Brief articleNumeracy moderates the influence of task-irrelevant affect on probability weighting
Introduction
Comprehension of numbers and numerical operations bears obvious psychological, health and economic benefits for everyday decisions. For instance, understanding information about a 30% chance of heavy rain tomorrow enables one to avoid getting wet on the way to an important meeting, similarly knowing the exact chances of car theft in the neighborhood can help to manage the risk by purchasing an insurance policy at an attractive price. Although efficient processing of numerical information (e.g., probability) could lead to superior decisions, many people systematically fail to do so and thus, tend to make suboptimal choices (e.g., some people pay more for a medical treatment with a 1 in 100 chance of producing side-effects than a less risky alternative, e.g., a treatment with a 1 in 1000 chance of producing side-effects, because the latter elicits more negative affective images, Traczyk, Sobkow, & Zaleskiewicz, 2015). In this study, we investigated how incidental affect distorts the optimal valuation of risky prospects and whether this process could be moderated by numerical abilities.
A growing body of research has demonstrated that people differ in statistical numeracy1—the basic ability to understand and process statistical and probability information (Reyna, Nelson, Han, & Dieckmann, 2009). High numeracy has been shown to be advantageous for superior decision making (Cokely and Kelley, 2009, Ghazal et al., 2014). For example, highly numerate individuals are more likely to choose an option with a higher expected value (Pachur & Galesic, 2013), more resistant to framing effects (Peters et al., 2006), show better metacognitive judgment calibration when inferring the predictive value of medical tests (Garcia-Retamero, Cokely, & Hoffrage, 2015), perform better in Bayesian reasoning tasks (Chapman & Liu, 2009), and are less inclined to neglect the denominator in probabilistic judgments (Reyna & Brainerd, 2008). One explanation for these results is that highly numerate individuals exhibit a more linear psychophysical response to changes in value and probability (Millroth & Juslin, 2015), and show more exact mappings of symbolic numbers (Schley & Peters, 2014). However, an influential finding is that numeracy extends beyond simple comprehension of numbers and mathematical operations (Peters, 2012). Specifically, in a seminal paper by Peters et al. (2006), highly numerate individuals were shown to draw stronger and more precise affective meaning from numbers. In other words, more numerate participants had more precise feelings about the probability of winning a prize and made objectively better choices. They based their choices on information about exact proportions (10%), rather than absolute numbers (1 chance in 10). Similarly, Petrova, van der Pligt, and Garcia-Retamero (2014) demonstrated that greater numeracy allowed individuals to precisely differentiate emotional reactions to probabilities leading to less biased (i.e., closer to linearity) probability weighting.
Intriguingly, a tendency to use affective information in the decision-making process among highly numerate individuals sometimes led to worse decisions (Peters et al., 2006). Such participants rated a loss bet (7/36 chance of winning $9, otherwise losing $0.05) as more attractive than a more beneficial no-loss bet (7/36 chance of winning $9). In this case, clear and strong affective reactions to number comparisons elicited the inaccurate impression that winning $9, in the context of a small potential loss, was more attractive than winning $9 in isolation. What, then, is the function of numeracy in affect-laden judgments and decision making? To the best of our knowledge, there is a dearth of research on the relationship between affect and optimal decision making where numerical abilities are considered as a potential moderator. Additionally, little is known about the role of distinct types of affective influences in this relationship. For example, according to the emotion-imbued choice model (EIC), which was recently proposed by Lerner, Li, Valdesolo, and Kassam (2015), there are two types of affective influences on decision making: (1) integral emotions that arise from imminent decisions; (e.g., affective reactions to probabilities) and (2) incidental emotions—causally unrelated to the decision itself (e.g., mood). In other words, integral affect is manifested in negative or positive feelings about some aspects of a decision problem that are experienced while making a decision, whereas incidental affect can be defined as positive or negative feelings that are independent of a decision problem but likely to be misattributed to it.
In this paper, we extend previous findings and hypothesize that, additionally to the fact that high numeracy individuals are more sensitive to number-related affect, they also have the advantage over less numerate ones in disentangling influences of affective responses that are irrelevant to a decision task. That is, on the one hand, highly numerate people are more sensitive to integral affect elicited by risky prospects. On the other hand, they are likely to reduce the impact of incidental affect which is unrelated directly to risky prospects and thus display a more linear probability weighting.
