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Correcting misperceptions of exponential coronavirus growth increases support for social distancing

Correcting misperceptions of exponential coronavirus growth increases support for social distancing Correcting misperceptions of exponential coronavirus growth increases support for social distancing a,1 b b Joris Lammers , Jan Crusius , and Anne Gast a b Psychology Department, University of Bremen, 28359 Bremen, Germany; and Social Cognition Center Cologne, University of Cologne, 50923 Cologne, Germany Edited by Susan T. Fiske, Princeton University, Princeton, NJ, and approved June 15, 2020 (received for review March 31, 2020) The most effective way to stem the spread of a pandemic such as consistently apply linear thinking have particularly strong confi- coronavirus disease 2019 (COVID-19) is social distancing, but the dence in their erroneous forecasts (9, 10). introduction of such measures is hampered by the fact that a size- The current work tests the role of exponential growth bias in able part of the population fails to see their need. Three studies shaping the public’s view on social distancing to contain the conducted during the mass spreading of the virus in the United coronavirus’s spreading. We first test, in study 1, whether people States toward the end of March 2020 show that this results par- underestimate the exponential growth of the coronavirus. More- tially from people’s misperception of the virus’s exponential over, we aim to show that the degree to which people show this growth in linear terms and that overcoming this bias increases bias depends, in part, on their political background. President support for social distancing. Study 1 shows that American partic- Trump displayed exponential growth bias during the initial stages ipants mistakenly perceive the virus’s exponential growth in linear of the coronavirus outbreak, when he focused only on the initially terms (conservatives more so than liberals). Studies 2 and 3 show low absolute numbers and ignored that exponential growth would that instructing people to avoid the exponential growth bias sig- quickly multiply those numbers (4). We test whether Republican nificantly increases perceptions of the virus’s growth and thereby supporters similarly show stronger exponential growth bias than increases support for social distancing. Together, these results liberals. show the importance of statistical literacy to recruit support for Building on this observation that some show an increased fighting pandemics such as the coronavirus. exponential growth bias in their perception of the coronavirus compared to others (due to incorrect information), we then test, coronavirus exponential growth bias statistical literacy comparison | | | in studies 2 and 3, whether the exponential growth bias can also be decreased with experimental instructions (that present correct he threat that a pandemic such as coronavirus disease 2019 information). Furthermore, we test whether such instructions T(COVID-19) poses is grave. Given the lack of a vaccine, the can also increase support for social distancing. On the one hand, most effective available measure to fight and contain such viruses literature until now shows that the exponential growth bias is is social distancing. This can buy time for medical science to de- strongly resistant against instructions to correct for it (5–10). On velop a treatment and can allow medical services the time to the other hand, the coronavirus outbreak is a unique moment in prepare for the ensuing surge in patients. Many countries across history that directly impacts people’s deepest concerns about the globe have followed this strategy and have introduced social their lives and those of their loved ones. Exposure to news showing distancing measures. At the same time, sizeable opposition among that the virus has grown remarkably quickly in other parts of the politicians and the general population has delayed, prevented, or world may increase the availability of the concept of exponential terminated early measures to increase social distancing. For ex- ample, toward the end of March 2020, a month in which, in the Significance United States, the number of infections increased from a few dozen to 200,000 cases, one in four Americans opposed social Given the current lack of an effective vaccine to prevent distancing measures (1). Most strikingly, at the same time, even coronavirus disease 2019 (COVID-19), one of the most effective heads of state such as American President Trump or Brazilian ways to prevent the illness is social distancing. At the same President Bolsonaro repeatedly downplayed the growth of the time, a sizeable portion of the public fails to see the necessity virus and opposed social distancing measures (2, 3). of such measures. We identify one root cause for this: People We propose that a root cause for why a sizeable portion of the mistakenly perceive the coronavirus to grow in a linear man- people doubt the necessity of introducing such drastic measures ner, underestimating its actual potential for exponential growth. is that people fail to recognize that the coronavirus can grow in We show that correcting this perceptual error significantly in- an exponential manner, and, instead, erroneously perceive its creases support for social distancing. This research shows the growth in linear terms. A striking example of this is President importance of statistical literacy among the general public for Trump, who remained