## Introduction

^{1}affects our information-seeking behavior throughout the day (e.g., curiosity determines which person our eyes fixate on at the bus stop or which link we click on when browsing the web), shapes the long-term progress of scientific discovery, and has been described as the essence of science. Given the persistent influence of curiosity throughout our daily lives (Berlyne, 1950; Kang et al., 2009; Loewenstein, 1994), and given that scientists have been curious about curiosity for a long time (e.g., Hall & Smith, 1903), it appears perplexing that only recently, studies have begun to systematically investigate the underlying mechanisms of curiosity (Dubey & Griffiths, 2020; Gottlieb & Oudeyer, 2018; Gottlieb et al., 2013; Kang et al., 2009; Kidd & Hayden, 2015; Wojtowicz & Loewenstein, 2020).

### Curiosity as a function of confidence

^{2}The questions were shown to cover different curiosity levels during pretesting. Specifically, their experiments followed the same basic procedure for all 40 questions: (1) participants were presented with a trivia question and were instructed to guess the corresponding answer in their head; (2) participants rated their curiosity on a scale from 1 to 7; and (3) participants rated their confidence concerning their guessed answer on a scale from 0 to 100%. The results of their first experiment mimicked the hunger metaphor of the information-gap theory for curiosity, with an inverted U-shaped relationship between curiosity and confidence ratings, with little curiosity at low and high confidence ratings and maximum curiosity ratings at medium confidence levels.

### Curiosity as a function of novelty

### A rational model combining the two perspectives of complexity and novelty

^{3}In Phase 3, 10 out of the 40 questions were shown again and the participants had to type in the respective answer/their guess (they received a small reward per right answer within a set time frame to prevent online research on this question).

^{4}

^{5}This further implies that asking people on whether knowing information would be important or not, in addition to asking them about their confidence in knowing the answer, may be a critical predictor for curiosity about knowing this information and consequently, their willingness to close this information gap. Here, we sought to explicitly test the influence of importance on the relationship between curiosity and confidence.

### The present research

^{6}(see Fig. 5 in Kang et al., 2009), and expected more willingness to spend effort (in terms of time) to reveal an answer on high curiosity levels

^{7}(see Fig. 5 in Kang et al., 2009).

Model formula | Exp 1: BIC | Exp 1: AIC | Exp 2: BIC | Exp 2: AIC |
---|---|---|---|---|

\({\text{Curiosity}}\, = \,b_{1} *{\text{confidence}}^{{2}} \, + \,b_{2} *{\text{confidence}}\, + \,b_{3} *{\text{importance}}\) | 2021.8 | 1984.1 | 2047.2 | 2010.1 |

\({\text{Curiosity}}\, = \,b_{1} *{\text{importance}}\) | 2081.4 | 2062.5 | 2058.6 | 2040.1 |

\({\text{Curiosity}}\, = \,b_{1} *{\text{confidence}}^{{2}} \, + \,b_{2} *{\text{confidence}}\) | 2251.1 | 2227.5 | 2139.6 | 2116.4 |

\({\text{Curiosity}}\, = \,b_{1} *{\text{ confidence}}\) | 2311.3 | 2292.4 | 2151.4 | 2132.9 |

\({\text{Curiosity}}\, = \,b_{1} *{1}\) | 2310.2 | 2296.1 | 2142.4 | 2128.5 |

Model formula | Exp1: BIC | Exp1: AIC | Exp 2: BIC | Exp 2: AIC |
---|---|---|---|---|

\({\text{Decision}}\, = \,b_{1} *{\text{curiosity}}\, + \,b_{2} *{\text{importance}}\) | 936.4 | 912.8 | 930.0 | 906.9 |

\({\text{Decision}}\, = \,b_{1} *{\text{curiosity}}\) | 937.2 | 923.1 | 917.6 | 903.7 |

\({\text{Decision}}\, = \,b_{1} *{\text{curiosity}}\, + \,b_{2} *{\text{confidence}}^{{2}} \, + \,b_{3} *{\text{confidence}}\) | 951.5 | 918.5 | 918.5 | 876.0 |

\({\text{Decision}}\, = \,b_{1} *{\text{curiosity}}\, + \,b_{2} *{\text{confidence}}^{{2}} \, + \,b_{3} *{\text{confidence}}\, + \,b_{4} *{\text{importance}}\) | 967.1 | 905.8 | 929.4 | 869.2 |

\({\text{Decision}}\, = \,b_{1} *{\text{confidence}}^{{2}} \, + \,b_{2} *{\text{confidence}}\, + \,b_{3} *{\text{importance}}\) | 984.4 | 951.5 | 906.8 | 874.4 |

\({\text{Decision}}\, = \,b_{1} *{\text{importance}}\) | 996.8 | 982.6 | 955.3 | 930.4 |

\({\text{Decision}}\, = \,b_{1} *{\text{confidence}}^{{2}} \, + \,b_{2} *{\text{confidence}}\) | 1067.5 | 1048.7 | 923.7 | 905.2 |

## Experiment 1

### Method

#### Participants

_{age}= 28.13 years; range 18–43) via Prolific to conduct the online study. All participants provided informed consent prior to the onset of the study. When planning the experiment, we reasoned that doubling the sample size used in Experiment 1 by Kang et al. (2009) should be sufficient to reveal the assumed inverted U-shaped relationship between curiosity and confidence. After we collected the data, we conducted a post hoc power analysis with the simr package in R (Green & Macleod, 2016). We describe the results of this power analysis in the results section.

