Human trust in automation and acceptance of algorithmic or AI advice

A survey on studies of human interactions with technology reveals that a variety of human factors, such as trust, mental workload, and automation accuracy, affect whether automation (defined in this case as a machine agent carrying out a previously human function) is used by a human or not (Parasuraman and Riley, Reference Parasuraman and Riley1997). Trust can be divided into beliefs or behavior, the latter of which is often referred to as reliance. While trust beliefs are often related to person-specific factors like prior experiences, trust behavior is often related to the specific task (Kahr et al., Reference Kahr, Rooks, Willemsen and Snijders2024). Humans can exhibit both overreliance and underutilization of automation, influenced by different combinations of these factors. Overreliance can be caused by using automation as a decision heuristic, a possibility for experts and non-experts alike. Underutilization, on the other hand, is often a result of a lack of trust from the human side (Parasuraman and Riley, Reference Parasuraman and Riley1997). Prior work frames the lack of proper reliance on “machine advice” as two conflicting human biases: algorithmic appreciation and algorithmic aversion. Algorithmic appreciation refers to humans preferring assistance from an algorithm over another human (Logg et al., Reference Logg, Minson and Moore2019), while algorithmic aversion refers to resistance to accepting recommendations from algorithms (even if they may outperform humans) (Dietvorst et al., Reference Dietvorst, Simmons and Massey2015). Experimental results relating to algorithmic appreciation vs. algorithmic aversion are inconsistent, with empirical evidence for some tasks supporting algorithmic appreciation and others indicating algorithmic aversion (Dietvorst et al., Reference Dietvorst, Simmons and Massey2015; Logg et al., Reference Logg, Minson and Moore2019; Dietvorst and Bharti, Reference Dietvorst and Bharti2020; Kumar et al., Reference Kumar, Patel, Benjamin and Steyvers2021). Prior work has found that appreciation of algorithmic advice reduces when people choose between the algorithm and their own judgment and when they have domain expertise. Notably, in forecasting experiments, experts exhibit reduced accuracy compared to non-experts due to their discounting of algorithmic advice (Logg et al., Reference Logg, Minson and Moore2019). Supporting algorithmic aversion, evidence shows that people are likely to disregard suggestions after observing a mistake, even if the algorithmic results outperform human decisions on average (Dietvorst et al., Reference Dietvorst, Simmons and Massey2015).

Additionally, studies have revealed that providing people with just the right amount of information can improve trust (Kizilcec, Reference Kizilcec2016) and perceptions of a model (Cai et al., Reference Cai, Jongejan and Holbrook2019). Particularly in the engineering field, humans may be more inclined to integrate AI suggestions into their work if they know how those suggestions were generated (Naser, Reference Naser2021). However, explaining the inner workings of a complex model at prediction time is a difficult task. Some studies of explainable AI methods reveal that explainability correlates with trust, accuracy, social competence, and performance (Leichtmann et al., Reference Leichtmann, Humer, Hinterreiter, Streit and Mara2023; Silva et al., Reference Silva, Schrum, Hedlund-Botti, Gopalan and Gombolay2023), but others indicate that explanations can also impair outcomes or depend on highly accurate models to be impactful (Papenmeier et al., Reference Papenmeier, Kern, Englebienne and Seifert2022; Westphal et al., Reference Westphal, Vössing, Satzger, Yom-Tov and Rafaeli2023; Kahr et al., Reference Kahr, Rooks, Willemsen and Snijders2024). Perceived explainability also varies across different methods, with simpler approaches like language-based and case-based explanations being perceived as more explainable than methods like probability scores (Silva et al., Reference Silva, Schrum, Hedlund-Botti, Gopalan and Gombolay2023). Case-based decision support, where related examples are shown in conjunction with a model’s prediction based on similarity, is an approach towards better aligning automation with humans when the final decision lies with the human decision-maker (Liu et al., Reference Liu, Tian, Chen, Feng, Chen and Tan2022). Because it may be difficult to generate language-based explanations for complicated engineering contexts (e.g., explaining the mechanism of a surrogate model for structural simulation), this study explores example-based explanations to investigate the potential influence of model explainability on decision-making.