According to normative decision theory (von Neumann & Morgenstern, 1944), a rational decision maker should prefer an option that maximizes the expected utility—a measure of value which is a result of weighting a function of consequences by objective probabilities and summing these outcomes across alternatives. One of the most influential descriptive theories, based on the expected utility calculus, prospect theory (Kahneman and Tversky, 1979, Tversky and Kahneman, 1992), also posits that individuals subjectively transform probabilities and that this process can be modeled by an inverse S-shaped probability weighting function (PWF; Gonzalez and Wu, 1999, Prelec, 1998).
In the past 20 years, a large amount of evidence has been accumulated to show that affective and emotional reactions play a crucial role in decisions under risk and uncertainty (Loewenstein, Weber, Hsee, & Welch, 2001). Emotions are not only a consequence of choices but also often drive the cognitive processes to arrive at a decision (Damasio, 1994, Slovic et al., 2007). For example, Rottenstreich and Hsee (2001) found that participants were less sensitive to changes in the probability scale in the case of affect-rich (i.e., European vacation) relatively to affect-poor outcomes (i.e., tuition payment). This affective decomposition of the PWF was subsequently described in greater detail in studies that demonstrated a decrease in probability discriminability, as a function of outcome’s affective value (neutral vs. affect-rich gift from a grandparent; Petrova et al., 2014). In other words, the PWF was more S-shaped if a decision outcome elicited negative affect, whereas a neutral condition produced less biased probability weighting. Crucially, numeracy moderated the relationship between integral affect and PWF, suggesting that individuals with high numerical abilities conveyed a greater sensitivity to changes in probability. In addition, this led to decisions that conformed more to the predictions of the normative model.
Additionally, it has been shown that incidental influences, such as negative mood, may also cause more biased probability weighting (Fehr-Duda et al., 2011, Kliger and Levy, 2008), but the moderating role of numeracy was not taken into consideration in this investigation. The influence of incidental emotions on PWF can be an example of the carry-over effect (i.e., previously elicited emotion alters subsequent, unrelated decision; Lerner, Small, & Loewenstein, 2004). However, to the best of our knowledge no studies exist that investigate the carry-over effect onto PWF and the role of numeracy in this relationship. Herein, we extended the concept of numeracy to be a moderator of the influence of integral emotion on probability weighting. We advanced the hypothesis that incidental emotions, activated through the carry-over effect, would influence the shape (i.e., curvature) of the PWF, signifying a more distorted probability weighing, but only in the case of less numerate participants.
Section snippets
Participants
Sixty-one undergraduate students (44 females, mean age = 26.8 years; SD = 6.3) participated in this study for course credits or 10 PLN (approximately US$3) compensation. All participants gave an informed consent before the experiment.
Design and materials
The experiment consisted of two tasks: a perceptual task and an insurance task. In a 2 × 9 mixed factorial design, affect (neutral vs. negative) was a between-subjects factor in the perceptual task, and probability (1%; 5%; 10%; 25%; 50%; 75%; 90%; 95%; 99%) was presented
Modeling the shape of the probability weighting function
The shape of the PWF was modeled using the WTP values provided in the insurance task. First, the WTP values for each participant and probability level were transformed into probability weights using the following equation (Petrova et al., 2014):
Next, we employed the nonlinear least-squares method (i.e., the nls package in the R statistical environment; R Core Team, 2014) to model the PWF using the two-parameter estimation
Discussion
The aim of this study was to investigate how incidental affect influences probability weighting and what is the role of numerical abilities in this process. We showed that preceding risky prospects with irrelevant affective stimuli led to the increased curvature of the PWF, thus resulting in more distorted probabilities weighting. Critically, this effect was significant only for less numerate participants, while probability weighting in more numerate people was not altered by
Acknowledgements
The research in this article were funded by the National Science Centre, Poland under grant 2015/17/D/HS6/00703. We would like to thank the three anonymous reviewers as well as Agata Sobkow and Tomasz Zaleskiewicz for their helpful comments regarding this article.
References (33)
- et al.
Risk and rationality: the effects of mood and decision rules on probability weighting
Journal of Economic Behavior & Organization
(2011) - et al.
On the shape of the probability weighting function
Cognitive Psychology
(1999) - et al.