#### Stimuli

#### Procedure

#### Data analysis

^{8}First, the raw curiosity ratings were normalized for each participant using the following equation:

### Results

#### Analysis 1a: replication results: curiosity as a function of confidence

_{1}estimate = − 7.43; t = − 7.94; p < 0.001) and a significant coefficient for confidence (b

_{2}estimate = 2.79; t = 2.98; p = 0.003).

Predictors | Curiosity | Curiosity | ||||||
---|---|---|---|---|---|---|---|---|

B | SE | t value | p | b | SE | t value | p | |

Intercept | − 0.00 | 0.03 | − 0.01 | 0.996 | − 0.64 | 0.07 | − 8.85 | < 0.001 |

Confidence [1st degree] | 2.79 | 0.94 | 2.98 | 0.003 | 4.03 | 1.37 | 2.94 | 0.003 |

Confidence [2nd degree] | − 7.43 | 0.94 | − 7.94 | < 0.001 | − 7.73 | 1.43 | − 5.40 | < 0.001 |

Importance | 0.34 | 0.02 | 18.13 | < 0.001 | ||||

Confidence [1st degree]: Importance | − 2.69 | 0.47 | − 5.76 | < 0.001 | ||||

Confidence [2nd degree]: Importance | 1.24 | 0.47 | 2.62 | 0.009 | ||||

N | 41 _{participants} | 41 _{participants} | ||||||

AIC | 2227.592 | 1984.182 |

#### Analysis 1b: replication results: probability of revealing the answer as a function of curiosity

Predictors | Decision | Decision | ||||||
---|---|---|---|---|---|---|---|---|

b | SE | z value | p | b | SE | z value | p | |

Intercept | − 0.28 | 0.19 | − 1.53 | 0.126 | − 0.79 | 0.23 | − 3.46 | 0.001 |

Curiosity | 1.09 | 0.10 | 11.13 | < 0.001 | 0.83 | 0.15 | 5.75 | < 0.001 |

Importance | 0.23 | 0.07 | 3.46 | 0.001 | ||||

Curiosity: importance | 0.04 | 0.06 | 0.65 | 0.513 | ||||

N | 41 _{participants} | 41 _{participants} | ||||||

AIC | 923.107 | 912.857 |

#### Model comparison results

^{9}The results of these two winning models are described below as well as in Tables 3 and 4.

#### Analysis 1c: curiosity as a function of confidence and importance

_{1}= − 7.73; t = − 5.40; p < 0.001), and the linear term (b

_{2}= 4.03; t = 2.94; p = 0.003). In line with our predictions about the influence of importance on curiosity, the main effect of importance was significant (b

_{3}= 0.34; t = 18.13; p < 0.001). In addition, the interaction between confidence and importance was significant, reflected by a significant quadratic term (b

_{4}= 1.24; t = 2.62; p = 0.009) and a significant linear term (b

_{5}= − 2.69; t = − 5.76; p = < 0.001). This interaction was in line with our predictions and showed that curiosity would asymptote on a high level for importance and low-to-moderate confidence ratings and decrease with higher confidence ratings. Furthermore, on lower importance ratings, curiosity followed an inverted U-shaped function of confidence (see Figs. 5, S1).

#### Analysis 1d: probability of revealing the answer as a function of curiosity and importance

_{3}= 0.23; z = 3.46; p < 0.001), with a higher probability to reveal the answer with increased importance ratings. The interaction between curiosity and importance was not significant (b

_{4}= 0.04; z = 0.65; p = 0.513).

#### Power analysis

## Discussion

^{10}(see Fig. 3) and participants were more likely to spend time to learn information which they were more curious about (see Fig. 4). While these findings supported the information-gap theory (Loewenstein, 1994), we tested whether participants’ perceived importance of information could modulate the resulting pattern of these two analyses. Therefore, we tested whether an extended model, which considered importance as an additional variable, fitted the data better compared to the model which replicated the analysis of Kang et al. (2009). We also compared these two models with other potential models. The model comparison results revealed that curiosity was best predicted by confidence and importance (see Table 1). In line with the theoretical predictions by Dubey and Griffiths (2020), our results indicated that curiosity asymptoted on a high level for information participants were low-to-moderate confident in knowing and rated as important. The results also indicated that if information was perceived as less important, curiosity dropped and followed an inverted U-shaped function of confidence, as suggested by the information-gap theory.

