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. Author manuscript; available in PMC: 2021 Jul 1.
Published in final edited form as: Psychol Res. 2019 Feb 12;84(5):1235–1248. doi: 10.1007/s00426-019-01152-y

The relation between state and trait risk taking and problem-solving

Carola Salvi 1,2, Edward Bowden 3
PMCID: PMC6690799  NIHMSID: NIHMS1521456  PMID: 30756178

Abstract

People can solve problems in two main styles: through a methodical analysis, or by a sudden insight (also known as ‘Aha!’ or ‘Eureka!’ experience). Analytical solutions are achieved primarily with conscious deliberation in a trial-and-error fashion. ‘Aha!’ moments, instead, happen suddenly, often without conscious deliberation and are considered a critical facet of creative cognition. Previous research has indicated an association between creativity and risk taking (a personality trait); however, few studies have investigated how a short-term situational state of risk modulates these two different problem-solving styles. In this research, we looked at how both state and trait risks taking is related to different problem-solving styles. To measure risk as a personality trait, we administered the Balloon Analog Risk Task. To investigate risk as a state, we created a scenario, where people had to bet on their problem-solving performance at the beginning of each trial, and we compared the performance of this group with a control group that did not have to bet. The results show no association between risk as a trait and problem-solving style; however, the risk state scenario did produce a shift in dominant problem-solving style with participants in the risk scenario group solving more problems via analysis. We also found that two factors are related to problem-solving accuracy: the amount bet (i.e., when people place higher bets, they solve more problems), and success on the previous trial, especially if the solution was achieved via analysis. Furthermore, the data reveal that when under risk, females are better problem solvers than males.

Introduction

There is an element of risk in any act of problem-solving. When we have a problem to solve, we are faced with a decision: should we try to solve the problem, with the possibilities of success or failure, or should we accept things the way they are? Making the decision to attempt to solve a problem requires confidence in our problem-solving skills and a willingness to take a risk (whether great or small). In essence, when we decide between accepting or declining a problem-solving challenge, we are betting on our ability to solve the problem and possibly gaining a reward or to offer something new and valuable. Either decision inherently carries some risk. There is the risk of a negative outcome as the result of accepting or declining the challenge, and there is the risk of declining the challenge and missing the opportunity to achieve a positive outcome.

When people are trying to solve a problem, they may generate a variety of ideas. Some ideas can arise by a largely trial-and-error or systematic analytical process, while others can arise suddenly in a moment of insight. Insight represents one, often critical, component of the complex behavior of creativity.

In this paper, we will refer to two different problem-solving styles: analytical solutions, achieved primarily with conscious deliberation in a trial-and- error fashion, and insightful solutions, or ‘Aha!’ moments, which happen suddenly, often without conscious deliberation. This dichotomy is reflected in behavioral, social, and neuroscientific markers. For example, solutions achieved by insight are on the average more accurate than those achieved through analysis; insight includes key subjective components such as pleasure, suddenness, and certainty; and insights are associated with liberal political orientation, and present distinct patterns of neural activity and eye blinks (Salvi, Cristofori, Grafman, & Beeman, 2016; Danek & Wiley, 2017; Danek & Salvi, 2018; Kounios & Beeman, 2014; Salvi, Bricolo, Franconeri, Kounios, & Beeman, 2015).

Cummings and Mize (1968) suggest that the willingness to take risks, and a high tolerance for ambiguity, increases the probability of generating and implementing creative ideas. In particular, the abilities to tolerate risk and ambiguity have been found to be components of creative entrepreneurs across different cultures (McGrath, MacMillan, & Scheinberg, 1992). Using two self-report measures, the Creative Personality Scale (CPS) and the Cognitive Risk Tolerance Scale (CRT), Charyton, Snelbecker, Rahman, and Elliott (2013) found that creative traits are associated with greater risk tolerance. Tyagi, Hanoch, Hall, Runco, and Denham (2017) found a correlation between creativity (measured using the Creative Personality Scale, the Creative Achievement Questionnaire, and the Runco Ideational Behavioral Scale) and self-reported risk taking in social, recreational, and financial fields. Recent studies highlighted that how creativity is associated with liberal political orientation, and suggests that this effect might be predicted by higher levels of risk propensity among creative people (Salvi, et al., 2016; Tyagi, Hanoch, Choma, Denham, 2018). Other studies, with different populations of workers, showed positive correlations between risk propensity and creativity (Dewett, 2006; Eisenman, 1987; El-Murad & West, 2003).

All of these results fit within the portrait of the ‘creative personality type.’ Creative people are often very original, oriented toward novelty seeking, curious and open to new experiences; all characteristics that are promoted by greater risk propensity. A recent study from Shen, Hommel, Yuan, and Zhang (2018) shows that the correlation between risk propensity and creativity differs according to the kind of creative tasks involved. Specifically, the authors found a negative correlation between self-rated risk (measured using the risk taking preference index; a tool for measuring individuals’ preferred level of risk taking; Hsee & Weber, 1997, 1999) and convergent thinking (measured using the RAT, Mednick, 1968), and a positive correlation between self-rated risk and divergent thinking (the Alternate Uses Task, Guilford, 1967).

Although these studies suggest that risk taking, as a trait, is associated with creativity, this relation may be complicated by state variables. Shen et al. (2018) point out that the true relation between risk taking remains unclear. They call for further investigation into the specific nature of risk taking in creativity, since “risk (-taking) can be situational (e.g., willingness to take risks; see Dewett, 2006), or cross-situational in nature, or can operate as (intrinsic) motivation or as propensity (e.g., Simmons & Ren, 2009).”