fixated on the low number of early infec- increasing support to fight the coronavirus using the most ef- tions in the United States and appeared not to realize how quickly fective method currently available. this low number could spiral out of control (4). But, more in general, this prediction builds on literature showing that people, in Author contributions: J.L. designed research; J.L. performed research; J.L. analyzed data; general, have difficulty understanding exponential growth and and J.L., J.C., and A.G. wrote the paper. erroneously interpret it in linear terms instead (5). This expo- The authors declare no competing interest. nential growth bias is remarkably robust. It is shown when people This article is a PNAS Direct Submission. extrapolate the growth of abstract numerical values, but it is also This open access article is distributed under Creative Commons Attribution License 4.0 shown when growth is made easier to relate to—such as that of (CC BY). duckweed in a pond (6). The effect also occurs when correct es- Data deposition: Data and code are available at Open Science Framework at https://osf.io/ xjwbg/. timates are incentivized, and it even shows up among those with greater mathematical sophistication or with relevant experience To whom correspondence may be addressed. Email: joris.lammers@uni-koeln.de. with growth processes (5, 7, 8). Making matters worse, people are This article contains supporting information online at https://www.pnas.org/lookup/suppl/ doi:10.1073/pnas.2006048117/-/DCSupplemental. overly confident in their ability to predict change. Particularly, those who have least knowledge about exponential growth and First published June 24, 2020. 16264–16266 | PNAS | July 14, 2020 | vol. 117 | no. 28 www.pnas.org/cgi/doi/10.1073/pnas.2006048117 significant ideology × linear trend (P < 0.0001) suggested that conservatives were more likely to underestimate the virus’s absolute growth compared to liberals. A significant ideology × quadratic trend (P = 0.006) showed that conservatives also underestimated the exponential nature of that growth more than did liberals (Fig. 1; data split across the neutral midpoint between liberals and conservatives, for presentation purposes). Again, note that, compared to liberals, conservatives did not underestimate but overestimated the number of virus infections in the first 3 d of the week (all P < 0.001). In other words, compared to liberals, conservatives did not underestimate the problem (defined as number of infections) per se, but underestimated its exponential growth. Study 2. Our next aim was to test whether this incorrect perception of the coronavirus’s growth could be corrected by instructing participants about exponential growth and whether doing so also affects support for social distancing measures. To do so, we repeated the design of study 1, but randomly assigned participants to one of two conditions. After providing consent, participants in the experimental condition received the following Fig. 1. Study 1: Participants, on average, show exponential growth bias and instructions, that were based on the virus’s recent developments (19): underestimate the slope of the coronavirus growth curve over the past week, falsely believing the number to be higher early in the week than it Please keep in mind that many people forget that the speed by which was (gray, dashed line shows actual total number). Conservatives (red) do so the corona virus spreads, increases each day. In other words, when more strongly than liberals (blue) (continuous data split across the neutral making these guesses, many people erroneously think that the coro- midpoint, for presentation purposes). navirus cases have increased at a steady and constant pace. In reality, in the USA (as in almost all other countries) the number of corona patients doubles and keeps doubling every three days. growth or at least the perceptual readiness to understand it and its In the control condition, participants did not receive these instructions. implications (11, 12). Indeed, earlier findings show that experience Next, participants guessed the number of coronavirus cases between Tues- day, March 17 and Monday, March 23. These experimental instructions af- with exponential growth—such as in the case of hyperinflation in fected participants’ perceptions of the growth of the virus (P = 0.003). Israel in the early 1980s—can increase susceptibility to informa- Following this up by testing interactions between condition and polynomial tion that can help to overcome exponential growth bias (13). contrasts, we found no significant condition × linear trend interaction (P = Based on this, we expected that people would be susceptible to 0.104), but only a significant condition × quadratic trend interaction (P = information that can help them to correct for their biased per- 0.001), suggesting that the experimental instruction primarily corrected ception of the coronavirus. participants’ misunderstanding of the virus’s exponential growth (Fig. 2). Consistent with predictions, participants in the experimental condition were Method and Results also significantly more supportive of social distancing than participants in To test these ideas, we conducted three studies in the second half of March the control condition (P = 0.019). 