Human-computer collaboration in engineering design

The vision for human-computer collaboration in engineering design has been to take advantage of engineers’ ability to formalize problems while overcoming the cognitive limitations of considering many variables (Egan and Cagan, Reference Egan and Cagan2016; Viros-i-Martin and Selva, Reference Viros-i-Martin and Selva2021). Models and algorithms that account for multi-objective decision-making are particularly useful in addressing the complexity of engineering design problems (Deb, Reference Deb2014). Prior work finds that bringing humans in the loop during multi-objective optimization, using a decision-making paradigm called trade space exploration or through an interactive algorithm, helps the search for optimal solutions in the face of complex design considerations (Simpson et al., Reference Simpson, Carlsen, Malone and Kollat2011; Souaille et al., Reference Souaille, Petiot, Misdariis and Lagrange2022). A study of side-by-side human-robot trade space exploration for system design finds that collaboration leads to better designs than solo efforts. However, downsides arise when humans become aware of and frustrated by the limitations of the agent and its suggestions (Law et al., Reference Law, Dhawan, Bang, Yoon, Selva and Hoffman2018).

The impact of algorithmic or AI advice for design has also been examined through tasks such as drone or truss structure design. In the case of drone design, AI assistance impacts the overall quality of an individual’s final design submissions over several objectives. Design quality is higher when participants (both self-reported experts and non-experts) are provided with AI assistance compared to when they design alone (Song et al., Reference Song, Soria Zurita, Nolte, Singh, Cagan and McComb2022). Beyond individual designers, AI assistance has also been shown to impact design teams in the case of truss design. Experimental results find that AI assistance appears to hurt the performance of high-performing teams (Zhang et al., Reference Zhang, Raina, Cagan and McComb2021). These studies demonstrate the potential for human-AI collaboration in engineering design by measuring differences in performance when participants either have or lack access to AI assistance (Law et al., Reference Law, Dhawan, Bang, Yoon, Selva and Hoffman2018; Zhang et al., Reference Zhang, Raina, Cagan and McComb2021; Song et al., Reference Song, Soria Zurita, Nolte, Singh, Cagan and McComb2022). However, performance improvements might only be realized if people are willing to accept helpful AI assistance when it is provided, as well as able to recognize erroneous AI assistance. The tasks in engineering design studies tend to be more open-ended compared to the tasks in many studies on acceptance of algorithmic advice, which have a ground truth for comparison. The study conducted here introduces some of the open-endedness typical of design by investigating multi-objective decisions while maintaining a similar structure to previous studies on algorithmic appreciation and aversion by utilizing repeated decision-making trials.

Task

The context for both experiments was the redesign of a jet engine bracket for additive manufacturing. The task was based on the real design challenge hosted by General Electric on GrabCAD, where engineers had to assess a weight vs. strength tradeoff and submit optimized bracket designs, which were then evaluated using finite element analysis.Footnote ¹ A dataset of these designs, their properties, and their performance was made publicly available, and a subset was used as the stimulus set for this study (Whalen et al., Reference Whalen, Beyene and Mueller2021). For both experiments, participants in our studies were asked to weigh several performance requirements (two or three depending on the experiment) for a set of design decisions. The context and instructions provided to participants are included below:

• • Background: “Loading brackets play a critical role on jet engines. They must support the weight of the engine during handling without breaking or warping. The brackets may be used only periodically, but they stay on the engine at all times, including during flight.”

• • Instructions: “In this task, you will have to weigh the tradeoff between [three] performance requirements: strength and deformation vs. size and weight [vs. manufacturing time], for a series of design options that optimize the bracket. The bracket will be additively manufactured.”

• • Load Conditions (with an accompanying figure from the original challenge¹): “To simulate engine transport and maximum load carrying capacity, the part has been subjected to the displayed individual load conditions.”

Participants were then introduced to the information that would be available to help them make their decisions during the task:

• • Designs: 3D models of the designs that could be inspected through rotation and zoom

• • Response to load: Visualizations of the displacement field from simulation under worst-case loading

• • Objective Values: Graphs showing the design’s mass, maximum displacement across any of the loading conditions, and (Experiment 2 only) manufacturing time via metal 3D printing

• • Model Assistance: The model’s suggestion for the better design choice (“You will receive help from the results of an optimization model trained on many designs. The best answer will be suggested based on the model results, though they may not always be right.”)