Regardless of whether a person has a more or less risk-oriented personality, everyone has to occasionally solve problems under risk. We speculate that being under risk induces a state of high arousal and need for focus (e.g., March & Shapira, 1992). For example, in physically threatening situations, people need to pay more attention to elements of the visual scene to find a way to escape. Other situ-ations, such as being under a deadline, may expose people to the risk of missing out on a promotion or losing their job. Interestingly, whether we are chased by a lion or by a work deadline, in most cases being under risk keeps us on task and increases our focus of attention. Results of our previous studies led us to hypothesize that state factors, such as risk and time pressure (the feeling that one is running out of time), may change the way people solve problems. Situations with higher levels of perceived risk would promote analytical processing, a problem-solving style that is associated with greater external attention allocation (Salvi, Bricolo, Kounios, Bowden, & Beeman, 2016; Salvi & Bowden, 2016; Wegbreit, Suzuki, Grabowecky, Kounios, & Beeman, 2012). Specifically, Salvi et al. (2016) showed that when people are under time pressure they are more likely to adopt analytical processing, guess more often, and make more errors.

While situations with higher levels of perceived risk might promote analytical processing, the relation between situational factors and the tendency to use a particular problem-solving style might be more complex and reciprocal. To illustrate, greater perceived risk might promote a more analytical problem-solving style; however, problem solutions that are reported as arising from insight processes are more likely to be correct than problem solutions that are reported as arising from analytic processes (Salvi, et al., 2016). If people are aware (at some level) of the relation between how a solution is produced and the probability of it being correct, we might expect people to be more willing to take risks following solutions resulting from a sudden insight. However, the confidence that could result from the greater accuracy of insight solutions would be for the accuracy of the particular solution, not for the ability to solve a similar problem in the future. In contrast, because solutions produced with analysis are less likely to be correct, people could be less confident of these solutions, therefore, less willing to take risks following solutions resulting from analytic processes. Yet, the steps involved in solving by analysis are more available to conscious scrutiny, so solvers may have greater confidence that they can repeat the analytic process that led to correct solutions, thus making them more willing to take risks following solutions resulting from analytic processes. In other words, situational or state risk might promote a certain problem-solving style (analytic), but the style actually used on any particular problem might affect the willingness to risk on future problems.

Research has shown that risk aversion increases when people are in a positive mood, and decreases when people are in a negative mood (see, e.g., Arkes, Herren, & Isen, 1988; Isen, Nygren, & Ashby, 1988; Isen & Patrick, 1983; Nygren, Isen, Taylor, & Dulin, 1996). Positive mood has been demonstrated to enhance cognitive flexibility in various settings, and specifically in creative problem-solving tasks (Isen, Johnson, Mertz, & Robinson, 1985; Isen & Daubman, 1984; Subramaniam, Kounios, Parrish, & Jung-Beeman, 2009). Being in a positive mood favors a global scope of attention, that is, a broader focus of attention rather than an internal or external focus of attention (Bolte, Goschke, & Kuhl, 2003; Gasper & Clore, 2002), facilitates access to distant or weakly activated associations (Federmeier, Kirson, Moreno, & Kutas, 2001; Friedman, Fishbach, Förster, & Werth, 2003; Isen, et al., 1985) which are necessary for insight problem-solving, and improves problem-solving on the Remote Associates Test—RAT (Rowe, Hirsh, & Anderson, 2007; Isen, Daubman, and Nowicki, 1987; Mednick, 1968). Positive mood also facilitates switching between strategies (Dreisbach & Goschke, 2004) or between global and local attentional states (Baumann & Kuhl, 2002) and selection of different perspectives (Ashby, Isen, & Turken, 1999). In contrast, negative mood is associated with deficits in cognitive control (Bishop, Duncan, Brett, & Lawrence, 2004) and has been shown to induce a narrow scope of attention (Easterbrook, 1959) which is more likely to lead to a more analytic problem-solving processing (Wegbreit, et al., 2012).

Based on this earlier research, and considering that the pressure created from being under situational risk narrows attention, impedes cognitive flexibility, problem restructuring, and insight solving, we hypothesized that the state of being under risk would promote an analytical problem-solving style.

To investigate the effect of risk taking and reward on problem-solving, we created a scenario, where we asked people to bet real money (from 1 to 5 cents) on their ability to solve the next problem. After providing a solution (whether it was accurate or inaccurate), participants were asked to report how they solved the problem (with insight or via analysis), and how confident they were in the solution given. If the solution given was correct, the amount of their bet was added to their total, and if the solution was incorrect, the amount of their bet was subtracted from their total. All participants started with an initial amount of $5 (USD). We compared the results of this risk group to a second group to which the risk scenario was not applied (we only asked this group to solve problems without making any bets).

In addition, for each participant in the risk condition, we collected measures of trait risk [using the Balloon Analog Risk Task (BART); Lejuez, et al., 2002]; mood [using the Positive and Negative Affect Scales (PANAS); Watson, (PANAS); Watson, Clark, & Tellegen, 1988]; impulsivity [using the Barratt Impulsiveness Scale-11 (BIS-11); Patton, Stanford, & Barratt, 1995]; and anxiety [using the State-Trait Anxiety Inventory (STAI); Spielberger & Lushere, 1971; Spielberger, 1987].

Based on research by Shen et al. (2018) showing a negative correlation between self-rated risk and convergent thinking (measured using the RAT, Mednick, 1968), we predict a negative correlation between trait risk and insight on the CRA problems.

