an adaptive strategy. The use of a lexicographic strategy seems very unlikely, because none of the Drift Diffusion Model parameters indicate the use of this strategy. Moreover, accuracy in the 1I-2I-1 is far lower than in the 1I-2I-2, which is counter indicative of the lexicographic strategy. Although some of the results, for example the results of Boundary Separation a, are congruent with the use of the integrative strategy, the use of an adaptive strategy seems to be more likely based on the results. If an integrative strategy is used, no differences in the DDM parameters between conditions were expected, because by using this strategy, all information is weighted. Results on, for example, Drift Rates show that, at least in some cases, there is a difference between Informative and Uninformative first attribute conditions and between Conflicting and Non-Conflicting conditions, indicating the use of an adaptive strategy. The results show some support that people take anticipation of Conflict into account when making the decision.
However, there are some unexpected results. First, although most results regarding Starting Point z appeared not to be biased, Starting Point z appeared to be biased in the opposite direction of the optimal choice if the first attribute was Informative, followed by an
Uninformative second attribute. This result is not congruent with any of the proposed strategies, but could be indicative for the risk-reward heuristic, proposed by Pleskac and Hertwig (2014). This entails that people expect that options high on Gain Value are low on Gain Probability and vice versa. So, this could explain why people are biased away from the optimal choice. In the current study, this tendency results in a probability bias, because Probability was always presented as the second attribute. So, rather than using the lexicographic, integrative or adaptive strategy, people seemed to have used a probability biased adaptive strategy.
This relates to the second unexpected result. Post hoc inspection of accuracy shows that the accuracy on the 1I-2I-1 trials, where the optimal decision is made when attended to Gain Value, is very low, namely 0.210. However, in the 1I-2I-2 condition, where the optimal decision is made when attended to Gain Probability, accuracy is much higher, namely 0.776. This can be another indication of a probability bias; people tend to attend more to Probability than to Value. This bias is known from previous research (i.e. Jansen, van Duijvenvoorde & Huizenga, 2012). As there are some indications that people use an adaptive strategy, but some of the results fail to support an adaptive strategy and show a probability bias, people might use a strategy that could be called a probability biased adaptive strategy. Results show that in some cases, anticipation of Conflict has an effect on the decision. However, the decision seems probability biased, because most of the time, people choose the optimal choice according to the Probability rather than according to Value. Together, these results indicate a probability biased adaptive strategy. The original sturdy of Dekkers et al. (in prep.) also found results indicating a probability biased adaptive strategy. A possibility to investigate if the probability biased adaptive strategy that seems to be used in the current study also holds for other sequential multi-attribute decisions, is to conduct the same experiment, but present Gain Probability first, followed by Gain Value. If
people use the probability biased adaptive strategy in this paradigm too, the same hypotheses regarding the DDM parameters are proposed, but accuracy in 1I-2I-1 condition would be higher in this case.
There are a lot of decisions in which there are multiple attributes and were these
attributes are presented sequentially in everyday life. By using DDM parameters, this experiment provides insight about how such decisions come about. People appeared to be as cautious in case of Informative first attributes as in case of Uninformative first attributes, as indicated by
Boundary Separation a. Starting Point indicates biases. This experiment showed that people judge Probability to be more important than Value for their decision, resulting in a probability bias. Drift Rate is an indication of speed of evidence accumulation. Results indicate that speed accumulation is faster for Uninformative compared to Informative first attributes, and, in some cases, slows down if Conflict is anticipated. Together, a probability biased adaptive strategy, in which people judge whether or not Conflict is anticipated to decide what strategy they will use to continue, and in which Probability is more important for the decision than Value, seems like the best way to describe the decision process in this experiment. This finding is congruent with the findings of Dekkers et al. (in prep.)
There are some limitations of this study. First, like in the original Dekkers at al. (in prep.) paper, the participants performed on this task under time pressure. Possibly, the provided time was too short to fully integrate the two decisions and make an optimal choice. Consequently, people could have been more tempted to use a lexicographic or adaptive strategy. In further research more time could be provided to make a decision. However, most decisions do have a time limit and require fast responses, so it is relevant to investigate people’s decision strategies in such cases.
Second, like in the original Dekkers at al. (in prep.) paper, people could have changed strategies over time during the task. In the current design, it is not possible to detect these changes, so results of this study have to be interpreted with some caution. A possible solution is to use less trials and test more participants in future research. Moreover, this would provide the opportunity to investigate individual differences in DDM parameter estimates and decision strategies, which would add valuable insight.
Finally, although the anticipation confound is resolved by adding a new condition and changing the proportions of trail distributions across conditions, there is still another factor that has to do with proportions of trail distributions across conditions and could be problematic. As in the original study of Dekkers et al. (in prep.), 2/3 of the conditions with an Informative first attribute have Conflicting attributes and only 1/3 of the conditions have Non-Conflicting attributes. Since it is impossible to optimize both the anticipation confound and the inequality of Conflicting and Non-Conflicting cases using the current paradigm, a decision has to be made on which problem should be solved. The current study chose to solve the anticipation confound, because this is more problematic than the Conflict confound. If people discover that an optimal choice could be made in 2/3 of the trials, they could assign more importance to the first attribute and thus the decision strategy could be biased. The Conflict confound is less harmful, because the only consequence of this might be that people expect Conflict. However, the Conflict factor is only relevant for one strategy, the adaptive strategy. People using this strategy might anticipate Conflict more often, resulting in more cases of continuation in a complex, integrative manner. To investigate the influence of the Conflict confound in further research, the proportions of trial distributions across conditions could be changed so that, in conditions with Informative first attributes, half the trials will be Conflicting and half Non-Conflicting. However, this would be accompanied by inequality of trials in which an optimal choice is made based on the first attribute versus based on the second attribute.
In conclusion, this study provided insight in sequential, multi-attribute decisions by using DDM parameter to analyze differences between conditions differing on an Informative and a Conflict factor. The best way to describe the strategy used by the participants is a probability
biased adaptive strategy. This matches the result of the original study (Dekkers et al., in prep). Thus, in case you have to choose between the two movies, chances are that you would use a probability biased adaptive strategy and end up choosing the movie for which you know that you could obtain a good seat.
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