• • Explanation (Experiment 2b only): An example-based explanation of the suggestion (“To help understand why the model is suggesting a particular design, you will also be shown an example of a similar design that would be suggested.”)

The “model” was simulated and the actual mechanism for determining the suggestion is explained in the “Dataset” section. This model could be erroneous, determined by whether it correctly suggested a better design according to the multi-objective criteria. Finally, before proceeding to the main set of trials, the participants completed practice to become familiar with the interface and task. Directly after the set of practice trials, they were given feedback on how many times they selected the optimal design during practice (e.g., “You selected the more optimal design 3/4 times”), but no information about which specific trials they answered correctly.

Dataset

There were 381 bracket designs in the dataset, representing the global design space explored during the GrabCAD challenge. Each design had an associated mass, maximum displacement (determined across the four loading conditions in the original challenge), and category (determined qualitatively in the dataset (Whalen et al., Reference Whalen, Beyene and Mueller2021)). Additionally, manufacturing time via metal 3D printing was estimated for each design using the Markforged Eiger software.Footnote ² Bracket designs were ranked based on the concept of Pareto optimality with two or three equally weighted objectives, using non-dominated sorting (Srinivas and Deb, Reference Srinivas and Deb1994). The Pareto frontier refers to where no individual criterion can be made better without making another criterion worse. Therefore, to classify the multi-objective performance of each design via non-dominated sorting, the Pareto optimal set was calculated iteratively across the designs: (1) the Pareto optimal set (designs on the Pareto frontier using the relevant criteria) was found across the full set of designs, (2) that optimal set was removed, (3) the Pareto optimal set was calculated again for the rest of the designs, and (4) the process was repeated until each design was in one of the sets. The results of this process are visualized for two objectives and three objectives in Figure 1, where the lower (i.e., earlier) iterations indicate the more globally optimal designs as opposed to the higher (i.e., later) iterations. Using two objectives, this procedure resulted in 21 sets with a median of 19 designs per set (range: [1, 38]). Using three objectives resulted in 11 sets with a median of 27 designs per set (range: [1, 88]). This method provided a quantification of designs that were “better,” “worse,” or “similar” in performance, considering all objectives. The rankings were used to quantify which design was suggested to the participants as the model’s suggestion.

Figure 1. Non-dominated sorting, an iterative process of calculating rankings based on Pareto optimality, was used to quantify comparisons between pairs of designs based on multi-objective criteria. Iteration 0 refers to the globally optimal set of designs.

This simulated model was intended to emulate data-driven models, which make use of large amounts of data that humans cannot synthesize on their own. In this experiment, participants could only access a local set of designs (the two designs they decided between), while the simulated model assessed which design was better based on the global set (all the designs that were submitted as solutions in the challenge). The non-dominated sorting calculation was based only on designs that were explored during the original challenge, excluding any potentially better (but unknown) designs left unexplored. Real data-driven models share this limitation, as they may struggle to reach new areas of a design space. While there was no fuzzing factor used to rank the design alternatives and subsequently classify trials and their suggestion type (i.e., the experimental design conditions), the Appendix contains a post-hoc analysis of the impact of conducting the ranking procedure with a fuzzing factor (i.e., a fuzzy Pareto front in each iteration).

Experiments

Table 1 outlines the different behavioral experiments conducted. The first experiment focused on the two objectives, weight vs. strength, originally emphasized in the challenge. However, we hypothesized that increasing the number of objectives increases the complexity of the task and may impact reliance on suggestions. Therefore, a second experiment was conducted with the addition of a third objective, manufacturing time, and an additional between-subjects manipulation to supplement the decision with an example-based explanation. Data collection for these experiments was IRB-approved and participants in all experiments were compensated $10 for their time ($20/hr). To be eligible for any part of the study, participants indicated that they were over the age of 18 and had taken at least one university course in structural/solid mechanics.

