The loss‐bet paradox: Actuaries, accountants, and other numerate people rate numerically inferior gambles as superior

Abstract

Psychologists have convincingly demonstrated that preferences are not always stable and, instead, are often “constructed” based on information available in the judgment or decision context. In 4 studies with experts (accountants and actuaries in Studies 1 and 2, respectively) and a diverse lay population (Studies 3 and 4), the evidence was consistent with the highly numerate being more likely than the less numerate to construct their preferences by rating a numerically inferior bet as superior (i.e., the bets effect). Thus, the effect generalizes beyond a college student sample, and preference construction differs by numeracy. Contrary to prior thinking about preference construction, however, high expertise and high ability (rather than low) consistently related to the paradoxical phenomenon. Results across studies including Study 3's experimental modifications of the task supported the hypothesized number comparison process (and not a lack of expertise with monetary outcomes and probabilities or numeracy‐related differences in attention to numbers) as the effect's underlying cause. The bets effect was not attenuated by Study 4's instructions to think about what would be purchased with bet winnings. Task results combined with free‐response coding supported the notion that highly numerate participants have a systematic and persistent inclination for doing simple and complex number operations that drive their judgments (even after controlling for nonnumeric intelligence). Implications for 3 types of dual‐process theories are discussed. The results were inconsistent with default‐interventionist theories, consistent or unclear with respect to fuzzy trace theory, and consistent with interactive theories.

The dark sides of people analytics: reviewing the perils for organisations and employees

“…Prescriptive analytics can be used to optimise the efficiency of employees' behaviour or to model complex strategic HR decisions (Fernandez & Gallardo-Gallardo, 2020;Leicht-Deobald et al, 2019). At this stage, decision-making becomes a joint human-algorithm decision-making process (Burton et al, 2019;Schafheitle et al, 2019).…”

How representations of number and numeracy predict decision paradoxes: A fuzzy‐trace theory approach

“…Here, we use measures of each kind of processing to determine empirically whether they predict variability in decisions. We present decision problems that produce what is called the Allais paradox and the loss–bet paradox (Allais, 1953; Duke, Goldsmith, & Amir, 2018; Peters et al, 2019). As explained below, FTT predicts that preferences in these problems are a function of both the formulation of each decision problem (e.g., whether one option contains an explicit null outcome) as well as individual differences in gist and verbatim processing.…”

“…However, research has moved beyond broad associations between numeracy and decision-making to examine how numerical processing shapes decisions (e.g., Schley & Peters, 2014). This focus on processing has highlighted paradoxes in which those higher in numeracy are more susceptible to specific decision biases than those who are lower in numeracy (Peters, Fennema, & Tiede, 2019). Here, we bring together research on representations of numbers in memory (e.g., Brainerd & Gordon, 1994; Thompson & Siegler, 2010), numeracy, and numerical cognition (e.g., Szkudlarek & Brannon, 2017) and an evidence-based theory of decision-making (e.g., Broniatowski & Reyna, 2018) to examine how individual differences in numerical representation and processing predict important decision paradoxes.…”

Despite high objective numeracy, lower numeric confidence relates to worse financial and medical outcomes

“…In particular, the highly numerate think longer in numeric decisions (16,17). They trust numeric information more (18) and do more (usually simple) numeric operations while attempting to understand what numbers, like dollar amounts, mean for a decision (19)(20)(21). The highly numerate "have a numeric hammer," and they use it.…”