4.1. Summary Statistics
Table 1 reports the summary statistics. Among the contestants in the sample, approximately 71% are males, 78% are aged 31 to 59 years old, 75% are married, 59% don’t have children, and only 8% have studies in finance or similar.
Knowledge of contestants is another factor that can influence the preference for uncertainty in a general culture contest. Therefore, we found that, on average, the contestants in the twelfth question take about 29 s to answer. Restricting the analysis to competitors who have a preference for uncertainty, we found that contestants who get the answer right (with mastery of the topic) need 27 s less, on average, than contestants with no knowledge of the topic. Another factor that can explain whether knowledge influences the preference for uncertainty is the confidence of contestants in the answer given in the final question. We found that, on average, JOKER’s contestants have some knowledge of the topic (1.24), but not total mastery.
Finally, we analyzed the contestants’ specific emotions, even when incidental to the decision in question, since they can systematically affect the perceptions, judgments, and behaviors of individuals in the preference for uncertainty in the twelfth question. We found that, on average, the facial expressions of the JOKER contestants with the highest expression are neutral (0.52), happy (0.125), and angry (0.093). Based on valence (calculation based on FaceReader 8.1 software), we found that, on average, competitors show negative emotions (1.38).
4.2. Empirical Results
We estimated the decision to game in the final question to measure the knowledge variable, with a series of one-way ANOVA tests on the explanatory variables.
Table 2 presents the estimated marginal effects and p-values for each of these variables.
The mean preference for uncertainty is greater than the center of the scale for any given response time. According to the ANOVA test, there are differences in means between the response times in the final question (
p-value = 0.00). We can define that the average response time of a contestant with high knowledge of the topic is significantly different from that of a contestant without knowledge. On average, it takes 27 s less for a contestant with mastery of a topic to answer the final question. These results are in line with several previous studies, where an inverse relationship between the time required to respond and the confidence expressed in that response is documented (
Kimble and Seidel 1991;
Varas and Watson 1994;
Fazio 1995;
Huizingh et al. 2002;
Voss et al. 2004;
Koriat et al. 2006;
Ratcliff et al. 2016;
Cox and Shiffrin 2017). After categorizing the latency variable, contestants who take less than the average time to answer the last question (0.00) have a greater preference for uncertainty compared to contestants who take more than the average time to answer the final question (0.56). The difference in means is statistically significant (
p-value = 0.00). Therefore, when the contestant dominates a topic or is an expert in an area, it takes, on average, less time to answer the final question. To ensure that the latency variable in our study measures the knowledge of contestants, we analyzed the response time for all the previous questions (from the 1st to the 11th question), concluding that, in any of the questions, the contestants who get the answer right need, on average, less time to respond (
p-value = 0.00).
Regarding the perceived knowledge, we found that the contestants have significantly different behaviors in the decision to game in the final question. According to the ANOVA test, there are differences in means between the levels of confidence in the response and the preference for uncertainty, and these differences are statistically significant (
p-value = 0.00). Contestants who show greater confidence in the correct answer are more likely to decide to game on the final question, and contestants with no confidence mostly opt for the safety payoff. According to Turkey’s post hoc tests, contestants who have no confidence about the answer tend to opt for a certain payoff, contestants with high confidence about the answer prefer to answer on the twelfth question, and contestants with some confidence about their answer tend to answer (
Table 3).
For the analysis of emotions, the facial expressions of the contestants of 59 episodes were recorded directly and examined by the RTP Play platform. From the recorded videos, between five to ten seconds of the contestants’ frontal faces were selected, when contestants must decide Game or No Game (after the presentation of the final question), using FaceReader.
According to the results presented in
Table 4, we verified that, on average, the contestants present facial expressions that show negative emotions (valence with −0.042). Subsequently, to measure the emotion variable, we estimated the decision to game in the last question with an independent sample t-test on the explanatory variable Facial. This variable results from the valence calculation obtained by FaceReader
which results from the difference between the intensity of the positive expression
(Ep) and the intensity of the negative expression with the greatest strength (
En).
Table 5 presents the estimated marginal effects and
p-values for this variable.