Table 1. Experiments conducted and the number of participants in each

Experimental design

Each experiment (1, 2a, and 2b) had one manipulation, which was the correctness of the model’s suggestion, as shown in Table 2. The model’s suggestion could be correct (suggesting the better design), incorrect (suggesting the worse design), or equivalent (both designs are considered optimal and a random one is suggested). Participants in each experiment were exposed to all conditions (suggestion types) with the 30 total trials shuffled pseudo-randomly. A prior study shows high initial confidence in AI among engineering designers, which rapidly decreases with exposure to a 20% accurate AI agent, but stays stable with an 80% accurate AI agent (Chong et al., Reference Chong, Raina, Goucher-Lambert, Kotovsky and Cagan2022). Therefore, in this study, the accuracy of the model was set to 71% (only counting trials where there is a “ground truth” for the better design), with only 20% of the total trials being completely incorrect. An increased level of accuracy means that fewer trials are presented for the incorrect condition compared to the correct and equivalent conditions. However, sufficiently high accuracy ensures that participants do not immediately lose trust in the suggestions due to a poorly performing model, reducing changes in trust across trials over time. Constraints on the task length and the number of suitable stimuli limited the number of trials conducted for each participant to 30. Every participant had the same four practice trials prior to the main task, containing only correct and incorrect suggestions with similar accuracy to the remaining trials (75%). This approach was intentional, allowing participants to develop an intuition for the approximate model accuracy before starting the main task. Participants were given feedback on how many times they selected the optimal design during practice (e.g., three out of four times), but no information about which trials they answered correctly or the true model accuracy that was specified (71%). Additionally, participants were required to have a basic level of expertise (understanding of the performance criteria), limiting the pool to those who had an engineering background, at minimum having taken a structural/solid mechanics course to ensure understanding of the strength criterion.

Table 2. Conditions and trials in each experiment

Stimuli

The stimulus sets were selected so that their multi-objective properties would represent the global space (shown in Figure 1) of designs. A total of 60 bracket designs (two designs per trial for 30 trials, shown in Figures 3 and 8) were presented to participants for the main block of each experiment, with an additional eight for four practice trials and one for the instructions. None of the stimuli were repeated within an experiment and the trials (i.e., the stimulus pairs) were presented in a randomized order to each participant during the task to account for ordering effects.

To mitigate potential confounds, several properties were balanced within the stimulus sets, ensuring that each condition contained stimuli with similar characteristics. First, the degree of domination between designs (i.e., the difference between iterations when each was considered optimal) was balanced (except for the equivalent condition, where the iteration was the same) resulting in trials both close and far apart in the multi-objective space. The designs had to be at least 4 iterations apart to avoid cases where they would be too similar to feasibly compare. Next, the difference between the performance values of each design pair was balanced, as this represents the primary information expected to guide decision-making. In particular, the displacement delta was balanced so that each condition contained approximately the same number of trials with smaller or larger differences in stiffness. Each design in the dataset was associated with a category label (block, flat, arch, beam, and butterfly), referring to the rough general shapes of the brackets. These labels were used to ensure that designs in each stimulus pair were matched and categories were balanced across conditions. Despite the careful selection of the stimulus set, some factors could not be fully accounted for due to the visual diversity of designs in the dataset, the qualitative nature of category labels, and the uneven distribution of designs across categories. Since the procedure was repeated for the three-objective tradeoff after the completion of the first experiment, we attempted to maintain similar stimuli properties between Experiments 1 and 2. Experiments 2a and 2b consisted of the same stimuli, with 2b containing an additional 30 unique designs that were presented as the example-based explanation for each trial.

Interface

The task was deployed online and participants were directed to a Google Forms survey after completion. The data from the task was collected through a custom online interface developed in Unity (using the Unity Experiment Framework (Brookes et al., Reference Brookes, Warburton, Alghadier, Mon-Williams and Mushtaq2020)) and sent to a database in Amazon Web Services. Since the two design alternatives were presented side-by-side, a counterbalancing factor was included within each suggestion type to account for whether the suggested design was on the right or left. There were slight modifications to the interface to incorporate the additional complexity of Experiment 2, explained in more detail in the “Interface” section within the “Experiment 2: Three Objective Tradeoff” section.

Survey

Participants completed a survey after the task and were asked questions about the perceived accuracy of the model, the information used to make their decisions, and the strategy used during the task. They also indicated their knowledge about the task domain and their experience in engineering or design. Knowledge of the relevant topics was rated from 1 to 7 [“Rate your knowledge of structural/solid mechanics (e.g., 4, taken 1 course)” and “Rate your knowledge of multi-objective optimization models (e.g., 4, familiar with multi-objective optimization models)”]. Participants in the group provided with an example-based explanation were given additional questions regarding their use and interpretation of these examples.