2020—a period in which the coronavirus in the United States increased particularly rapidly. This allows us to compare subjective growth perception Study 3. An even more effective way to increase support for social distancing and prediction with actual growth rates. Across these studies, we recruited (compared to changing people’s beliefs about past growth) may be cor- American participants online via Amazon MTurk, a web-based tool for recting beliefs about the virus’s future growth. After providing consent, all recruiting and paying participants to perform tasks. MTurk samples have participants read the current estimated number of coronavirus infections in been shown to be as representative of the US population as other sam- the United States and the current statistic that it doubles every 3 d (19). pling methods (14, 15). To avoid the most critical problem with MTurk Next, all participants guessed the development of the virus’s spread over the samples—nonnaïveté (16)—participants were barred from taking part in next 15 d. In the experimental condition, participants were instructed to more than one study. All three studies were conducted consistent with the arrive at their estimate in five steps, first guessing the number of active Declaration of Helsinki, and all three are exempt from Institutional Review coronavirus cases in four intermediate steps, each 3 d apart. Because this Board approval by guidelines of the German Psychological Society DGPS time frame matched the statistic (provided to all participants) that the (Deutsche Gesellschaft für Psychologie) (17). Data and code are available at number of cases doubles every third day, this helped participants under- https://osf.io/xjwbg/ (18). stand the implications of exponential growth. In the control condition, participants instead made an immediate estimate of the number of cases Study 1. After providing consent, participants guessed the total number of after 2 wk. Importantly, these participants received the same statistical in- coronavirus cases over the past 5 d, from Tuesday, March 17 to Saturday, formation (including the current number of cases and its speed of doubling) March 21. As expected, participants displayed exponential growth bias. Al- though some participants accurately included exponential growth in their estimates, thus producing an overall significant quadratic trend (F = 18.78, P < 0.0001), its size was dwarfed by the strong linear trend (F = 470.55, P < 0.0001), meaning that participants’ averaged estimates of the virus’s growth could, for practical purposes, be described as linear (Fig. 1, dark gray line). Comparing participants’ estimates against linear and quadratic trends in the actual data of the virus’s growth (Fig. 1, dashed black line), drawn from the Worldometer COVID-19 database (19), we found that participants under- estimated both the virus’s linear (P < 0.0001) and exponential growth (P < 0.0001). Note that, as a result of their failure to see exponential growth, participants did not simply underestimate the number of cases throughout the observed time period. In fact, they overestimated the number of known coronavirus cases in the first 3 d of the week (all P < 0.0001) and under- estimated the number in the last 2 d of the week (both P < 0.0001). On average, they underestimated the actual growth of the virus’s over that time period by 45.7% (P < 0.0001). As also expected, this tendency to underestimate exponential growth was Fig. 2. Study 2: Instructing participants to correct for exponential growth not fixed but instead depended on participants’ political ideology (P < bias (blue) partially reduces the biased perception the coronavirus growth, 0.0001), which we measured using a validated continuous scale (20). A compared to a control condition (red). Dashed line shows actual total number. Lammers et al. PNAS | July 14, 2020 | vol. 117 | no. 28 | 16265 PSYCHOLOGICAL AND COGNITIVE SCIENCES in largely linear terms. This effect was stronger among conser- vatives than liberals (study 1), who followed President Trump’s incorrect remarks about the virus. This shows the danger of politicians’ downplaying of the virus. Furthermore, we found that participants can be helped to correct for the exponential growth bias in estimating the virus’s development in the recent past (study 2) and immediate future (study 3). These interventions not only help overcome exponential growth bias, but they also significantly increase support for social distancing—the most effective available way to prevent spreading of the coronavirus. Our results stand in contrast to earlier literature that shows that the exponential growth bias is difficult to overcome (5–10, 21). Instead, in our studies, a three-sentence instruction not to make the mistake (study 2) or an instruction to estimate through four intermediate steps (study 3) effectively reduced the bias. A Fig. 3. Study 3: Instructing participants to estimate the number of cases at difference between our and earlier studies is that we focused on the end of 2 wk by making four intermediate steps helps them understand a threat with great personal relevance and media presence, which the potential implications of exponential growth (blue), compared to a likely increases subjective availability and thus estimated proba- control condition (red). bility of the risk. This possibly increases the readiness to un- derstand exponential growth when instructed about it and reduces the underestimation of exponential growth (11–13). but were not instructed to make the four intermediate guesses. As expected, These findings demonstrate the real-life implications of ex- participants in the experimental condition produced 173% higher final es- ponential growth bias. Earlier work shows