Both contestants with positive (0.76) and negative (0.87) emotions show a preference for uncertainty above the center of the scale, being higher in contestants with negative emotional states. The difference in means is statistically significant (
p-value = 0.05). Contestants with positive emotions tend to be more satisfied with the payoff achieved in the last question, taking into account game performance, knowledge, and sociodemographic characteristics, while contestants with negative emotions tend to be more rational because they are not satisfied with their progress in the game or, despite not having mastered the topic of the last question, they are more likely to opt for a preference for uncertainty to try to recover or show their cognitive abilities. If we evaluate these results in the light of the Theory of Expected Utility (
Von Neumann and Morgenstern 1947), a rational individual, regardless of their emotional state, should always choose the option with the highest value, since the game’s alternatives are evaluated separately and independently, and the option with the highest value is always selected. Bearing in mind that in JOKER, for any payoff in the game, the expected value of playing is always higher than the certain payoff, the contestant should always choose Game regardless of how they feel emotionally. Considering Cumulative Prospect Theory (
Tversky and Kahneman 1992), individuals systematically tend to overestimate small probabilities and undervalue large probabilities. Consequently, they exhibit uncertainty-prone behavior when buying a lottery ticket, overestimating the low probability of winning, and exhibit uncertainty-averse behavior when buying auto insurance because they underestimate the high probability of not being harmed. Therefore, in a television contest where the jackpots are represented as the “lottery ticket”, there seems to be a greater preference for uncertainty. The hypothesis that contestants with negative emotions are more likely to game in the last question is valid and is in agreement with the literature that argues that negative emotions can induce individuals to process the available information with greater attention, which facilitates rational thinking and a preference for uncertainty (e.g.,
Kahneman 2012;
Schwarz 2012;
Thaler 2017).
To validate the joint role of knowledge and emotions in the preference for uncertainty, we defined the explanatory variables: Latency (time used to answer the final question), Confidence (dummy variable that has a value of zero when the contestant does not have confidence in the response, one when having some confidence, and two when having high confidence), and Emotions Type (dummy variable that presents the value of zero for contestants with neutral emotions, one for negative emotions, and two for positive emotions).
The representation for the CART model is a binary tree, which is presented in
Figure 1. Each root node represents a single input variable (Latency, Confidence, and Emotion type) and a split point on that variable (which was defined at the median of each variable).
The leaf nodes of the tree contain an output variable (decision to game, i.e., preference for uncertainty) which is used to make a prediction.
With the binary tree representation of the CART model described, we are able to make predictions and explain the output. Given a new input, the tree is traversed by evaluating the specific input started at the root node of the tree. A learned binary tree is actually a partitioning of the input space. One can think of each input variable as a dimension on a p-dimensional space. The decision tree split this up into rectangles (or final nodes). New data are filtered through the tree and land in one of the rectangles, and the output value for that rectangle is the prediction made by the model.
CART analysis was centered on the variables of knowledge and emotions since this method reflects a decision tree and endogenizes the variables that the individual considers in the decision. In JOKER, after the presentation of the final question, the contestant only depends on knowledge and emotions. Based on the improvements, we obtained the importance of variables as shown in
Table 6:
Our results show asymmetrically large importance of Latency (Knowledge) in explaining an individual’s preference for uncertainty (decision to game) and only a residual impact of Confidence and Emotions Type on that decision.
Our classification results are robust. The estimated risk of misclassification is zero. The total of correct classifications is 100%, and the model equally predicts the preference for uncertainty (Game) or the option for the payoff insurance (No Game), both with 100% (
Table 7).
We analyze the results of our CART to understand the differential impact of Knowledge and Emotions by looking at the terminal nodes obtained on the classification tree, presented in
Figure 1.
Node 3, made up of contestants who take less time to respond (less than 49 s) and who are either totally confident or completely lacking in confidence, represents 62.7% of the sample. This is the segment where most individuals show a preference for uncertainty (100%), as shown in
Table 8. The next highest concentrations of preference for uncertainty are located at nodes 5, 7, and 10. Node 5 includes contestants who respond quickly, have some confidence in the answer, and show positive emotions in decision-making. Nodes 7 and 10 include an improvement in the Latency variable, and node 7 presents individuals who respond in less than 39 s, while node 10 presents individuals who respond in more than 42 s; both nodes have contestants with some confidence in the answer and show negative emotions in decision-making.
