The processing of sequentially presented numerical information is a prerequisite for decisions from experience, where people learn about potential outcomes and their associated probabilities and then make choices between gambles. Little is known, however, about how people's preference for choosing a gamble is affected by how they perceive and process numerical information. To address this, we conducted a series of experiments wherein participants repeatedly sampled numbers from continuous outcome distributions. They were incentivized either to estimate the means of the numbers or to state their minimum selling prices to forgo a consequential draw from the distributions (i.e., the certainty equivalents or valuations). We found that participants valued distributions below their means, valued high-variance sequences lower than low-variance sequences, and valued left-skewed sequences lower than right-skewed sequences. Though less pronounced, similar patterns occurred in the mean estimation task where preferences should not play a role. These results are not consistent with prior findings in decision from experience such as the overweighting of high numbers and the underweighting of rare events. Rather, the qualitative effects, as well as the similarity of effects in valuation and estimation, are consistent with the assumption that people process numbers on a compressed mental number line in valuations from experience.

Scientific theories reflect some of humanity's greatest epistemic achievements. The best theories motivate us to search for discoveries, guide us towards successful interventions, and help us to explain and organize knowledge. Such theories require a high degree of specificity, and specifying them requires modeling skills. Unfortunately, in psychological science, theories are often not precise, and psychological scientists often lack the technical skills to formally specify existing theories. This problem raises the question: How can we promote formal theory development in psychology, where there are many content experts but few modelers? In this paper, we discuss one strategy for addressing this issue: a Many Modelers approach. Many Modelers consist of mixed teams of modelers and non-modelers that collaborate to create a formal theory of a phenomenon. We report a proof of concept of this approach, which we piloted as a three-hour hackathon at the SIPS 2021 conference. We find that (a) psychologists who have never developed a formal model can become excited about formal modeling and theorizing; (b) a division of labor in formal theorizing could be possible where only one or a few team members possess the prerequisite modeling expertise; and (c) first working prototypes of a theoretical model can be created in a short period of time.

In the age of digitalization and globalization, our decision environments have become increasingly complex. However, it remains unclear under what circumstances complexity affects risk taking. In two experiments (one with a representative sample), we go beyond the behavioral effects and provide a cognitive explanation for the impact of complexity on risk taking. Results show that complexity, defined as the number of outcomes of a risky lottery, decreased choice propensity in choices between two lotteries but had a smaller effect on valuations of individual lotteries. Importantly, participants who spent less time looking at the complex option in choices, were less affected by complexity. Thus, a dislike of cognitive effort can explain the effect of complexity and the difference between choice and valuation. The small effect of complexity on valuations could be explained by individual differences in cognitive ability. Together, we showed that the decision environment as well as individual differences affected the impact of complexity on risk taking and we discuss cognitive explanations for these phenomena.

Past research on numerical cognition has suggested that both symbolic and non-symbolic numbers are mapped onto the same compressed mental analogue representation. However, experiments using magnitude estimation tasks show logarithmic compression of symbolic numbers while the compression of non-symbolic numbers has a power-function shape. This warrants closer inspection of what differentiates the two processes. In this study, we hypothesized that estimates of symbolic numbers are systematically shaped by the format in which they are represented, namely, the place value system. To investigate this, we tested adults (N = 188) on a magnitude estimation task with unfamiliar base-26 and base-5 scales. Results reveal that adults showed systematic, logarithmic-looking underestimation on both scales, indicating that the place value system itself can cause the pattern. Additionally, the observed shape of participants’ estimates on both scales could be well explained with a simple model that assumed insufficient understanding of exponential growth (i.e., a characteristic of place value systems). Taken together, our results suggest that the discrepancy between symbolic and non-symbolic number compression can be explained by taking the effect of the place value system into account.