Method

Materials

Balloon Analog Risk Task (BART; Lejuez et al., 2002)

The BART was chosen as the measure of the trait of risk taking, because it involves a direct measure of the persons’ behavior rather than a self-rating of their tendency to take risks.

In the BART, participants are asked to inflate a simulated balloon presented on a computer screen. Their task is to ‘pump up’ the balloon by pressing a ‘Pump’ button. Each pump inflates the balloon a small amount and adds a constant amount of money (1¢ in our experiment) to a temporary bank account (displayed at the side of the screen). However, pumping too many times will cause the balloon to pop, the balloon trial to immediately end, and participants to lose the money they had accumulated on that current trial. The BART has proven to be a powerful and useful method in studying and identifying real-world risk takers (e.g., smoking, illegal drug use, and having unprotected sex) and is currently the most widely used sequential risk taking task in a broad range of populations (Aklin, Lejuez, Zvolensky, Kahler, & Gwadz, 2005 ; Lejuez, Simmons, Aklin, Daughters, & Dvir, 2004). In addition, recent evidence showed its link to neurobehavioral correlates of risk behavior (e.g., Fecteau, et al., 2007; Fein & Chang, 2008).

Positive and Negative Affect Scales (PANAS; Watson, et al., 1988)

The PANAS questionnaire consists of a 20-item self-report mood scale and measures of general positive and negative affect (‘How do you feel generally?’). The rating comprises ten positive and ten negative adjectives on a Likert scale from 5 (very or extremely) to 1 (very little or not at all).

Barratt Impulsiveness Scale‑11 (BIS‑11; Patton, et al., 1995)

The questionnaire consists of 30 items on a 4-point Likert scale from rarely/never = 1 to almost always/always = 4. The items are structured into six factors and three subscales: (1) attention impulsivity and cognitive instability (attentional domain); (2) motor impulsivity and perseverance (motor domain); and (3) self-control and cognitive complexity (non-planning domain) (Patton, et al., 1995).

State–Trait Anxiety Inventory (STAI; Spielberger & Lushere, 1971; Spielberger, 1987)

The STAI is a 20-item scale that measures the person’s current state of anxiety, asking how respondents feel ‘right now,’ using items that measure subjective feelings of apprehension, tension, nervousness, and worry.

Compound remote associate problems (CRA; Bowden & Jung‑Beeman, 2003)

In each of these problems, participants are presented with three stimulus words (e.g., crab, pine, and sauce) simultaneously and they have to generate an additional word (e.g., apple) that forms a compound word or a familiar two-word phrase with each of the three problem words (i.e., crab apple, pineapple, and apple sauce). Studies have shown that, according to solvers’ self-reports, these problems can be solved with insight or analytically. The effectiveness of self-reports in differentiating between insight and analytic solving has been established in numerous behavioral and neuroimaging studies (Cristofori, Salvi, Beeman, & Grafman, 2018; Jung-Beeman et al., 2004; Kounios, et al., 2006; Salvi, et al., 2015; Laukkonen & Tangen, 2018). Self-reports of problem-solving style (insight or analysis) are outcome reports which have been shown to be related to differences in behaviors and in neural activity. Thus, these self-reports are used as a marker that the person has perceived a difference and that marker is used to determine what factors lead to the perceived difference. Introspection of this type has been used effectively in a variety of areas of research, e.g., self-reports, in the form of verbal protocols, have been used in studies of analytic problem-solving (Ericsson & Simon, 1987 ; Newell & Simon, 1972) and in other areas of cognition, such as memory (Holmes, Waters, & Rajaram, 1998; Tulving, 1985). If insight involves an abrupt change from a state of not knowing how to solve the problem to a state of knowing how to solve the problem (or, in some cases, knowing the solution), with no conscious awareness of what caused the change, the person experiencing the insight can still be expected to be able to report that the change occurred (Grunewald & Bowden, 2018).

CRAs, and the similar RAT (Mednick, 1968), have frequently been used to study problem-solving, cognitive flexibility, and creative thinking (e.g., Ansburg & Dominowski, 2000 ; Bowden & Beeman, 1998 ; Dominowski & Dallob, 1995; Schooler & Melcher, 1995; Salvi, Costantini, Bricolo, Perugini & Beeman, 2016). Specifically, remote associates solving rate are significantly correlated with the self-reported creative achievements measure with the Creative Achievement Questionnaire (e.g., Salvi, Costantini, Pace, & Palmiero, 2018).

Risk and reward version of CRAs

For this study, we created a specific procedure, where participants could bet and win or lose money when solving problems. Specifically, before each of the CRAs were presented on the screen, participants are asked to bet from 1 to 5 cents on whether they believed they would solve the following problem. If they solved the problem correctly they would win the amount of money that they bet, if they failed to solve the problem correctly, they would lose the amount of money that they bet. After providing a possible solution to a problem, participants were also asked to rate, from 1 to 5, how confident they were in correctness of the solution provided (see Fig. 1). 1 cent is accepted as a baseline reward in several reward paradigms (e.g., Cristofori, et al., 2018; Pessiglione, et al., 2007). No feedback on the accuracy of the solution was given until the end of the experiment when participants were paid. Participants also indicated, via self-report, whether they solved the problem by analysis or by insight. The specific instructions for describing solutions via insight and via analysis were: “Insight means that the answer suddenly (i.e., unexpectedly) came to your mind, while you were trying to solve the problem, even though you are unable to articulate how you achieved the solution. This kind of solution is often associated with surprise exclamations such as ‘Aha!’. Analysis means that you figured out the answer after you deliberately and consciously tested out different words until you found the correct one. In this case, you are usually able to report the steps that you used to reach the solution.”