CART is used in research about, for example, facial recognition, spam detection in e-mail, and disease diagnosis (
Verikas et al. 2011). The CART estimation function is difficult to visualize and does not generate estimates of coefficients and confidence intervals. Thus, it is not possible to define tables and figures that characterize it succinctly. One of the key advantages of the recursive binary tree is its interpretation. The resource space partition is fully described by a single tree. With more than two entries, partitions like the one in our study are difficult to draw, but the representation of the binary tree works the same way.
Results obtained with CART analysis allow us to argue that knowledge plays a more immediate role in the preference for uncertainty and that emotions are considered, regardless of being positive or negative, when individuals do not have complete confidence in their response. Firstly, superior knowledge and total lack of knowledge were generally associated with a greater willingness to game. These results are in line with the literature, namely the competence hypothesis of
Heath and Tversky (
1991) in which individuals who feel knowledgeable tend to bet on their judgment and in the case of total absence of knowledge (when they feel ignorant) they choose by the lottery. In the field of emotions, positive or negative, the results showed that they were only associated with a decision to game when the contestant’s confidence in the response was medium. Unlike
Maffioletti and Santoni (
2019) that concluded that individuals who showed stronger positive emotions and superior knowledge of the decision context were more willing to opt for a preference for uncertainty, while negative emotions were associated with a more neutral attitude towards uncertainty. In our study, both individuals with positive and negative emotions showed a preference for uncertainty. Thus, regardless of the emotional state of a contestant in the face of the twelfth question, we find that preference for uncertainty increases when the contestants have a full domain or total absence of knowledge. This result is in line with
Tversky and Fox (
1995), who argue that any uncertain choice involves feelings of hope or fear that may reflect the affective responses of individuals to positive and negative outcomes. If the contestant had the opportunity to have an additional question, it would likely increase their hope and, therefore, their choice preference for uncertainty, but it would not double their probability of winning. Therefore, emotions influence decision-making under uncertainty but are neutral to the outcome. These results are in line with the study by
Conte et al. (
2018) which observed that both happy and sad, fearful, and angry participants are more tolerant of uncertainty than participants in a neutral state. In this study, the authors demonstrated that positive and negative emotions involve separate cognitive processes, so different models are needed to explain their effect on preference for uncertainty. Happy participants, who are in a positive emotional state, seem more likely to evaluate uncertainty positively. Sad, fearful, and angry participants who are in a negative emotional state appear to be willing to change that unwanted state because they hope to improve their current state. Understanding the reasons for the different cognitive mechanisms induced by positive and negative emotions can enhance the theoretical framework of the decision-making process under uncertainty.
Consequently, our results support the idea that preference for uncertainty can be modeled as a two-stage process in which decision weights are a function of judgment probability and that knowledge and emotions impact the decision. Hence, we argue that either knowledgeable and more competent individuals or individuals with a total lack of knowledge opt for a preference for uncertainty. The former act accordingly because they trust their abilities, and the latter because they prefer uncertainty over opting for payoff insurance (
Heath and Tversky 1991;
Kilka and Weber 2001;
Rottenstreich and Hsee 2001;
Conte et al. 2018). Emotions are also responsible for the preference for uncertainty and play a leading role when individuals’ trust is not full and, as such, can be used as an excuse and/or justification for the decision taken (
De Sousa 1987;
Fazio 1995). Our results differ from the study by
Maffioletti and Santoni (
2019), where stronger positive emotions are associated with a greater willingness to choose uncertainty and negative emotions are associated with neutral behaviors under uncertainty. Both positive and negative emotions drive the preference for uncertainty in our study. Hypothetically, and in line with several studies, positive emotions, when inducing individuals to trust simpler heuristics, may signal that the cognitive process is not necessary, and they choose to prefer uncertainty because they feel positive about their choice (
Kahneman 2012;
Thaler 2017;
Conte et al. 2018). On the other hand, negative emotions can induce individuals to process the available information with greater attention, which facilitates rational thinking, in which case they will choose the preference for uncertainty as it always leads to higher results, being the most rational option of the game for any payoff (
Kahneman 2012;
Schwarz 2012;
Thaler 2017).