Methods

Interface

The original interface was designed to provide participants with information to make their own decisions, as well as indicate which option the model would suggest. Figure 2 shows the interface and the types of information available, including a rotatable 3D object.

Figure 2. Participants were instructed to select designs using the interface shown.

Stimuli

The stimuli seen by each participant were selected to represent the design space available in the dataset, considering the two objectives of mass and maximum displacement. The performance values across each objective for the stimuli in each condition are shown in Figure 3 compared to full design space.

Figure 3. Performance values of bracket stimuli in each condition.

Results

Data was collected about the designs selected by the participants as well as the time spent on each trial. Prior to analyzing the data from the first experiment, four trials (of 990 trials total, not including practice trials) were removed because the response time was not greater than 500 milliseconds. This threshold is above the time required to consciously recognize and respond to a visual stimulus and was chosen prior to data analysis (Grill-Spector and Kanwisher, Reference Grill-Spector and Kanwisher2005).

The effect of model error on suggestion acceptance and performance

The trials were analyzed to investigate how the simulated model’s suggestion of a better or worse-performing design solution impacted participants’ decision-making. Thus, only conditions with a ground truth (“correct” and “incorrect”) were included in these analyses. Figure 4 shows the proportion of participants’ decisions that aligned with the provided suggestions (median = 0.57). The proportion of decisions that was expected to align with the suggestions, if the participant and the simulated model agreed completely, was 71%, the actual proportion of correct suggestions. A non-parametric Wilcoxon signed-rank test was conducted as the data violated the assumption of normality, showing a significant difference between the hypothesized value and the observations (W = 24.0, p < 0.001). When the performance of the two alternatives differed, participants’ selection of the suggested design was lower than expected. The participants’ performance was also quantified by participant accuracy, the proportion of the time the better-performing design was selected (the same design as the model’s suggestion in the correct condition and the non-suggested design in the incorrect condition). The median overall participant accuracy was 0.76 and participant accuracy was higher when given the incorrect suggestion (median = 0.83) vs. the correct suggestion (median = 0.73). A Wilcoxon signed-rank test was conducted, indicating that there was a significant difference in the participant accuracy (i.e., participants’ likelihood to accurately ignore a bad suggestion compared to accurately use a good suggestion) across the incorrect and correct conditions (W = 152.0, p = 0.02).

Figure 4. Probability of selecting the suggested design across all participants (median = 0.57) vs. the expected proportion (0.71) (W = 24.0, p < 0.001).

The effect of suggestions in uncertain scenarios

The equivalent condition was analyzed to investigate how suggestions impacted participants’ decision-making when both options were similar in overall multi-objective performance. These design pairs were ranked optimal in the same iteration, but differed in values along each objective (e.g., high mass and low displacement vs. low mass and high displacement). Figure 5 shows the proportion of selections that aligned with the model’s suggestions for each participant (median = 0.78). Considering that the suggestion in this condition was arbitrarily left or right, it was expected that the participants’ design selections would align with the model’s suggestions 50% of the time. However, a Wilcoxon signed-rank test shows a significant difference in participants’ proportional selection of the suggested design compared to the expected value in this experiment (W = 5.0, p < 0.001). When both design options were close in performance, but involved a bi-objective tradeoff, participants chose the model’s suggestion more frequently than chance alone. A Pearson correlation indicates a moderate positive correlation between the proportion of a participant’s selections aligned with the model’s suggestion (in the equivalent condition) and the participant’s accuracy (r_p = 0.36, p = 0.04). Participant accuracy (incorrect and correct conditions only) tended to be higher for those who followed the model’s suggestion even when both choices were valid as the “better” design (the equivalent condition).

Figure 5. The proportion of trials in the equivalent condition where participants chose what the model suggested (median = 0.78) vs. the expected proportion (0.50) (W = 5.0, p < 0.001).

Trial-by-trial design properties and implications on decision-making

To qualitatively examine if specific properties (i.e., the mass or displacement) of the designs affected suggestion selection in a way that may explain the findings, a follow-up analysis was also conducted by considering each trial separately and aggregating across participants. Each trial was then examined by condition and the difference in properties between its suggested and non-suggested design. Differences across the correct trials for Experiment 1 (shown in Figure 6a) implied that the group (and not just individuals) made some decisions with an implicit weighting of criteria. If the suggested design had a higher deformation but the tradeoff for lower mass was not subjectively enough, the suggestion was followed less often (though the mass tradeoff for those trials was considered “enough” by the optimization procedure).