the bias affects timates of the number of known cases of coronavirus infection after 2 wk, households’ financial decisions (22), but the current findings show than control participants (P < 0.0001; Fig. 3). Furthermore, being helped to that it also influences political opinions about matters of life and realize the potential implications of exponential growth in the near future, participants in the experimental condition were significantly more sup- death. Given that social distancing is the most effective way to portive of measures to increase social distancing and a lockdown than combat the coronavirus currently available, these findings are of control participants (P = 0.024). Finally, a mediation analysis showed that the great impact. More generally, our findings show the importance of latter effect of condition on support for social distancing was statistically statistical literacy and echo calls to improve that skill among the mediated by the former effect on participants’ final estimates (P = 0.011). general public (23, 24). Discussion ACKNOWLEDGMENTS. This research was supported by Deutsche For- Across three studies, we found evidence of exponential growth schungsgemeinschaft (German Research Foundation) Grant LA 3566/1-1, and bias in people’s perceptions of the coronavirus’s spread, meaning by a grant under Germany´s Excellence Strategy, Grant EXC 2126/1– that people erroneously perceive the virus’s exponential growth 390838866. 1. Morning Consult/Politico, As Trump eyes restarting economy, nearly 3 in 4 voters 13. G. Keren, Cultural differences in the misperception of exponential growth. Percept. support national quarantine. https://morningconsult.com/2020/03/25/coronavirus-national- Psychophys. 34, 289–293 (1983). 14. C. Huff, D. Tingley, “Who are these people?” Evaluating the demographic charac- quarantine-trump/ (2020). Accessed 28 May 2020. teristics and political preferences of MTurk survey respondents. Research Politics 2, 2. A. Karni, D. G. McNeil Jr, Trump wants U.S. ‘opened up’ by Easter, despite health 1–12 (2015). officials’ warnings. NY Times, 24 March 2020. https://www.nytimes.com/2020/03/24/us/ 15. A. J. Berinsky, G. A. Huber, G. S. Lenz, Evaluating online labor markets for experi- politics/trump-coronavirus-easter.html (2020). Accessed 28 May 2020. mental research: Amazon.com’s Mechanical Turk. Polit. Anal. 20, 351–368 (2012). 3. BBC News, Coronavirus: Bolsonaro downplays threat of pandemic to Brazil. https:// 16. J. Chandler, G. Paolacci, E. Peer, P. Mueller, K. A. Ratliff, Using nonnaive participants www.bbc.com/news/world-latin-america-52040205 (2020). Accessed 28 May 2020. can reduce effect sizes. Psychol. Sci. 26, 1131–1139 (2015). 4. White House, Remarks by President Trump, Vice President Pence, and members of the 17. Deutsche Gesellschaft für Psychologie, Ethisches Handeln in der psychologischen Coronavirus Task Force in press conference. https://www.whitehouse.gov/briefings- Forschung: Empfehlungen der Deutschen Gesellschaft für Psychologie für Forschende statements/remarks-president-trump-vice-president-pence-members-coronavirus-task-force- und Ethikkommissionen, (Hogrefe, Göttingen, Germany, 2018). press-conference/ (2020). Accessed 28 May 2020. 18. J. Lammers, J. Crusius, A. Gast, Correcting misperceptions of exponential coronavirus 5. W. A. Wagenaar, S. D. Sagaria, Misperception of exponential growth. Percept. Psy- growth increases support for social distancing. Open Science Framework. https://osf. chophys. 18, 416–422 (1975). io/xjwbg. Deposited 19 June 2020. 6. W. A. Wagenaar, H. Timmers, The pond-and-duckweed problem: Three experiments 19. Worldometer, Worldometer COVID-19 database: USA data. https://www.worldometers. on the misperception of exponential growth. Percept. Psychophys. 43,239–251 (1979). info/coronavirus/country/us/ (2020). Accessed: 28 May 2020. 7. F. Christandl, D. Fetchenhauer, How laypeople and experts misperceive the effect of 20. M. Baldwin, J. Lammers, Past-focused environmental comparisons promote pro- economic growth. J. Econ. Psychol. 30, 381–392 (2009). environmental outcomes for conservatives. Proc. Natl. Acad. Sci. U.S.A. 113, 14953–14957 8. M. Levy, J. Tasoff, Exponential-growth bias and lifecycle consumption. J. Eur. Econ. (2016). Assoc. 14, 545–583 (2016). 21. W. A. Wagenaar, H. Timmers, Extrapolation of exponential time series is not en- 9. M. R. Levy, J. Tasoff, Exponential-growth bias and overconfidence. J. Econ. Psychol. hanced by having more data points. Percept. Psychophys. 24, 182–184 (1978). 58,1–14 (2017). 22. V. Stango, J. Zinman, Exponential growth bias and household finance. J. Finance 64, 10. E. F. Williams, D. Dunning, J. Kruger, The hobgoblin of consistency: Algorithmic 2807–2849 (2009). judgment strategies underlie inflated self-assessments of performance. J. Pers. Soc. 23. G. Gigerenzer, W. Gaissmaier, E. Kurz-Milcke, L. M. Schwartz, S. Woloshin, Helping Psychol. 104, 976–994 (2013). doctors and patients make sense of health statistics. Psychol. Sci. Public Interest 8, 11. J. S. Bruner, On perceptual readiness. Psychol. Rev. 64, 123–152 (1957). 53–96 (2007). 12. A. Tversky, D. Kahneman, Availability: A heuristic for judging frequency and proba- 24. K. K. Wallman, Enhancing statistical literacy: Enriching our society. J. Am. Stat. Assoc. bility. Cognit. Psychol. 5, 207–232 (1973). 88,1–8 (1993). 16266 | www.pnas.org/cgi/doi/10.1073/pnas.2006048117 Lammers et al. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Proceedings of the National Academy of Sciences of the United States of America Pubmed Central