Fig. 1.

Fig. 1

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Procedure used for the experimental (a) and control groups (b). In both cases, participants were given 15 s to solve each problem. If they found a solution, participants had to press the spacebar, tell the solution word to the experimenter, and report how they had solved the problem, either via insight or via analysis. In the experimental condition, participants were asked to make a bet on solving the following problem and how confident they were on the solution found

Participants

A total of 78 Northwestern University (IL) students, all right-handed and native English speakers, participated in the study. The experiments were undertaken with the understanding and consent of each subject and were approved by the Institutional Review Board. Participants were divided into two groups: experimental group (n = 40, 29 females and 11 males, mean age 22.4 ± 2.9 years) and control group (n = 38, 24 females and 14 males, mean age 20.12 ± 3.04 years). Participants were compensated with partial course credit (control group) or money (experimental group). Each experimental session lasted approximately 1 h.

Design and procedure

Participants were asked to solve 120 CRA problems taken from Bowden and Jung-Beeman (2003). The problem words were presented in black text on a white background and were displayed in 28-point Times New Roman. The three CRA words were centered horizontally, with one word above, one at, and one below the vertical center of the monitor.

Participants were assigned to one of the two groups: the experimental group which placed bets on each problem or the control group which attempted to solve the same problems, but did not place bets.

Experimental group

Participants completed the BIS-11, PANAS, and STAI questionnaires, after which the BART and the risk and reward version of CRAs were administered.

BART procedure

The experimental block of 20 trials was administered following instructions. For each trial, participants saw a small simulated balloon accompanied by a balloon pump button, and a reset button labeled ‘Collect $ $ $’ on a PC screen. Each click on the pump button inflated the balloon 1° [about 0.125 in. (0.3 cm) in all directions]. With each pump, 1 cent was accrued in a temporary bank (the amount of money in this bank was revealed to the participant only at the end of the BART task). A ‘pop’ sound effect was generated from the computer when a balloon was pumped past its individual explosion point and all money in the temporary bank was lost. The next uninflated balloon appeared immediately on the screen. Participants could stop pumping the balloon and click the ‘Collect $ $ $’ button at any point during each trial. When they clicked this button, the accumulated money was transferred from the temporary bank to the permanent bank and added to the total money made by each participant (for more details, see Lejuez, et al., 2002). Note that participants did actually receive the final sum of money stored in the permanent bank. The balloons were set to explode on a variable ratio (average of 64 responses) schedule.1

Risk and reward version of CRAs procedure

Prior to the experimental trials, participants were given an amount of $5 and were instructed on how to distinguish insight from analytic solving. After three practice trials, problems were presented in three randomized blocks of 40 trials each that were equated for difficulty. Each trial began with a central fixation cross lasting 1 s, followed by a response prompt screen (see Fig. 1a). Once participants were ready, they had to indicate how much they would bet (from 1 to 5 cents) on solving the following problem. They had to press on the keyboard the number corresponding to their bet, and then, the three problem words were presented simultaneously on the screen for a maximum of 15 s. Participants had to press the spacebar if they thought that they had found the solution to the problem, and then say it aloud. Following the verbal production of a solution, words were cleared and participants had to report, via button press, whether they had solved the problem via insight or analysis, and how confident (from 1 = not confident to 5 = very confident) they were that the solution provided was correct. No feedback was given to participants regarding whether the solution they had provided was correct or incorrect. If they did not find any solution within the time limit the problem disappeared, the reports of solution type and confidence, where skipped for that problem, and they were asked to indicate how much they would bet (from 1 to 5 cents) on solving the following problem. Participants were informed that if they solved the problem correctly, they would be compensated according to the amount bet, whereas if they made an error, they would be penalized by losing the amount that they bet. There was no penalty on those trials when they ran out of time without offering a solution. At the end of the experiment, participants were compensated with the total amount of money gained.

Control group

Participants of the control group were asked to solve 120 CRAs. This group was created as a baseline to compare the data of the experimental group’s risk and reward version of CRAs. Prior to the experimental trials, participants were given three practice CRA problems and instructed how to distinguish insight from analytic solving. Problems were presented in three randomized blocks of 40 trials each that were equated for difficulty. Each trial began with a central fixation cross lasting 1 s, followed by a response prompt screen. Once participants were ready, they had to press the spacebar to initiate the fixation cross appearing for another second, and then, the three problem words were presented simultaneously on the screen. Following the verbal production of a solution, or at the time limit (15 s), the problem words were cleared and participants had to report, via button press, whether they had solved the problem via insight or analysis. If they did not find any solution within the time limit the problem disappeared and the reports of solution type were skipped. No feedback was given to participants regarding whether the solution they had provided was correct or incorrect.

Results

Risk as a state2

We investigated how (and if), the risk scenario we created influenced problem-solving performance and/or problem-solving style. We compared the percentage of problems solved between the risk group (i.e., risk and reward version in Fig. 1a, where participants had to bet on the problem they were going to solve) and the control group (i.e., where participants did not have to bet before problem-solving). Descriptive results are reported in Table 1.

Table 1.