## Experiment 2

### Method

#### Participants

_{age}= 26.59 years; range 18–37) were recruited via Prolific to conduct the online study. All participants provided informed consent prior to the onset of the study. The sample size was based on the same sample size as in Experiment 1 for which power was sufficient (> 80% for a 0.05 alpha level) to reveal an interaction effect between confidence and importance on curiosity.

#### Stimuli, procedure, and data analysis

### Results

Predictors | Curiosity | Curiosity | ||||||
---|---|---|---|---|---|---|---|---|

b | SE | t value | p | b | SE | t value | p | |

Intercept | − 0.00 | 0.04 | − 0.01 | 0.994 | − 0.93 | 0.10 | − 9.60 | < 0.001 |

Confidence [1st degree] | 0.34 | 0.97 | 0.35 | 0.723 | 1.03 | 1.77 | 0.58 | 0.559 |

Confidence [2nd degree] | − 3.42 | 0.97 | − 3.53 | < 0.001 | − 4.36 | 1.76 | − 2.48 | 0.013 |

Importance | 0.27 | 0.02 | 12.58 | < 0.001 | ||||

Confidence [1st degree]: Importance | − 1.26 | 0.46 | − 2.75 | 0.006 | ||||

Confidence [2nd degree]: Importance | 0.32 | 0.45 | 0.72 | 0.470 | ||||

N | 38 _{participants} | 38 _{participants} | ||||||

AIC | 2116.445 | 2010.199 |

Predictors | Decision | Decision | ||||||
---|---|---|---|---|---|---|---|---|

b | SE | t value | p | b | SE | t value | p | |

Intercept | − 0.57 | 0.19 | − 2.94 | 0.003 | − 1.53 | 0.29 | − 5.22 | < 0.001 |

Curiosity | 0.54 | 0.09 | 6.09 | < 0.001 | ||||

Confidence [1st degree] | 1.55 | 5.20 | 0.30 | 0.766 | ||||

Confidence [2nd degree] | − 0.79 | 5.30 | − 0.15 | 0.881 | ||||

Importance | 0.28 | 0.06 | 4.67 | < 0.001 | ||||

Confidence [1st degree]: Importance | − 3.95 | 1.32 | − 2.99 | 0.003 | ||||

Confidence [2nd degree]: Importance | − 3.18 | 1.32 | − 2.41 | 0.016 | ||||

N | 38 _{VPcount} | 38 _{VPcount} | ||||||

AIC | 903.772 | 874.416 |

#### Analysis 2a: curiosity as a function of confidence

_{1}estimate = − 3.42; t = − 3.53; p < 0.001), while the main effect for the coefficient for confidence was not (b

_{2}estimate = 0.34; t = 0.35; p = 0.723).

#### Analysis 2b: probability of revealing the answer as a function of curiosity

#### Model comparison results

^{11}In contrast to Experiment 1, participants’ decision to wait for an answer was best predicted by a model of confidence and importance (see Table 2). The results of these two winning models are described below as well as in Tables 5 and 6.

#### Analysis 2c: curiosity as a function of confidence and importance

_{1}= − 4.386 t = − 2.48; p < 0.001), but not the linear term (b

_{2}= 1.03; t = 0.58; p = 0.559). In addition, the main effect of importance was significant (b

_{3}= 0.26; t = 12.58; p < 0.001). The interaction between the quadratic confidence term and importance was not significant (b

_{4}= 0.32; t = 0.72; p = 0.47), but the interaction between the linear confidence term and importance was significant (b

_{5}= − 1.26; t = − 2.74; p < 0.001). This interaction mimicked our predictions (see Fig. 1) that curiosity would asymptote on a high level for important and low-to-moderate confidence ratings and decrease with higher confidence ratings. Furthermore, on lower importance ratings, curiosity followed an inverted U-shaped function of confidence (see Figs. 5, S1).

#### Analysis 2d: probability of revealing the answer as a function of confidence and importance

_{1}= − 0.79; z = − 0.15; p = 0.881), and the linear term (b

_{2}= 1.55; z = 0.29; p = 0.766). In line with our predictions on the influence of importance on curiosity, the main effect of importance was significant (b

_{3}= 0.28; z = 4.66; p < 0.001). The interaction between the quadratic confidence term and importance was significant (b

_{4}= − 3.18; z = − 2.41; p = 0.016), and the interaction between the linear confidence term and importance was significant (b

_{5}= − 3.95; z = − 2.99; p = 0.003). This interaction pattern suggested that the willingness to spend time to reveal the answer—a behavioral marker for being curious—would asymptote on a high level for important and low-to-moderate confidence ratings and decrease with higher confidence ratings. Furthermore, on lower importance ratings, the decision to wait for an answer followed an inverted U-shaped function of confidence.