Correcting misperceptions of exponential coronavirus growth increases support for social distancing

Proceedings of the National Academy of Sciences of the United States of America , Volume 117 (28) – Jun 24, 2020

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Abstract

Correcting misperceptions of exponential coronavirus growth increases support for social distancing a,1 b b Joris Lammers , Jan Crusius , and Anne Gast a b Psychology Department, University of Bremen, 28359 Bremen, Germany; and Social Cognition Center Cologne, University of Cologne, 50923 Cologne, Germany Edited by Susan T. Fiske, Princeton University, Princeton, NJ, and approved June 15, 2020 (received for review March 31, 2020) The most effective way to stem the spread of a pandemic such as consistently apply linear thinking have particularly strong confi- coronavirus disease 2019 (COVID-19) is social distancing, but the dence in their erroneous forecasts (9, 10). introduction of such measures is hampered by the fact that a size- The current work tests the role of exponential growth bias in able part of the population fails to see their need. Three studies shaping the public’s view on social distancing to contain the conducted during the mass spreading of the virus in the United coronavirus’s spreading. We first test, in study 1, whether people States toward the end of March 2020 show that this results par- underestimate the exponential growth of the coronavirus. More- tially from people’s misperception of the virus’s exponential over, we aim to show that the degree to which people show this growth in linear terms and that overcoming this bias increases bias depends, in part, on their political background. President support for social distancing. Study 1 shows that American partic- Trump displayed exponential growth bias during the initial stages ipants mistakenly perceive the virus’s exponential growth in linear of the coronavirus outbreak, when he focused only on the initially terms (conservatives more so than liberals). Studies 2 and 3 show low absolute numbers and ignored that exponential growth would that instructing people to avoid the exponential growth bias sig- quickly multiply those numbers (4). We test whether Republican nificantly increases perceptions of the virus’s growth and thereby supporters similarly show stronger exponential growth bias than increases support for social distancing. Together, these results liberals. show the importance of statistical literacy to recruit support for Building on this observation that some show an increased fighting pandemics such as the coronavirus. exponential growth bias in their perception of the coronavirus compared to others (due to incorrect information), we then test, coronavirus exponential growth bias statistical literacy comparison | | | in studies 2 and 3, whether the exponential growth bias can also be decreased with experimental instructions (that present correct he threat that a pandemic such as coronavirus disease 2019 information). Furthermore, we test whether such instructions T(COVID-19) poses is grave. Given the lack of a vaccine, the can also increase support for social distancing. On the one hand, most effective available measure to fight and contain such viruses literature until now shows that the exponential growth bias is is social distancing. This can buy time for medical science to de- strongly resistant against instructions to correct for it (5–10). On velop a treatment and can allow medical services the time to the other hand, the coronavirus outbreak is a unique moment in prepare for the ensuing surge in patients. Many countries across history that directly impacts people’s deepest concerns about the globe have followed this strategy and have introduced social their lives and those of their loved ones. Exposure to news showing distancing measures. At the same time, sizeable opposition among that the virus has grown remarkably quickly in other parts of the politicians and the general population has delayed, prevented, or world may increase the availability of the concept of exponential terminated early measures to increase social distancing. For ex- ample, toward the end of March 2020, a month in which, in the Significance United States, the number of infections increased from a few dozen to 200,000 cases, one in four Americans opposed social Given the current lack of an effective vaccine to prevent distancing measures (1). Most strikingly, at the same time, even coronavirus disease 2019 (COVID-19), one of the most effective heads of state such as American President Trump or Brazilian ways to prevent the illness is social distancing. At the same President Bolsonaro repeatedly downplayed the growth of the time, a sizeable portion of the public fails to see the necessity virus and opposed social distancing measures (2, 3). of such measures. We identify one root cause for this: People We propose that a root cause for why a sizeable portion of the mistakenly perceive the coronavirus to grow in a linear man- people doubt the necessity of introducing such drastic measures ner, underestimating its actual potential for exponential growth. is that people fail to recognize that the coronavirus can grow in We show that correcting this perceptual error significantly in- an exponential manner, and, instead, erroneously perceive its creases support for social distancing. This research shows the growth in linear terms. A striking example of this is President importance of statistical literacy among the general public for Trump, who remained fixated on the low number of early infec- increasing support to fight the coronavirus using the most ef- tions in the United States and appeared not to realize how quickly fective method currently available. this low number could spiral out of control (4). But, more in general, this prediction builds on literature showing that people, in Author contributions: J.L. designed research; J.L. performed research; J.L. analyzed data; general, have difficulty understanding exponential growth and and J.L., J.C., and A.G. wrote the paper. erroneously interpret it in linear terms instead (5). This expo- The authors declare no competing interest. nential growth bias is remarkably robust. It is shown when people This article is a PNAS Direct Submission. extrapolate the growth of abstract numerical values, but it is also This open access article is distributed under Creative Commons Attribution License 4.0 shown when growth is made easier to relate to—such as that of (CC BY). duckweed in a pond (6). The effect also occurs when correct es- Data deposition: Data and code are available at Open Science Framework at https://osf.io/ xjwbg/. timates are incentivized, and it even shows up among those with greater mathematical sophistication or with relevant experience To whom correspondence may be addressed. Email: joris.lammers@uni-koeln.de. with growth processes (5, 7, 8). Making matters worse, people are This article contains supporting information online at https://www.pnas.org/lookup/suppl/ doi:10.1073/pnas.2006048117/-/DCSupplemental. overly confident in their ability to predict change. Particularly, those who have least knowledge about exponential growth and First published June 24, 2020. 16264–16266 | PNAS | July 14, 2020 | vol. 117 | no. 28 www.pnas.org/cgi/doi/10.1073/pnas.2006048117 significant ideology × linear trend (P < 0.0001) suggested that conservatives were more likely to underestimate the virus’s absolute growth compared to liberals. A significant ideology × quadratic trend (P = 0.006) showed that conservatives also underestimated the exponential nature of that growth more than did liberals (Fig. 1; data split across the neutral midpoint between liberals and conservatives, for presentation purposes). Again, note that, compared to liberals, conservatives did not underestimate but overestimated the number of virus infections in the first 3 d of the week (all P < 0.001). In other words, compared to liberals, conservatives did not underestimate the problem (defined as number of infections) per se, but underestimated its exponential growth. Study 2. Our next aim was to test whether this incorrect perception of the coronavirus’s growth could be corrected by instructing participants about exponential growth and whether doing so also affects support for social distancing measures. To do so, we repeated the design of study 1, but randomly assigned participants to one of two conditions. After providing consent, participants in the experimental condition received the following Fig. 1. Study 1: Participants, on average, show exponential growth bias and instructions, that were based on the virus’s recent developments (19): underestimate the slope of the coronavirus growth curve over the past week, falsely believing the number to be higher early in the week than it Please keep in mind that many people forget that the speed by which was (gray, dashed line shows actual total number). Conservatives (red) do so the corona virus spreads, increases each day. In other words, when more strongly than liberals (blue) (continuous data split across the neutral making these guesses, many people erroneously think that the coro- midpoint, for presentation purposes). navirus cases have increased at a steady and constant pace. In reality, in the USA (as in almost all other countries) the number of corona patients doubles and keeps doubling every three days. growth or at least the perceptual readiness to understand it and its In the control condition, participants did not receive these instructions. implications (11, 12). Indeed, earlier findings show that experience Next, participants guessed the number of coronavirus cases between Tues- day, March 17 and Monday, March 23. These experimental instructions af- with exponential growth—such as in the case of hyperinflation in fected participants’ perceptions of the growth of the virus (P = 0.003). Israel in the early 1980s—can increase susceptibility to informa- Following this up by testing interactions between condition and polynomial tion that can help to overcome exponential growth bias (13). contrasts, we found no significant condition × linear trend interaction (P = Based on this, we expected that people would be susceptible to 0.104), but only a significant condition × quadratic trend interaction (P = information that can help them to correct for their biased per- 0.001), suggesting that the experimental instruction primarily corrected ception of the coronavirus. participants’ misunderstanding of the virus’s exponential growth (Fig. 2). Consistent with predictions, participants in the experimental condition were Method and Results also significantly more supportive of social distancing than participants in To test these ideas, we conducted three studies in the second half of March the control condition (P = 0.019). 2020—a period in which the coronavirus in the United States increased particularly rapidly. This allows us to compare subjective growth perception Study 3. An even more effective way to increase support for social distancing and prediction with actual growth rates. Across these studies, we recruited (compared to changing people’s beliefs about past growth) may be cor- American participants online via Amazon MTurk, a web-based tool for recting beliefs about the virus’s future growth. After providing consent, all recruiting and paying participants to perform tasks. MTurk samples have participants read the current estimated number of coronavirus infections in been shown to be as representative of the US population as other sam- the United States and the current statistic that it doubles every 3 d (19). pling methods (14, 15). To avoid the most critical problem with MTurk Next, all participants guessed the development of the virus’s spread over the samples—nonnaïveté (16)—participants were barred from taking part in next 15 d. In the experimental condition, participants were instructed to more than one study. All three studies were conducted consistent with the arrive at their estimate in five steps, first guessing the number of active Declaration of Helsinki, and all three are exempt from Institutional Review coronavirus cases in four intermediate steps, each 3 d apart. Because this Board approval by guidelines of the German Psychological Society DGPS time frame matched the statistic (provided to all participants) that the (Deutsche Gesellschaft für Psychologie) (17). Data and code are available at number of cases doubles every third day, this helped participants under- https://osf.io/xjwbg/ (18). stand the implications of exponential growth. In the control condition, participants instead made an immediate estimate of the number of cases Study 1. After providing consent, participants guessed the total number of after 2 wk. Importantly, these participants received the same statistical in- coronavirus cases over the past 5 d, from Tuesday, March 17 to Saturday, formation (including the current number of cases and its speed of doubling) March 21. As expected, participants displayed exponential growth bias. Al- though some participants accurately included exponential growth in their estimates, thus producing an overall significant quadratic trend (F = 18.78, P < 0.0001), its size was dwarfed by the strong linear trend (F = 470.55, P < 0.0001), meaning that participants’ averaged estimates of the virus’s growth could, for practical purposes, be described as linear (Fig. 1, dark gray line). Comparing participants’ estimates against linear and quadratic trends in the actual data of the virus’s growth (Fig. 1, dashed black line), drawn from the Worldometer COVID-19 database (19), we found that participants under- estimated both the virus’s linear (P < 0.0001) and exponential growth (P < 0.0001). Note that, as a result of their failure to see exponential growth, participants did not simply underestimate the number of cases throughout the observed time period. In fact, they overestimated the number of known coronavirus cases in the first 3 d of the week (all P < 0.0001) and under- estimated the number in the last 2 d of the week (both P < 0.0001). On average, they underestimated the actual growth of the virus’s over that time period by 45.7% (P < 0.0001). As also expected, this tendency to underestimate exponential growth was Fig. 2. Study 2: Instructing participants to correct for exponential growth not fixed but instead depended on participants’ political ideology (P < bias (blue) partially reduces the biased perception the coronavirus growth, 0.0001), which we measured using a validated continuous scale (20). A compared to a control condition (red). Dashed line shows actual total number. Lammers et al. PNAS | July 14, 2020 | vol. 117 | no. 28 | 16265 PSYCHOLOGICAL AND COGNITIVE SCIENCES in largely linear terms. This effect was stronger among conser- vatives than liberals (study 1), who followed President Trump’s incorrect remarks about the virus. This shows the danger of politicians’ downplaying of the virus. Furthermore, we found that participants can be helped to correct for the exponential growth bias in estimating the virus’s development in the recent past (study 2) and immediate future (study 3). These interventions not only help overcome exponential growth bias, but they also significantly increase support for social distancing—the most effective available way to prevent spreading of the coronavirus. Our results stand in contrast to earlier literature that shows that the exponential growth bias is difficult to overcome (5–10, 21). Instead, in our studies, a three-sentence instruction not to make the mistake (study 2) or an instruction to estimate through four intermediate steps (study 3) effectively reduced the bias. A Fig. 3. Study 3: Instructing participants to estimate the number of cases at difference between our and earlier studies is that we focused on the end of 2 wk by making four intermediate steps helps them understand a threat with great personal relevance and media presence, which the potential implications of exponential growth (blue), compared to a likely increases subjective availability and thus estimated proba- control condition (red). bility of the risk. This possibly increases the readiness to un- derstand exponential growth when instructed about it and reduces the underestimation of exponential growth (11–13). but were not instructed to make the four intermediate guesses. As expected, These findings demonstrate the real-life implications of ex- participants in the experimental condition produced 173% higher final es- ponential growth bias. Earlier work shows the bias affects timates of the number of known cases of coronavirus infection after 2 wk, households’ financial decisions (22), but the current findings show than control participants (P < 0.0001; Fig. 3). Furthermore, being helped to that it also influences political opinions about matters of life and realize the potential implications of exponential growth in the near future, participants in the experimental condition were significantly more sup- death. Given that social distancing is the most effective way to portive of measures to increase social distancing and a lockdown than combat the coronavirus currently available, these findings are of control participants (P = 0.024). Finally, a mediation analysis showed that the great impact. More generally, our findings show the importance of latter effect of condition on support for social distancing was statistically statistical literacy and echo calls to improve that skill among the mediated by the former effect on participants’ final estimates (P = 0.011). general public (23, 24). Discussion ACKNOWLEDGMENTS. This research was supported by Deutsche For- Across three studies, we found evidence of exponential growth schungsgemeinschaft (German Research Foundation) Grant LA 3566/1-1, and bias in people’s perceptions of the coronavirus’s spread, meaning by a grant under Germany´s Excellence Strategy, Grant EXC 2126/1– that people erroneously perceive the virus’s exponential growth 390838866. 1. Morning Consult/Politico, As Trump eyes restarting economy, nearly 3 in 4 voters 13. G. Keren, Cultural differences in the misperception of exponential growth. Percept. support national quarantine. https://morningconsult.com/2020/03/25/coronavirus-national- Psychophys. 34, 289–293 (1983). 14. C. Huff, D. Tingley, “Who are these people?” Evaluating the demographic charac- quarantine-trump/ (2020). Accessed 28 May 2020. teristics and political preferences of MTurk survey respondents. Research Politics 2, 2. A. Karni, D. G. McNeil Jr, Trump wants U.S. ‘opened up’ by Easter, despite health 1–12 (2015). officials’ warnings. NY Times, 24 March 2020. https://www.nytimes.com/2020/03/24/us/ 15. A. J. Berinsky, G. A. Huber, G. S. Lenz, Evaluating online labor markets for experi- politics/trump-coronavirus-easter.html (2020). Accessed 28 May 2020. mental research: Amazon.com’s Mechanical Turk. Polit. Anal. 20, 351–368 (2012). 3. BBC News, Coronavirus: Bolsonaro downplays threat of pandemic to Brazil. https:// 16. J. Chandler, G. Paolacci, E. Peer, P. Mueller, K. A. Ratliff, Using nonnaive participants www.bbc.com/news/world-latin-america-52040205 (2020). Accessed 28 May 2020. can reduce effect sizes. Psychol. Sci. 26, 1131–1139 (2015). 4. White House, Remarks by President Trump, Vice President Pence, and members of the 17. Deutsche Gesellschaft für Psychologie, Ethisches Handeln in der psychologischen Coronavirus Task Force in press conference. https://www.whitehouse.gov/briefings- Forschung: Empfehlungen der Deutschen Gesellschaft für Psychologie für Forschende statements/remarks-president-trump-vice-president-pence-members-coronavirus-task-force- und Ethikkommissionen, (Hogrefe, Göttingen, Germany, 2018). press-conference/ (2020). Accessed 28 May 2020. 18. J. Lammers, J. Crusius, A. Gast, Correcting misperceptions of exponential coronavirus 5. W. A. Wagenaar, S. D. Sagaria, Misperception of exponential growth. Percept. Psy- growth increases support for social distancing. Open Science Framework. https://osf. chophys. 18, 416–422 (1975). io/xjwbg. Deposited 19 June 2020. 6. W. A. Wagenaar, H. Timmers, The pond-and-duckweed problem: Three experiments 19. Worldometer, Worldometer COVID-19 database: USA data. https://www.worldometers. on the misperception of exponential growth. Percept. Psychophys. 43,239–251 (1979). info/coronavirus/country/us/ (2020). Accessed: 28 May 2020. 7. F. Christandl, D. Fetchenhauer, How laypeople and experts misperceive the effect of 20. M. Baldwin, J. Lammers, Past-focused environmental comparisons promote pro- economic growth. J. Econ. Psychol. 30, 381–392 (2009). environmental outcomes for conservatives. Proc. Natl. Acad. Sci. U.S.A. 113, 14953–14957 8. M. Levy, J. Tasoff, Exponential-growth bias and lifecycle consumption. J. Eur. Econ. (2016). Assoc. 14, 545–583 (2016). 21. W. A. Wagenaar, H. Timmers, Extrapolation of exponential time series is not en- 9. M. R. Levy, J. Tasoff, Exponential-growth bias and overconfidence. J. Econ. Psychol. hanced by having more data points. Percept. Psychophys. 24, 182–184 (1978). 58,1–14 (2017). 22. V. Stango, J. Zinman, Exponential growth bias and household finance. J. Finance 64, 10. E. F. Williams, D. Dunning, J. Kruger, The hobgoblin of consistency: Algorithmic 2807–2849 (2009). judgment strategies underlie inflated self-assessments of performance. J. Pers. Soc. 23. G. Gigerenzer, W. Gaissmaier, E. Kurz-Milcke, L. M. Schwartz, S. Woloshin, Helping Psychol. 104, 976–994 (2013). doctors and patients make sense of health statistics. Psychol. Sci. Public Interest 8, 11. J. S. Bruner, On perceptual readiness. Psychol. Rev. 64, 123–152 (1957). 53–96 (2007). 12. A. Tversky, D. Kahneman, Availability: A heuristic for judging frequency and proba- 24. K. K. Wallman, Enhancing statistical literacy: Enriching our society. J. Am. Stat. Assoc. bility. Cognit. Psychol. 5, 207–232 (1973). 88,1–8 (1993). 16266 | www.pnas.org/cgi/doi/10.1073/pnas.2006048117 Lammers et al.

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