Frequencies of problems solved correctly, incorrectly, and problem unsolved across the two groups

Frequencies
Correct (%) Incorrect (%) Unsolved (%) Correct (%) Incorrect (%) Unsolved (%)
Control group 40.7 7.2 52.1 Risk group 41.0 9.5 49.5
 Females 24.3 4.5 34.0 Females 31.8 6.1 36.6
 Males 16.4 2.7 18.1 Males  9.2 3.4 12.9
Insight 24.6 2.0 – Insight 20.1 3.2 –
 Females 15.5 1.6 – Females 15.2 1.8 –
 Males  9.1 0.5 – Males  4.9 1.4 –
Analysis 16.1 5.0 – Analysis 20.9 6.3 –
 Females  8.8 2.9 – Females 16.6 4.3 –
 Males  7.2 2.1 – Males  4.3 2.0 –
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The percent of solutions (correct or incorrect) via insight and via analysis are also reported. Note that frequencies for the control group reflect a typical pattern for CRAs, where the percent of problems solved with insight is higher than the percentage solved with analysis (see, e.g., Salvi, et al., 2015; Salvi, Bricolo, et al., 2016; Salvi, Cristofori, et al., 2016; Subramaniam, et al., 2009)

No differences were found in the total percent of problems solved (correctly and incorrectly) and unsolved between the experimental group and control group. A 2 (control group vs. risk group) × 2 (insight vs. analysis) ANOVA showed a significant interaction between being asked to bet on solving problems and the problem-solving style used, indicating a decrease in solutions by insight and an increase in solutions by analysis when betting was involved [F(1, 74) = 5.79; p < 0.05; η2 = 0.069], see Fig. 2.

Fig. 2.

Fig. 2

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Averages percent of problems solved via insight and via analysis in the control group and in the risk group

A 2 (males vs. females) × 2 (control group vs. risk group) × 2 (insight vs. analysis) analysis of problem-solving style showed a significant 2 (males vs. females) × 2 (control group vs. risk group) interaction [F(3, 72) = 4.14; p < 0.05; η2 = 0.054],3 indicating that females solved more problems than males in the risk group, whereas females in the control group solved fewer problems than males. No significant difference was found in male participants across the two groups.4 No gender differences were found within either the experimental or control group. No differences were found for problems solved incorrectly or unsolved (Fig. 3).

Fig. 3.

Fig. 3

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Averages percent of problems solved by females and males in the control group and in the risk group

Betting

Within the risk group, we conducted an analysis on the amount bet and overall solution accuracy. We compared the average amount bet (possible range 1¢ to 5¢) prior to problems that were solved correctly, ‘solved’ incorrectly, and unsolved. The mean bet was 3.09¢ (SD 1.19) for problems solved correctly, 2.82¢ (SD 1.35) for those ‘solved’ incorrectly, and 2.88¢ (SD 1.28) for unsolved problems. The ANOVA shows that participants placed higher bets on problems solved correctly than on problems that were incorrectly solved or that were unsolved [F(2, 36) = 13.77; p < 0.001; η2 = 0.277] (see Table 2). Post hoc comparison using Bonferroni correction is reported in Table 2. No gender differences were found. No significant differences were found between the amounts bet prior to problems that were solved with insight or analysis; therefore, it seems that the amount bet on a trial did not influence the problem-solving style used on that trial. These results might suggest that higher self-determined monetary reward motivates problem-solving ability and that this state of greater motivation facilitates participants’ likelihood of solving the next problem correctly even before they have seen the actual problem. However, we believe that a better explanation is that people ‘sense’ that they are in a state that is more conducive to solving and then bet accordingly (cf. Kounios, et al., 2006).

Table 2.

Post hoc comparison using Bonferroni correction of bet averages within the risk group of problems solved correctly, incorrectly, and unsolved

Post hoc comparisons
Mean difference SE t pbonf
Correct Incorrect   0.303 0.059   5.136 < 0.001
Unsolved   0.206 0.059   3.501   0.002
Incorrect Unsolved − 0.096 0.059 − 1.635   0.319
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Confidence

At the end of each trial, whether the problem was solved correctly or incorrectly, participants were asked to report their confidence level (see Fig. 1a). Results showed that problems solved correctly were rated with higher confidence (M 4.1; SD 0.55) than those ‘solved’ incorrectly ( M 2.1; SD 0.67); t(37) = 21.08; p < 0.001; d = 3.4; CI [1.8, 2.1]. T tests comparing the confidence ratings for problems solved correctly via insight and via analysis revealed a significantly higher level of confidence for problems solved via insight (M 4.3; SD 0.61) than for problems solved via analysis (M 4; SD 0.66); t(37) = − 3.07; p < .005; d = − 0.49; CI [− 0.502, − 0.103]. However, for incorrectly ‘solved’ problems, no difference was found in confidence rating between insight (M 2.3; SD 1.1), and analysis (M 2.2; SD 0.82), t(37) = −0.196; p > 0.05; d = −0.037; CI [− 0.572, − 0.472]. These results suggest that overall confidence is a good marker of solution accuracy, and correct solutions via insight produce even higher levels of confidence than correct solutions via analysis. Therefore, confidence is a good predictor of accuracy regardless of solution style, and when the feeling of insight accompanies an incorrect solution, participants are not falsely overconfident due to that feeling of insight. This suggests that higher confidence is not solely a consequence of the subjective insight experience, but is related to the accuracy of the solution. No gender differences were found for this variable.