Figure 6. The difference in stimuli properties along each objective (a positive value indicates a higher value for the suggested design): (a) for all conditions and (b) as a visualized interpolation for the “equivalent” condition only.

Yet preferential weighting of criteria was not necessarily applied in the equivalent condition. The preferential weighting of the deformation objective might lead participants to select the suggested design only if its deformation was lower in this condition (a negative difference). However, this was not the case. Even in trials where the deformation was higher for the suggested design, most of the participants selected the suggestion, as shown in Figure 6a. Looking only at the equivalent condition, Figure 6b demonstrates that lower suggestion selection in this condition was unlikely because of dependence on one objective over another. Instead, when the differences between both of the properties were close to zero, the decision was arbitrary and the suggested design was selected by closer to 50% of the participants. The percentage of participants selecting the suggested design was much higher when the designs were similar, but the tradeoff was not as easy to assess (larger differences in mass and displacement).

Methods

Interface

The interface was modified slightly from Experiment 1 to indicate that three objectives should be considered. Notably, in both Experiment 2a and 2b, the graph was updated to include a third axis indicating manufacturing time. In Experiment 2b only, an additional 3D model was included that was explained as “an example of a similar design that was considered to determine the suggestion.” This 3D model could be clicked to show and hide an additional performance graph for the example. Figure 7 shows the modified interface for Experiment 2b and the types of information available.

Figure 7. Interface for three objective decisions with an example-based explanation. The examples (highlighted on the left) are present only in Experiment 2b, while the additional objective (highlighted on the right) is present in both Experiment 2a and 2b.

Stimuli

The stimuli seen by each participant for Experiment 2 were selected to represent the design space available in the dataset, using the three objectives of mass, maximum displacement, and print time, while maintaining similar coverage to the stimuli in Experiment 1. The performance values across each objective for the stimuli in each condition are shown in Figure 8.

Figure 8. Performance values of stimuli in each condition across three objectives.

Results

Similar to Experiment 1, trials with a response time below 500 milliseconds were removed before analyzing the data.

The effect of model error on suggestion acceptance and performance

The trials were again analyzed to investigate how the simulated model’s suggestion of a better or worse-performing design solution impacted participants’ decision-making. Figure 9 shows the proportion of participants’ decisions that aligned with the provided suggestions (median = 0.62).

Figure 9. Probability of selecting the suggested design across all participants (median = 0.62 for both Experiment 2a and 2b) vs. the expected proportion (0.71) (W = 40.0, p = 0.00056, W = 35.0, p = 0.00013).

The proportion of decisions that were expected to align with the suggestions if the participant and the simulated model agreed was 71%, the actual proportion of correct suggestions. A non-parametric Wilcoxon signed-rank test was conducted as the data violated the assumption of normality, showing a significant difference between the hypothesized value and the observations (W = 40.0, p = 0.00056, W = 35.0, p = 0.00013). When the performance of the two alternatives differed, participants’ selection of the suggested design was again, lower than expected. Participants had a median overall accuracy of 0.76 in the no-explanation group and 0.75 in the example-based explanation group, respectively. In these experiments, there was no significant difference observed across participant accuracy in the incorrect (median = 0.67 and median = 0.83) and correct (median = 0.76 and median = 0.73) conditions based on Wilcoxon signed-rank tests (W = 173.0, p = 0.50, W = 77.0, p = 0.39), indicating that participants were just as likely to miss a correct suggestion as they were to follow an incorrect one.

The effect of suggestions in uncertain scenarios

The equivalent condition (design pairs sorted as optimal on the same iteration, but differing in values along each objective) was again analyzed to investigate how suggestions impacted participants’ decision-making when both options were close in multi-objective performance. Figure 10 shows the proportion of selections that aligned with the model’s suggestions for each participant (median = 0.45 and median = 0.44). Considering that arbitrarily the left or right was suggested for the equivalent condition, it was again expected that the participants’ design selections would align with the model’s suggestions 50% of the time. A Wilcoxon signed-rank test shows no significant difference in participants’ proportional selection of the suggested design compared to this expected value (W = 165.0, p = 0.56 and W = 160.0, p = 0.22). When both design options were close in performance, but involved a three-objective tradeoff, there was no evidence that participants chose the model’s suggestion differently than selection by chance. Correspondingly, there was no significant correlation between participants’ suggestion selection in the equivalent condition and their accuracy (r_p = 0.16, p = 0.41 and r_p = 0.12, p = 0.55).