Mood impacts on probability weighting functions: “Large-gamble” evidence
Journal of Socio-Economics
(2008) - et al.
Prospect evaluation as a function of numeracy and probability denominator
Cognition
(2015) - et al.
Numeracy, ratio bias, and denominator neglect in judgments of risk and probability
Learning and Individual Differences
(2008) - et al.
The affect heuristic
European Journal of Operational Research
(2007) - et al.
Numeracy, frequency, and Bayesian reasoning
Judgment and Decision Making
(2009) - et al.
Measuring risk literacy: the Berlin numeracy test
Judgment and Decision Making
(2012) - et al.
Cognitive abilities and superior decision making under risk: a protocol analysis and process model evaluation
Judgement and Decision Making
(2009) Descartes’ error: emotion, reason, and the human brain
(1994)
Visual aids improve diagnostic inferences and metacognitive judgment calibration
Frontiers in Psychology
Predicting biases in very highly educated samples: numeracy and metacognition
Judgment and Decision Making
Prospect theory: an analysis of decision under risk
Econometrica
International affective picture system (IAPS): affective ratings of pictures and instruction manual
Emotion and decision making
Annual Review of Psychology
Heart strings and purse strings: carryover effects of emotions on economic decisions
Psychological Science
Cited by (44)
Conditionality of adaptiveness: Investigating the relationship between numeracy and adaptive behavior
2023, Journal of Economic PsychologyBetter decision making through objective numeracy and numeric self-efficacy
2023, Advances in Experimental Social PsychologyExperience of losses and aversion to uncertainty - experimental evidence from farmers in Mexico
2022, Ecological EconomicsCitation Excerpt :Hence, we find that probability weighting decreases with distance to the nearest city and assets, our proxy for wealth, which is in contrast to Liebenehm and Waibel (2014) and Nguyen and Leung (2010). Potentially, greater wealth is partly due to greater financial or numerical literacy, which has been shown to go along with less pronounced probability weighting (Traczyk and Fulawka, 2016). An increase of λ for any value of λ > 1 denotes an increase in loss aversion.
Puzzles of insurance demand and its biases: A survey on the role of behavioural biases and financial literacy on insurance demand
2021, Journal of Behavioral and Experimental FinanceCitation Excerpt :However, the study found inconsistent results for higher probabilities as well as insignificant results for underweighting. Traczyk and Fulawka (2016) found experimentally the S-shaped effect of affect-rich events in insurance decisions, but decisions of high numerate people (i.e. good ability to understand and process statistical information) were found to be unaltered by affection. The literature on insurance demand has found compelling motivations for its puzzles through behavioural biases, but it lacks insights on how to mitigate them and how to solve the insurance demand problems.
Flood insurance demand and probability weighting: The influences of regret, worry, locus of control and the threshold of concern heuristic
2020, Water Resources and EconomicsCitation Excerpt :Individual risk attitudes are determined by the combination of utility curvature, loss aversion and probability weighting under CPT, which allows for describing a wider diversity of observed individual behaviour than EUT. Empirical evidence about factors related to the probability weighting function and/or utility curvature include, among others, the influence of the size and spacing of outcomes [12–14], gender [15], age [16,17], mood [18,19], time pressure [20], as well as induced affect and numerical skill [21–25]. Many of these studies elicited preference parameters under neutrally framed decisions, which is useful if the aim is to perform controlled theoretical tests, because specific context framing can add noise to results [26].
Multiple numeric competencies predict decision outcomes beyond fluid intelligence and cognitive reflection
2020, IntelligenceCitation Excerpt :In other words, people with high numeracy are more sensitive to numbers and magnitudes because of number-related relevant affective reactions that help them to derive the gist of a decision problem and guide better decisions (Reyna, 2004). This effect has been illustrated in several studies showing that people with high numeracy usually reported clearer feelings of the goodness or badness of values and probabilities (Peters et al., 2006), reported more differentiated affective reactions to probabilities (Petrova et al., 2014), and were more sensitive to affect relevant to a decision problem (Traczyk, Lenda, et al., 2018), but at the same time were less prone to negative incidental affective influences irrelevant to a decision task (Traczyk & Fulawka, 2016). Importantly, Petrova et al. (2019) demonstrated that the accuracy of symbolic-number mapping outperformed conventional measures of numeracy and cognitive reflection in predicting probability distortions.