>[!abstract] >Exponential growth bias is the phenomenon that humans intuitively underestimate exponential growth ([[Schonger & Sele, 2021]]). ^a9cd55 The exponential growth bias (EGB) manifests itself whenever there is a self-reinforcing multiplicative effect over time, such as financial compounding (e.g., economic growth, personal loans, or personal savings), feedback loops (e.g., in the spread of a disease, or climate change), or asymptotic changes past an inflection point (e.g., the moment artificial intelligence starts improving itself in runaway fashion). ## Terminology Note that the word "exponential" is slightly inaccurate here. The cognitive bias applies when humans underestimate any form of *multiplicative* growth, which applies broadly to all exponential-style growth, whether it is strictly *geometric* (discrete doubling, such as $2^n$) or actually exponential (continuous compounding, such as $N_0 \times e^{rt}$). In practice, the cognitive bias and the resulting error is the same in both cases, because we tend to think linearly and assume that growth *adds*, not *multiplies*. ## Examples - The [[Wheat-and-chessboard problem|wheat-and-chessboard problem]]: an ancient mathematical parable from India where doubling one grain of rice 64 times in a row (geometric growth) amounts to more rice than there are grains of sand on Earth. - The [[Penny-doubling riddle|penny-doubling riddle]]: is it preferable to receive $1 million upfront or to have one penny double every day for 30 days (geometric growth)? The latter is more than five times larger than the former by day 30. - [[Amara's law]]: assuming technological growth is multiplicative and not additive, we tend to overestimate its effects in the short run and underestimate them in the long run. ## Studies Studies have consistently observed the exponential growth bias effect in household finance, infectious disease estimation, etc. - [[Wagenaar & Sagaria, 1975|Wagenaar & Sagaria (1975)]] found that the effect is not reduced by special instructions to test subjects about the nature of exponential growth nor daily experience with growth processes. - [[Wagenaar & Timmers, 1979|Wagenaar & Timmers (1979)]] found that the effect is not limited to situations in which the process is presented in tables and graphs, but extends to those situations in which it is presented as a visual development over time. - [[Stango & Zinman, 2009|Stango & Zinman (2009)]] found that the effect can explain the tendency for households to underestimate an interest rate given other loan terms, *and* the tendency to underestimate a future value given other investment terms (i.e., it applies negatively to both borrowing and investing). - [[Mckenzie & Liersch, 2019|Mckenzie & Liersch (2019)]] found that the effect leads people to underestimate the amount of interest their savings will have accrued at retirement, leading them to put off saving. - [[Lammers et al., 2020|Lammers et al. (2020)]] showed that the effect led to people underestimating the spread of COVID–19, and that actively correcting that bias promoted support for social distancing measures. - [[Teichman & Zamir, 2022|Teichman & Zamir (2022)]] showed that the EGB extends to policymaking, and requires that we design new institutions and decision making processes to respond promptly to risks involving exponential growth, such as pandemics and climate change. ## Causal factors I assume that the effect is caused by at least two factors: 1. Our brains are shaped by evolutionary forces that span tens or hundreds of thousands of years (Homo sapiens in its current form is approximately 300,000 years old). Throughout that evolutionary period, most change has occurred linearly and slowly. The [[Great Acceleration]] (in carbon emissions, cultural shifts, demographic explosion, energy consumption, hyper-financialization of the economy, manufacturing output, technological innovation, travel intensity, etc.) is only a recent inflection point, coinciding with the rise of the [[Anthropocene]]. Adapting our primate brains to what this unprecedented era of human history is about to unlock requires that we make a conscious and unintuitive mental effort that does not come naturally. 2. It is easy to calculate a terminal value from a starting value by applying a non-compounding growth rate multiple times, because the underlying mechanism is a simple sum (e.g., $100 plus $5 interest paid out ten times = $150). Conversely, it is very difficult to calculate a terminal value if the interests are compounding (e.g., $100 plus 5% CAGR over ten periods = $162.89). >[!related] >- **North** (upstream): — >- **West** (similar): — >- **East** (different): — >- **South** (downstream): [[Amara's law]]; [[Penny-doubling riddle]]; [[Wheat-and-chessboard problem]]