Figure 10. The proportion of trials in the equivalent condition where participants chose what the model suggested (median = 0.45 and median = 0.44) vs. the expected proportion (0.50) (W = 165.0, p = 0.56 and W = 160.0, p = 0.22).

Trial-by-trial design properties and implications on decision-making

A heatmap surface for the trials in the three objective case (mass, displacement, and print time), aggregated across participants, is shown in Figure 11a. The comparison of mass and maximum displacement differs from the heatmap in Figure 6a implying that manufacturing time was, in fact, utilized by participants to make decisions in the second experiment. In this more complex case, however, no clear trends emerge regarding the impact of specific stimulus pairs’ performance values on suggestion selection. However, prioritization of the strength criterion can be seen: when the correctly suggested design has a lower mass and print time, but a higher maximum displacement, the suggested design (a good suggestion) was often ignored (“green” area in the heat map).

Figure 11. The difference in stimuli properties along each objective (a positive value indicates a higher value for the suggested design): (a) for all three objectives and (b) as pairwise comparisons of each objective.

GLMM for design selection

For the first model, the outcome variable was coded as follows: selection of the suggested design (1) or the non-suggested design (0). The main predictor was the condition (using dummy coding). Covariates were also included for the suggestion side (1 for left, 0 for right), which was balanced in each condition, and the trial order (numeric, starting at 1 for the first trial), since the different trial types were presented in a randomized order. For Experiment 2, an additional predictor was included to account for whether or not the participant was in the group exposed to the example-based explanation (0 for no explanation, 1 for example) and its two-way interaction with the condition (i.e., suggestion type). The considered random effects were variations by participant (to account for repeated measures) and by trial (to account for differences in the stimuli). Several models were compared using the Akaike Information Criterion (AIC) with varying random effects structures. The final model selected for each experiment contained both random effects due to trials and participants, but only varying intercepts, balancing model complexity with the limited amount of data available. These random effects account for the impact the specific participant or type of trial might have on variability in the dependent variable (i.e., selecting a specific design) compared to a group-level estimate. The results are shown in Table 3 where the reference levels of the categorical predictors are the correct condition and the right suggestion side.

Table 3. Suggestion selection models for Experiments 1 and 2

*p < 0.05, ^** p < 0.01, ^*** p < 0.001.

For Experiment 1, the model shows that, in the correct condition, the suggested design is selected more (accurately following a good suggestion) than the non-suggested design (mistakenly ignoring a good suggestion) (b = 1.59, p < 0.001). The suggested design is selected less in the incorrect condition (accurately avoiding a bad suggestion) than in the correct condition (b = –3.01, p < 0.001). There is no significant difference in selecting the suggested option between the equivalent and correct conditions (b = 0.23, p = 0.643), indicating very similar slopes (i.e., no sign of participants treating the equivalent and correct conditions differently). Figure 12a shows the predicted probabilities that result from the GLMM fit data from Experiment 1.

Figure 12. Group-level predicted probabilities from GLMMs compared to real participant selection data.

The interpretation of the GLMM for Experiment 2 remains largely the same, with the additional reference level being the no-example-explanation group. However, the suggested design is now selected less often in the equivalent condition compared to the correct condition (b = –1.15, p < 0.001). Figure 12b shows the predicted probabilities that result from the GLMM fit to data from Experiment 2. The results also indicate that the example-based explanation is not a statistically significant predictor of suggestion selection, accounting for interactions with the condition (i.e., suggestion correctness). There is some evidence in Experiment 2 of a tendency to select the suggested design more often on the left side compared to the right (b = 0.81, p = 0.002), but trial order is not a significant predictor in either experiment. In both experiments, consideration of random effects (clustering structure induced by repeated measurements within the subject and repeated trial types) reveals that variability due to the trial type is greater than variability due to the participant (tau ₀₀, the between-subject or -item variance). The Intraclass Correlation Coefficient (ICC) shows that approximately 32% and 17% of the variance in the model is explained by the random effects for Experiments 1 and 2, respectively.

