Forecasting exponential growth and exponential decline: similarities and differences

How well do ordinary Americans forecast the growth of COVID-19?

Across three experiments (N = 1565), we investigated how forecasts about the spread of COVID 19 are impacted by data trends, and whether patterns of misestimation predict adherence to social-distancing guidelines. We also investigated how mode of data presentation influences forecasting of future cases by showing participants data on the number of COVID-19 cases from a 5-week period in either graphical, tabular, or text-only form. We consistently found that people shown tables produced more accurate forecasts compared to people shown line-graphs of the same data; yet people shown line-graphs were more confident in their estimates. These findings suggest that graphs engender false-confidence in the accuracy of forecasts, that people's forecasts of future cases have important implications for their attitudes concerning social distancing, and that tables may be better than graphs for informing the public about the trajectory of COVID-19.

Mathematical media literacy in the COVID-19 pandemic and its relation to school mathematics education

In the first months of 2020, as the COVID-19 pandemic became a top concern worldwide, media coverage became full of information that demands mathematical literacy, or numeracy, to interpret. In this study, we examine the public's understanding of mathematical notions that are required for understanding the pandemic and predicting its spread. We also explore its correlations with several variables: age group and gender, educational attainment in mathematics, and mathematics identity. To do so, we conducted a cross-sectional survey focusing on mathematical knowledge relevant to the pandemic. The survey was distributed to a representative sample of the Jewish Israeli population (n = 439). Findings showed that participants' educational attainment in mathematics was positively correlated with their success in the mathematical media literacy tasks. However, even those with high attainment levels did not always perform well. Moreover, the explanatory variable with the strongest relationship to mathematical media literacy was found to be participants' mathematical identity. These results suggest that school mathematics, especially in its high levels, may prepare adults to understand critical information important for their well-being, such as at a time of global pandemic. However, they also demonstrate that a weak mathematical identity may significantly hinder adults' engagement with such information.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s10649-021-10075-8.

Without a mask: Judgments of Corona virus exposure as a function of inter personal distance

In order to minimize the risk of infection during the Covid-19 pandemic, people are recommended to keep interpersonal distance (e.g., 1 m, 2 m, 6 feet), wash their hands frequently, limit social contacts and sometimes to wear a face mask. We investigated how people judge the protective effect of interpersonal distance against the Corona virus. The REM model, based on earlier empirical studies, describes how a person’s virus exposure decreases with the square of the distance to another person emitting a virus in a face to face situation. In a comparison with model predictions, most participants underestimated the protective effect of moving further away from another person. Correspondingly, most participants were not aware of how much their exposure would increase if they moved closer to the other person. Spectral analysis of judgments showed that a linear ratio model with the independent variable = (initial distance)/(distance to which a person moves) was the most frequently used judgment rule. It leads to insensitivity to change in exposure compared with the REM model. The present study indicated a need for information about the effects of keeping interpersonal distance and about the importance of virus carrying aerosols in environments with insufficient air ventilation. Longer conversations emitting aerosols in a closed environment may lead to ambient concentrations of aerosols in the air that no distance can compensate for. The results of the study are important for risk communications in countries where people do not wear a mask and when authorities consider removal of a recommendation or a requirement to wear a face mask.

Different heuristics and same bias: A spectral analysis of biased judgments and individual decision rules

We used correlation and spectral analyses to investigate the cognitive structures and processes producing biased judgments. We used 5 different sets of driving problems to exemplify problems that trigger biases, specifically: (1) underestimation of the impact of occasional slow speeds on mean speed judgments, (2) overestimation of braking capacity after a speed increase, (3) the time saving bias (overestimation of the time saved by increasing a high speed further, and underestimation of time saved when increasing a low speed), (4) underestimation of increase of fatal accident risk when speed is increased, and (5) underestimation of the increase of stopping distance when speed is increased. The results verified the predicted biases. A correlation analysis found no strong links between biases; only accident risk and stopping distance biases were correlated significantly. Spectral analysis of judgments was used to identify different decision rules. Most participants were consistent in their use of a single rule within a problem set with the same bias. The participants used difference, average, weighed average and ratio rules, all producing biased judgments. Among the rules, difference rules were used most frequently across the different biases. We found no personal consistency in the rules used across problem sets. The complexity of rules varied across problem sets for most participants.

Modeling and debiasing resource saving judgments

Svenson (2011) showed that choices of one of two alternative productivity increases to save production resources (e.g., man-months) were biased. Judgments of resource savings following a speed increase from a low production speed line were underestimated and following an increase of a high production speed line overestimated. The objective formula for computing savings includes differences between inverse speeds and this is intuitively very problematic for most people. The purpose of the present studies was to explore ways of ameliorating or eliminating the bias. Study 1 was a control study asking participants to increase the production speed of one production line to save the same amount of production resources (man-months) as was saved by a speed increase in a reference line. The increases judged to match the reference alternatives showed the same bias as in the earlier research on choices. In Study 2 the same task and problems were used as in Study 1, but the participants were asked first to judge the resource saving of the reference alternative in a pair of alternatives before they proceeded to the matching task. This weakened the average bias only slightly. In Study 3, the participants were asked to judge the resources saved from each of two successive increases of the same single production line (other than those of the matching task) before they continued to the matching problems. In this way a participant could realize that a second production speed increase from a higher speed (e.g., from 40 to 60 items /man-month) gives less resource savings than the same speed increase from a first lower speed (e.g., from 20 to 40 items/man-month. Following this, the judgments of the same problems as in the other studies improved and the bias decreased significantly but it did not disappear. To be able to make optimal decisions about productivity increases, people need information about the bias and/or reformulations of the problems.

The Accuracy of Consumers’ Perception of Future Inflationary Price Changes

Four laboratory experiments were conducted to investigate the extent to which and how consumers encountering inflationary increases in product prices are able to accurately extrapolate future price increases. Between 32 and 48 undergraduates participated in the different experiments. In Experiment 1 it was found that participants were more able to extrapolate a proportional increase when presented with two consecutive proportional price increases compared to one price increase. This finding was not replicated for decreasing prices in Experiment 2. Experiment 3 showed that varying the time interval between prices counteracted an accurate extrapolation of proportional price increases despite that two price increases were presented. In Experiment 4 it was found that presenting the same (vs. different) proportional price increases for two products made participants able to extrapolate the common proportional price increase.

Decisions among time saving options: when intuition is strong and wrong

When people judge the time that can be saved by increasing the speed of an activity, they are often victims of a time saving bias. That is, they overestimate the time that can be saved by increasing the speed. Judgments of time savings following speed increase when driving follow the Proportion heuristic [Svenson, O. (1970). A functional measurement approach to intuitive estimation as exemplified by estimated time savings. Journal of Experimental Psychology, 86, 204-210]. In a choice between time saving options, this heuristic simplifies to the Ratio rule. The first study tested this rule and found that the Ratio rule predicted incorrect decisions when planning to save traveling time in road traffic. The second study showed that the time saving bias was also present in planning of health care; to specify, in decisions about which one of two clinics to reorganize to save more of the doctors' time for personal contacts with patients. To further test the Ratio rule, Study 3 used a matching procedure in which two decision alternatives were made equal by the participants. The results supported the Ratio rule. Practical implications of the results are discussed including the Planning fallacy. In conclusion, the present set of studies have illustrated a time saving bias and provided evidence explaining why people make systematic errors when judging and deciding about time saved following a speed increase.