Numeracy moderates the influence of task-irrelevant affect on probability weighting

Highlights

• We tested whether decision-irrelevant incidental affect alters probability weighting.

• Negative affect influenced the curvature of the probability weighting function.

• Numeracy moderated this relationship.

• Less numerate individuals exhibited more biased probability weighting.

• Affect did not distort probability weighting in more numerate individuals.

Abstract

Statistical numeracy, defined as the ability to understand and process statistical and probability information, plays a significant role in superior decision making. However, recent research has demonstrated that statistical numeracy goes beyond simple comprehension of numbers and mathematical operations. On the contrary to previous studies that were focused on emotions integral to risky prospects, we hypothesized that highly numerate individuals would exhibit more linear probability weighting because they would be less biased by incidental and decision-irrelevant affect. Participants were instructed to make a series of insurance decisions preceded by negative (i.e., fear-inducing) or neutral stimuli. We found that incidental negative affect increased the curvature of the probability weighting function (PWF). Interestingly, this effect was significant only for less numerate individuals, while probability weighting in more numerate people was not altered by decision-irrelevant affect. We propose two candidate mechanisms for the observed effect.

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.