Risk as a trait

We investigated the relation between risk as a personality trait and problem-solving performance and style. The primary-dependent measures for this task were the number of balloon pumps and number of balloon explosions. For balloon pumps, adjusted values were used for all analyses. These values were calculated based on the average number of balloon pumps on unexploded balloons. As described in Hunt (2005, p. 419) these values are preferable, “[…] because including balloon pumps from all trials (including those in which balloons exploded) would have resulted in the inclusion of trials in which the participants were forced to stop pumping because of the explosion. Because the adjusted value consisted only of non-explosion trials, it is considered an index of a more adaptive (non-punitive) form of risk-taking behavior. In contrast, evaluating the frequency of balloon explosions provides an index of a more maladaptive form of risk taking whereby risk exceeds an acceptable level and ultimately is punished (via explosion and loss of money).” The number of pumps on unexploded balloons in the BART did not correlate with overall solving percentage [r = 0.095, p > 0.05], with percentage of solutions by analysis [r = − 0.014, p > 0.05], or with solutions by insight [r = 0.13, p > 0.05]. This provides no support for the idea that the trait of willingness to risk can be used to predict a person’s tendency to experience one problem-solving style (analysis or insight) over the other.

There was also no correlation between the number of balloon explosions in the BART and the overall amount bet on the CRAs [r = − 0.17, p > 0.05] or with the amount bet on solutions by insight or analysis [r = − 0.16, p > 0.05, and r = − 0.15, p > 0.05, respectively], indicating that risk taking behavior in the BART did not predict risk taking behavior in the CRA solving task.5 No gender differences were found for this variable. Several measures were extracted from the BART task (e.g., n of balloons exploded; amount of money gained etc.) none of these was found significantly correlated to the problem-solving task.

Effects of problem‑solving on risk

Furthermore, consistent with a recent study which showed the different effects of implicit/explicit expected reward on problem-solving, and specifically solutions via insight (Cristofori, et al., 2018), we expected situational factors related to risk and reward (betting) to influences solving style. Therefore, we analyzed whether solutions on the immediately previous trial influenced the amount bet on the following trial. A linear regression analysis showed that having solved a problem correctly increased the amount bet on the following trial ( β = 4.17, SE 1.3, p < 0.005; see Fig. 4). This result is led by solutions via analysis (β = 4.28, SE 1.5, p < 0.01) but not via insight (β = 0.94, SE 1.83, p > 0.05). This supports the proposal that solutions by analysis will lead to a greater willingness to risk, because the steps involved in these solutions are more available to conscious scrutiny than are solutions by insight, thus giving solvers higher feelings of efficacy for solving future problems.

Fig. 4.

Fig. 4

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Scatterplot indicating the relation between the percent of problem solved and the bets on the following trial per participant (each dot represents a participant and the graph indicates the intersection between the amount bet and percent of problems solved on the following trial). Data on the following trial include problems solved correctly, incorrectly, and unsolved

Money earned

As a measure of concrete success and problem-solving style, we ran a correlation between the amount of money earned and the percent of problems solved correctly, incorrectly, unsolved, problems solved correctly via analysis and via insight, amount bet on problems solved correctly, incorrectly, unsolved. As reported in Table 3, the analysis was significant for problems solved correctly, specifically via analysis but not via insight, for problems unsolved, and for bets on problems solved correctly, incorrectly, and unsolved.

Table 3.

Correlations between the amount of money earned and percent of problems solved correctly, incorrectly, unsolved, problems solved correctly via analysis and via insight, amount bet on problems solved correctly, incorrectly, unsolved

Solved correctly Solved incorrectly Unsolved Solved correctly via analysis Solved correctly via insight Bet on corrects Bet on incorrect Bet on time outs
Money
 earned		 Pearson’s r    0.790*** − 0.154 − 0.577***    0.653*** 0.209    0.702***    0.614***    0.667***
p value < 0.001    0.357 < 0.001 < 0.001 0.209 < 0.001 < 0.001 < 0.001
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The bolded values indicate significant results with statistical thresholds of

*

p < 0.05

**

p < 0.01

***

p < 0.001 respectively

Questionnaires

Overall, the risk trait, measured by the BART, was positively correlated with negative affect. Negative affect (PANAS-NA) was positively correlated with impulsiveness (BIS-11) and anxiety (STAI). Anxiety (STAI) was negatively correlated with positive affect (PANAS-PA) and positively correlated with impulsiveness (BIS-11), see results of the linear regression model below.

Descriptive statistics and correlations for the BART, PANAS-NA, PANAS-PA, BIS-11, and STAI are reported in Table 4.

Table 4.

Descriptive statistics for BART (measured in number of pumps on balloons that did not explode)

M SD BART PANAS-PA PANAS-NA BIS-11 STAI
BART 30.78 11.38 Pearson’s r – 0.136 0.328* 0.033 0.237
p value – 0.403 0.039 0.843 0.146
PANAS-PA 27.65 7.22 Pearson’s r – − 0.176 0.116 − 0.380*
p value – 0.278 0.480 0.017
PANAS-NA 20.23 4.3 Pearson’s r – 0.381* 0.600*
p value – 0.017 < 0.001
BIS-11 44.72 8.02 Pearson’s r – 0.401*
p value – 0.013
STAI 35.74 7.73 Pearson’s r –
p value –
Open in a new tab

The bolded values indicate significant results with statistical thresholds of

*

p < 0.05

**

p < 0.01

***

p < 0.001 respectively

Average (M); Standard deviation (SD) and correlation between BART, PANAS Positive and Negative Affect Schedule; BIS-11and STAI

An analysis of gender revealed a significantly higher positive affect score for males (M 31.8; SD 7.62) compared to females (M 25.4; SD 6.1) [F(1, 37) = 6.95; p < 0.05; η2 = 0.162]; and higher anxiety levels (STAI) for females (M 37.7; SD 6.9) compared to males (M 29.9; SD 7.6) [F(1, 37) = 8.3; p < 0.01; η2 = 0.192].