GLMM for accuracy

For the second GLMM, the outcome variable was coded as follows: selection of the better design (1) or the worse design (0). Again, the covariates for the suggestion side (1 for left, 0 for right) and the trial order (numeric, starting at 1 for the first trial) were included. This model analyzes the accuracy across the correct and incorrect conditions at a trial level, rather than the overall accuracy aggregated for participants and conditions. The results of the GLMMs are shown in Table 4, with the predicted probabilities and real participant-level data shown in Figure 13.

Table 4. Accuracy models for Experiments 1 and 2

*p < 0.05, ^**p < 0.01, ^***p < 0.001.

Figure 13. Group-level predicted probabilities from GLMMs compared to real participant accuracy data.

Despite a statistically significant difference between accuracy across the correct and incorrect conditions at the participant level in Experiment 1, the condition is not a statistically significant predictor of accuracy at a trial prediction level. For Experiment 2, neither the condition nor the presence of an explanation is a statistically significant predictor of accuracy, shown as predicted probabilities with interactions and real participant-level data in Figure 13b. There is no evidence of trial order or suggestion side significantly predicting better design selection in either experiment.

Perception of model accuracy

The effect of several self-reported factors related to knowledge and perceptions was inspected to determine if these factors were related to participants’ performance and decision-making. There was no evidence of a correlation between accuracy and participants’ self-reported knowledge (1–7 Likert scale value) in the topics of structural mechanics (r_s = 0.18, p = 0.32, r_s = 0.12, p = 0.53) and multi-objective optimization (r_s = 0.26, p = 0.88, r_s = 0.15, p = 0.27,) in Experiment 1 or 2. Figure 14 shows the distribution of self-reported perceived model accuracy, with a median of 70% in Experiment 1, 70% in Experiment 2a, and 60% in Experiment 2b. Given that the accuracy of the suggestions was set to be 71% (excluding trials in the equivalent condition), participants demonstrated a clear ability to assess how often they were receiving correct suggestions. (This perception may have developed at the practice stage.) The range of perceived accuracy responses was slightly greater for Experiment 2b than for Experiment 2a or 1. Participants in Experiment 2, as a whole, followed suggestions less than in Experiment 1, driven primarily by the difference in the equivalent condition. Yet, their overall perception of the model’s accuracy remained relatively unaffected, with only a slight decrease in Experiment 2b, where the example-based explanation was provided.

Figure 14. Distribution of participants’ answers to the question “What percentage of the time do you think the model suggested the better design?” (median = 70%). The answer choices ranged from 0 – 100% in increments of 10.

Self-reported decision-making strategies

Participants’ design selections revealed the outcomes of their decision-making, while survey questions provided more insight into how suggestions were used and why a person may have performed poorly/well. Overall decision-making strategies were described in answers to the open-ended questions (“Please describe your decision-making process and strategy in detail.” and “Did the examples help explain the model’s suggestions to you? Based on your answer above, why or why not?”) and are briefly outlined below. Table 5 shows common strategies that appeared across experiments.

Table 5. Strategies and reasoning from open-ended survey questions

Experiment 1: 2 Obj. One of the participants [P15] who achieved the highest accuracy had the following strategy, using their own judgment by synthesizing the provided information, but also recognizing when they would benefit from assistance from the suggestion:

Experiment 2a: 3 Obj. One of the participants who achieved the highest accuracy (90%) in this experiment had the following strategy, using the third objective to help make a final choice:

Experiment 2b: 3 Obj. + example. In this experiment, when asked whether the examples helped explain the model’s suggestions, responses were divided (15 yes and 14 no). When asked about why or why not the examples helped, one participant [P5] identified how the simulated model worked, stating “the model did I believe [take] all factors in equally, instead of having some ranking or prioritizing (when it would fail).” However, this participant’s accuracy score was lower, likely because they used their knowledge to prioritize an objective instead of agreeing with how the model worked. Another participant [P6] was unable to understand how the simulated model worked using the example-based explanation, stating “…there was little correlation between the examples and the part, especially in their graphs.” A participant’s response to being asked about the example-based explanation demonstrates the challenge of finding the right way to explain the model’s suggestion: