scholarly journals Intuition and exponential growth: bias and the roles of parameterization and complexity

Author(s):  
Martin Schonger ◽  
Daniela Sele

AbstractExponential growth bias is the phenomenon that humans intuitively underestimate exponential growth. This article reports on an experiment where treatments differ in the parameterization of growth: Exponential growth is communicated to one group in terms of growth rates, and in terms of doubling times to the other. Exponential growth bias is much smaller when doubling times are employed. Considering that in many applications, individuals face a choice between different growth rates, rather than between exponential growth and zero growth, we ask a question where growth is reduced from high to low. Subjects vastly underestimate the effect of this reduction, though less so in the parameterization using doubling times. The answers to this question are more severely biased than one would expect from the answers to the exponential growth questions. These biases emerge despite the sample being highly educated and exhibiting awareness of exponential growth bias. Implications for teaching, the usefulness of heuristics, and policy are discussed.

2020 ◽  
Author(s):  
Martin J. Prince ◽  
Atalay Alem ◽  
Dixon Chibanda ◽  
Lara Fairall ◽  
Abebaw Fekadu ◽  
...  

ABSTRACTBackgroundThe COVID-19 outbreak in sub-Saharan African countries started after those in Asia, Europe and North America, on 28th February 2020. The susceptibility to infection of populations in that region has been debated. Outbreaks on the scale of those seen elsewhere would pose substantial challenges. There are reasons for concern that transmission may be high and difficult to control, rapidly exceeding capacity to meet the needs for hospitalization and critical care.MethodsWe obtained data on daily new confirmed cases for all 46 countries from the World Health Organization, and used these to model and visualize growth trajectories using an AutoRegressive Integrated Moving Average (ARIMA) model. We then estimated doubling times from growth rates estimated from Poisson regression models, and by back counting from the most recent observation. We also calculated the time from 1st to 50th case, and the time from 5th to 100th case. These indicators were compared with the same summary indicators of growth at the same stage of the outbreak in highly affected European countries.ResultsKenya was the only country with clear evidence of exponential growth. Nineteen countries had either reported no cases, were in the first few days of the outbreak, or had reported fewer than 10 cases over a period of two or more weeks. For the remaining 27 countries we identified four growth patterns: slow linear growth, more rapid linear growth, variable growth patterns over the course of the outbreak, and early signs of possible exponential growth. For those in the last three groups, doubling times ranged from 3 to 4 days, times from 1st to 50th case from 12 to 29 days, and from 5th to 100th case from eight to 15 days. These early indicators are comparable to those in European countries that have gone on to have substantial outbreaks, and time to 50th case was shorter suggesting lesser effectiveness of contact-tracing and quarantine in the early phase.ConclusionThe 46 sub-Saharan African countries, home to over one billion people, are at a tipping point with clear potential for the outbreak to follow a similar course as in HIC in the global north. Radical population-level physical distancing measures may be required, but their impact on poor, disadvantaged and vulnerable people and communities need mitigating. Health systems in the region need urgent technical and material support, with testing, personal protection, and hospital/ critical care.


PLoS ONE ◽  
2020 ◽  
Vol 15 (12) ◽  
pp. e0242839
Author(s):  
Martin Schonger ◽  
Daniela Sele

Exponential growth bias is the phenomenon whereby humans underestimate exponential growth. In the context of infectious diseases, this bias may lead to a failure to understand the magnitude of the benefit of non-pharmaceutical interventions. Communicating the same scenario in different ways (framing) has been found to have a large impact on people’s evaluations and behavior in the contexts of social behavior, risk taking and health care. We find that framing matters for people’s assessment of the benefits of non-pharmaceutical interventions. In two commonly used frames, most subjects in our experiment drastically underestimate the number of cases avoided by adopting non-pharmaceutical interventions. Framing growth in terms of doubling times rather than growth rates reduces the bias. When the scenario is framed in terms of time gained rather than cases avoided, the median subject assesses the benefit of non-pharmaceutical interventions correctly. These findings suggest changes that could be adopted to better communicate the exponential spread of infectious diseases.


Author(s):  
Michael Ahmed

This paper re-evaluates the significance of Sir Curtis Seretse, a black character from the 1960s television series Department S (ITV 1969-70) which has largely been ignored. While earlier critical and academic discourse of Department S has primarily centred on the flamboyant Jason King, the importance of Seretse’s character has been overlooked. Seretse, as the head of Department S, is in a position of authority and power over the other (white) characters of the show. Furthermore, he represents a highly educated character that converses on equal terms with Prime Ministers and Presidents, a unique representation of a black character on British television at that time. Seretse’s appearance on prime time television, at a period when black performers in the media were invariably confined to little more than token characters, is therefore worthy of further attention. This paper examines how Seretse represents a different type of black character not previously seen on British television, when compared to the representations of racial problems on other television crime dramas.


2020 ◽  
Vol 4 (Supplement_1) ◽  
pp. 445-445
Author(s):  
Mengya Wang ◽  
Suzanne Bartholomae

Abstract Financial security in retirement is a major concern for many Americans. Numerous studies document that Americans are not prepared for retirement, with financial illiteracy cited as one reason Americans fail to plan. Employing data from the 2018 National Financial Capability Study (N=27,091), this study investigates actual financial literacy (AFL) and perceived financial literacy (PFL) and how combinations of this measure influences retirement planning, and varies based on years from retirement. This study found relatively low financial literacy and retirement preparedness levels among the US sample, even for those pre-retirees ages 55 to 64. Individually, PFL and AFL increased as one approached retirement. When combined, adults nearing retirement (55 to 64) comprised the greatest proportion of the high AFL and high PFL (29.9%) group compared to adults 20 years or more from retirement (18-44) who largely made up the low AFL and PFL (48%) group. Based on a logistic regression, adults closest to retirement (ages 55 to 64) are more likely to be planning compared to the other groups, as are adults who were financially confident, risk takers, highly educated, males, and white. Compared to adults with high AFL and high PFL, adults with low AFL and low PFL, or a combination (low PFL and high AFL, high PFL and low AFL) have lower odds of preparing for retirement. Both PFL and AFL influences retirement planning, and PFL may be as important as AFL. Our highlight the importance of policies and programs to support Americans with retirement planning.


2014 ◽  
Vol 25 (08) ◽  
pp. 937-953
Author(s):  
ARSENY M. SHUR

We study FAD-languages, which are regular languages defined by finite sets of forbidden factors, together with their “canonical” recognizing automata. We are mainly interested in the possible asymptotic orders of growth for such languages. We analyze certain simplifications of sets of forbidden factors and show that they “almost” preserve the canonical automata. Using this result and structural properties of canonical automata, we describe an algorithm that effectively lists all canonical automata having a sink strong component isomorphic to a given digraph, or reports that no such automata exist. This algorithm can be used, in particular, to prove the existence of a FAD-language over a given alphabet with a given exponential growth rate. On the other hand, we give an example showing that the algorithm cannot prove non-existence of a FAD-language having a given growth rate. Finally, we provide some examples of canonical automata with a nontrivial condensation graph and of FAD-languages with a “complex” order of growth.


1980 ◽  
Vol 94 (1) ◽  
pp. 95-104 ◽  
Author(s):  
G. J. Rowlands

SummaryBlood samples were taken at 9, 10 and 11 weeks of age from 230 male Hereford × Friesian calves, the progeny of 12 Hereford bulls. Concentrations of blood glucose, serum albumin, inorganic phosphate and sodium were measured and correlated with body weights and growth rates until slaughter at 19½ months of age.Correlations between growth rates and glucose concentrations (0·44) and between growth rates and albumin concentrations (0·38) were observed until 4 months of age. Similar correlations between body weights and blood glucose or albumin concentrations persisted until 6 months of age. By 10 months, however, the correlations had begun to decline, and by slaughter they had become insignificant.Correlations between growth rates and inorganic phosphate or sodium concentrations were smaller, and also decreased with age.The effect of hypoglycaemia on growth rate was compared with the effect of enzootic pneumonia. Although the 10% of calves with the lowest glucose concentrations were growing 24% more slowly than the other calves at the time of sampling, this growth depression was not related to pneumonia, and they subsequently made up for most of the early loss of growth.Three blood samples were also taken from 22 Hereford bulls. No significant correlations were observed between the blood composition of the bulls and the body weights or weight gains of their progeny.


2021 ◽  
Author(s):  
Sevtap Tırınk ◽  
Alper Nuhoğlu ◽  
Sinan Kul

Abstract This study encompasses investigation of treatment of pistachio processing industry wastewaters in a batch reactor under aerobic conditions, calculation of kinetic parameters and comparison of different inhibition models. The mixed microorganism culture used in the study was adapted to pistachio processing industry wastewaters for nearly one month and then concentrations from 50-1000 mg L− 1 of pistachio processing industry wastewaters were added to the medium and treatment was investigated in batch experiments. The Andrews, Han-Levenspiel, Luong and Aiba biokinetic equations were chosen for the correlations between the concentration of pistachio processing industry wastewaters and specific growth rates, and the kinetic parameters in these biokinetic equations were calculated. The µmax, Ks and Ki parameters, included in the Aiba biokinetic equation providing best fit among the other equations, had values calculated as 0.25 h− 1, 19 mg L− 1, and 516 mg L− 1, respectively.


10.37236/413 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
M. H. Albert ◽  
M. D. Atkinson ◽  
R. Brignall ◽  
N. Ruškuc ◽  
Rebecca Smith ◽  
...  

Pattern classes which avoid $321$ and other patterns are shown to have the same growth rates as similar (but strictly larger) classes obtained by adding articulation points to any or all of the other patterns. The method of proof is to show that the elements of the latter classes can be represented as bounded merges of elements of the original class, and that the bounded merge construction does not change growth rates.


1998 ◽  
Vol 42 ◽  
pp. 499-507 ◽  
Author(s):  
M. Koubi

1995 ◽  
Vol 32 (3) ◽  
pp. 591-608 ◽  
Author(s):  
Chinsan Lee ◽  
Grace L. Yang

Asymptotic formulas for means and variances of a multitype decomposable age-dependent supercritical branching process are derived. This process is a generalization of the Kendall–Neyman–Scott two-stage model for tumor growth. Both means and variances have exponential growth rates as in the case of the Markov branching process. But unlike Markov branching, these asymptotic moments depend on the age of the original individual at the start of the process and the life span distribution of the progenies.


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