Affect and trait risk taking

We used a linear regression model to test the relation between positive/negative affect (measured with the PANAS) and risk taking (measured using the BART). Overall, the analysis showed that negative affect is positively related to risk taking (β = 0.86, SE 0.42, p < 0.05).

Problem‑solving style and affect

Consistent with prior studies (Subramaniam et al., 2009 ), our results showed that positive affect correlates with a tendency for solving problems via insight. For each participant, we first transformed our data into a continuous variable, we calculated a ratio between the number of problems solved with insight and with analysis (Log A/I) and we correlated it with each PANAS score.6 Linear regression analysis showed that positive affect was positively related to problem-solving with insight and, therefore, negatively related to problem-solving via analysis (β = 0.055, SE 0.023, p < 0.05) (Fig. 5).

Fig. 5.

Fig. 5

Open in a new tab

Scatterplot indicating the relation between the ratio of solutions achieved with analysis or with insight [on a continuous measure represented by Log A/I] and positive affect (PANAS)

Problem‑solving style, impulsivity, and anxiety

No correlation between was found between impulsivity (BIS-11) or anxiety (STAI) and either problem-solving style.

Discussion

There are at least two broad categories of problem-solving mechanisms which people can engage when they encounter a problem: insight and analysis. We have referred to these mechanisms as problem-solving styles. Personality traits may lead some people to rely primarily on analytic processes and other people to rely primarily on insight processes. It is likely that most people will rely on a more flexible combination of the two, emphasizing one, or the other approach depending on the problem and the situation.

In this study, we considered the influence of risk taking, as both a personality trait (measured by the BART) and a situational state (induced by a scenario in which we asked participants to bet on their ability to solve the following problem) on preferred problem-solving style (whether a person tends to solve problems with insight or analysis). Previous research suggests that people who are creative have a greater willingness to take risks, and a higher tolerance for ambiguity than do people who are less creative. Therefore, we hypothesized that the personality trait of risk taking would be correlated with a tendency to solve problems with insight more often than with analysis. However, the results show that the trait of risk taking, as measured by the BART, was not predictive of problem-solving style.

We also hypothesized that any relation between the trait of risk taking and problem-solving style would be complicated by state or situational variables. Situational factors could lead people to favor one or the other problem-solving style, above and beyond or contradictory to their nature tendency, depending on the problem and the situation. Our previous studies led us to hypothesize that state factors, specifically time pressure (the feeling of running out of time), would narrow participants’ focus of attention, promoting analytical processing, more frequent guessing, and more frequent errors (Salvi, et al., 2016 ). Several studies have demonstrated that external monetary rewards are detrimental to creativity (e.g., Amabile, 1998; Amabile, Hennessey, & Grossman, 1986). However, if the reward is presented sub-liminally (i.e., below awareness when our attention system is distracted) it motivates solutions via insight (Cristofori, et al., 2018). In this study, we let participants decide the amount they would bet at the beginning of each trial (self-determined monetary reward) and we observed the effects on problem-solving style. We predicted that situations that create a perception of risk (for winning or losing the amount bet) would lead to greater use of analytic problem-solving style. The results supported this prediction, showing that situational factors related to possible risk and reward modulate problem-solving style, and allow us to conclude that a state of risk created by the possibility of winning or losing a monetary reward (even when the reward is self-determined), does impair creativity to the advantage of analytical solving. The scenario created mimics the everyday life circumstance of when people have to decide between accepting or declining a problem-solving challenge and, therefore, risk and invest resources in their ability to solve a problem to gain an external reward. Our results allow us to conclude that in these cases, the pressure created by accepting a problem-solving challenge will orient our problem-solving style toward analytical solutions at the cost of creative ideas.

A second important finding was that higher bets, made before participants had seen the next problem, predicted more correct solutions. Recent studies point out that correct and incorrect solutions differ in problem-solving processing and are preceded by different states, with special regard to problem-solving style (Danek & Salvi, 2018). Indeed, Kounios et al. (2006) found that, prior to seeing the problem, people showed distinct brain preparative states that predicted insight and analytic solving. Perhaps, there are distinct brain preparation states that are predictive of the likelihood of solving (whether by insight or analysis) that can influence confidence and thus betting behavior. Our findings complement prior research on the role that preparation time (Kounios, et al., 2006) and expected reward (Friedman & Foster, 2005; Cristofori, et al., 2018) play in modulating problem-solving style. Friedman & Foster (2005) found that anticipatory states of reward promoted creative solutions and increased relative right-hemispheric activation (activation also seen during insight solving, Jung-Beeman, et al., 2004), whereas avoidance of punishment promoted an analytical problem-solving style and increased relative activation of the left hemisphere. Kounios et al. (2006) showed distinct brain preparative states manifest prior to insight and analytic solving. Our results provide more evidence that situational factors, such as possible risk and reward, where one has to bet on one’s ability to solve a problem, play a role by modifying preparation states and modulating problem-solving style.

A third important result is related to confidence. We know that solutions via insight are more accurate than solutions via analysis (Salvi et al., 2016) and that people feel more confident in their insight solutions than in their analytic solutions (Danek & Wiley, 2017; Webb, Little, & Cropper, 2016, Danek & Salvi, 2018); however, the current results show that people are not more confident in their incorrect solutions when the solution is produced via insight (cf. Danek & Wiley, 2017). This suggests that higher confidence is not solely a consequence of the subjective insight experience but is related to the accuracy of the solution, since people do not feel more confident for false insights compared to false solutions via analysis. This result allows us to conclude that: confidence is a good predictor of the accuracy of a solution regardless of solution style; confirms that people have more confidence in the accuracy of their correct solutions via insight; and when the feeling of insight accompanies an incorrect solution, participants are not falsely overconfident due to that feeling of insight.

We reasoned that the BART—because the outcome may be seen as based on luck—may measure a general willingness to risk, whereas bets on CRAs may measure a specific situational willingness to bet on one’s ability to solve the specific type of problem. Therefore, to better understand the relation between situational (state) risk and problem-solving approach, we examined the pattern of bets following solutions. Our results show that correct solutions, regardless of whether they were produced by insight or analysis, were followed by higher bets. Further analysis showed that how a previous solution was reached (insight or analysis) had an impact on willingness to take a risk on future problems. People were willing to bet greater amounts on their ability to solve a future problem when the previous problem had been solved via analysis. This may seem unexpected, because solutions by analysis are less likely to be correct than solutions by insight (Salvi, et al., 2016). Despite the findings that solutions by insight are more likely to be correct and that people are more confident that solutions reached by insight are correct (result seen also in Danek & Wiley, 2017; Webb, et al., 2016), people are likely to be more motivated by a feeling of predictability by the believe that they can repeat the steps that led to solutions produced by analysis. They can consciously explain the process used for successfully solving a problem when they use analysis, so they believe that they can replicate the process on future trials, thus increasing their willingness to bet that they can solve those future problems. In contrast, insight solutions feel surprising (see Danek & Wiley, 2017, for features of insight solutions) and they are difficult to explain (people cannot retroactively report how they solved the problem), so people are not sure that they can repeat the process. Because if its ineffability, it seems likely that people are more confident (after the fact) that solutions produced by insight are correct, but they are more confident that they can replicate the process responsible for solutions by analysis.

A fourth important outcome of our study shows that problem-solving under risk is highly sensitive to gender. Though we did not predict a difference, our results revealed that in the risk scenario, females were more successful problem solvers than males. These data contradict the majority of research in the field of behavioral and financial economics, indicating that males are more risk tolerant, and make riskier financial decisions than females who appear to be less risk seeking (e.g., Bannier & Neubert, 2016; Lemaster & Strough, 2014; Powell & Ansic, 1997). By contrast, our data show no difference in risk aversion between males and females; however, when under risk females solve a higher percent of problems than males. This result calls for replication, since we did not hypothesize any gender difference and we did not balance our groups for gender.

In addition, because of the need to place bets, solve problems, and rate confidence, participants in the risk group experienced greater cognitive load and more task switching than those in the control. We acknowledge that this represents a potential confounding variable that needs to be further investigated in future studies.

The results of our study also show that risk preferences are related to mood and to problem-solving style. Positive mood is positively correlated with solutions via insight and creativity (Subramaniam et al., 2009), whereas negative mood is associated with trait risk.

The role of mood in the expression of risk attitudes has been widely documented in experimental setups (see, e.g., Isen and Patrick, 1983; Arkes et al., 1988; Isen et al., 1988; Nygren, et al., 1996; Nygren, 1998). Positive mood induces a state of diffuse attention and promotes creativity. Solutions via insight, and creative ideas are associated with spontaneous internal cognition, which has a greater chance of being expressed when a person is at rest, in a positive mood, or when attention is away from a demanding task as during mind wandering. We recognize that future studies will be needed to determine the relationship between affect or mood, risk taking, and problem-solving style. Risky situations may moderate a person’s affect (either positively or negatively), impulsiveness, and/or level of anxiety, which may then change their dominant problem-solving style. On the other hand, affect, impulsiveness, and/or level of anxiety may moderate a person’s willingness to risk which may then change their dominant problem-solving style. A previous study (Salvi, et al., 2016) found that people tend to shift toward more analytical solutions when under the pressure of running out of time. Being in a situation of risk might induce a similar threatening state and need for alertness that orients our attention externally hindering creativity which calls for a more relaxed atmosphere, and internally oriented attention. The relation between situations of risk and reward and problem-solving style, seen in our data, can be explained by suggesting that being under risk may generally increase negative mood and alertness, narrow the focus of attention keeping us on task, and increase the desire to avoid negative outcomes. This cluster of factors orients people toward a more analytical problem-solving style.

Acknowledgements

We thank the two reviewers and the Editor for their constructive criticisms on the earlier draft of this article, and for motivating further analysis that allowed us to find unpredicted results. This work was supported by NIH under Grant no. T32 NS047987 to CS.

Footnotes

Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00426–019-01152-y) contains supplementary material, which is available to authorized users.

1

The instructions about this ratio read as: “The explosion point varies across balloons, ranging from the first pump to the 128th pump. The ideal number of pumps is 64. What that means is that if you were to make the same number of pumps on every balloon, your best strategy would be to make 64 pumps for every balloon. This would give you the most money over a long period of time. However, the actual number of pumps for any particular balloon will vary, so the best overall strategy may not be the best strategy for any one balloon.”

2

Two participants were removed from the problem‑solving analysis because they rarely reported using one of the solution styles. Participant 1, female, reported solving by analysis for only 0.02% of her solutions, while participant 2, male, did not report solving any problems by analysis.

3

No main effects within or between groups were found.

4

No main effects within or between groups were found.

5

One possible explanation is that participants bet differently on the two tasks because they viewed outcomes in the BART as based on luck but viewed outcomes in the CRA task as based on ability.

6

Because we transformed the data in a continuous variable we did not need to exclude those two participants who reported solving too few problems via either insight or analysis.

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