Misperception of Exponential Growth: Are People Aware of Their Errors? | Decision Analysis

People Reject Algorithms in Uncertain Decision Domains Because They Have Diminishing Sensitivity to Forecasting Error

Will people use self-driving cars, virtual doctors, and other algorithmic decision-makers if they outperform humans? The answer depends on the uncertainty inherent in the decision domain. We propose that people have diminishing sensitivity to forecasting error and that this preference results in people favoring riskier (and often worse-performing) decision-making methods, such as human judgment, in inherently uncertain domains. In nine studies ( N = 4,820), we found that (a) people have diminishing sensitivity to each marginal unit of error that a forecast produces, (b) people are less likely to use the best possible algorithm in decision domains that are more unpredictable, (c) people choose between decision-making methods on the basis of the perceived likelihood of those methods producing a near-perfect answer, and (d) people prefer methods that exhibit higher variance in performance (all else being equal). To the extent that investing, medical decision-making, and other domains are inherently uncertain, people may be unwilling to use even the best possible algorithm in those domains.

Misunderstanding Savings Growth: Implications for Retirement Savings Behavior

People systematically underestimate exponential growth. This article illustrates this phenomenon, its implications, and some potential interventions in the context of saving for retirement, where savings grow exponentially over long periods of time. Experiment 1 shows that a majority of participants expect savings over 40 years to grow linearly rather than exponentially, leading them to grossly underestimate their account balance at retirement. Experiment 2 demonstrates that this misunderstanding leads to underestimates of the cost of waiting to save, which makes putting off saving more attractive than it should be. Finally, Experiments 3–5 show that highlighting the exponential growth of savings motivates both college students and employees to save more for retirement. Making clear to employees the exponential growth of savings before they make crucial decisions about how much to save may be a simple and effective means of increasing retirement savings.

Behavioral Impediments to Valuing Annuities: Complexity and Choice Bracketing

Abstract This paper examines two behavioral factors that diminish people's ability to value a lifetime income stream or annuity, drawing on a randomized experiment with about 4,000 adults in a U.S. nationally representative sample. We find that increasing the complexity of the annuity choice reduces respondents' ability to value the annuity, measured by the difference between the sell and buy values they assign to the annuity. When we limit narrow choice bracketing by inducing people to think first about how quickly or slowly to spend down assets in retirement, their ability to value an annuity increases.

Rational Inattention: A Review

We review the recent literature on rational inattention, identify the main theoretical mechanisms, and explain how it helps us understand a variety of phenomena across fields of economics. The theory of rational inattention assumes that agents cannot process all available information, but they can choose which exact pieces of information to attend to. Several important results in economics have been built around imperfect information. Nowadays, many more forms of information than ever before are available due to new technologies, and yet we are able to digest little of it. Which form of imperfect information we possess and act upon is thus largely determined by which information we choose to pay attention to. These choices are driven by current economic conditions and imply behavior that features numerous empirically supported departures from standard models. Combining these insights about human limitations with the optimizing approach of neoclassical economics yields a new, generally applicable model.

Exponential Growth Bias and Household Finance

ABSTRACT Exponential growth bias is the pervasive tendency to linearize exponential functions when assessing them intuitively. We show that exponential growth bias can explain two stylized facts in household finance: the tendency to underestimate an interest rate given other loan terms, and the tendency to underestimate a future value given other investment terms. Bias matters empirically: More‐biased households borrow more, save less, favor shorter maturities, and use and benefit more from financial advice, conditional on a rich set of household characteristics. There is little evidence that our measure of exponential growth bias merely proxies for broader financial sophistication.

Behaviorally Informed Policies for Household Financial Decisionmaking

Low incomes, limited financial literacy, fraud, and deception are just a few of the many intractable economic and social factors that contribute to the financial difficulties that households face today. Addressing these issues directly is difficult and costly. But poor financial outcomes also result from systematic psychological tendencies, including imperfect optimization, biased judgments and preferences, and susceptibility to influence by the actions and opinions of others. Some of these psychological tendencies and the problems they cause may be countered by policies and interventions that are both low cost and scalable. We detail the ways that these behavioral factors contribute to consumers’ fiancial mistakes and suggest a set of interventions that the federal government, in its dual roles as regulator and employer, could feasibly test or implement to improve household financial outcomes in a variety of domains: retirement, short-term savings, debt management, the take-up of government benefits, and tax optimization.

Eliciting Beliefs with Random Generation Tasks

Elicitation methods, such as asking people to produce the deciles of a distribution, are standard practices in policy or applied statistics. Similarly, much of cognitive science and psychology focuses on determining people's people's beliefs or latent traits through questionnaires or judgment tasks. However, these approaches often only capture a rough outline of what people know and are usually limited to point estimates of people's beliefs. Here, we present a novel experimental paradigm that allows us to access people's beliefs and how variable these beliefs are. Our task is based on an established random generation paradigm in which participants produce quantities from a particular domain as randomly as possible. We hypothesize that due to the minds' general-purpose mechanisms for probabilistic inferences, these random sequences represent the participants' underlying prior beliefs. We show that our method can infer participants' beliefs for a wide range of numeric quantities at comparable accuracy as an established elicitation method. Moreover, these inferred beliefs are consistent with individual participants' generalization and inference patterns in a subsequent conditional prediction task. We then extend our approach to non-numeric belief elicitation, highlighting how our method can go beyond numeric elicitation and provide insight into complex beliefs that are challenging to assess experimentally. Empirically, our results highlight that people know the rough shapes of environmental distributions, and these beliefs guide inference and generalization. Moreover, using our novel approach, we also show that people know the fine details of environmental distributions. Finally, our experimental results show that random generation paradigms can be a useful tool for cognitive scientists, psychologists, and applied statisticians.

Resource-rational belief revision can mitigate as well as amplify polarization

People's beliefs sometimes diverge after observing the same information, which has been interpreted as evidence of irrationality. This behaviour has been proposed to result from people's limited cognitive resources and motivated reasoning, but how belief revision differs across these explanations has not been formalized or compared to a rational norm. Further, while people may be biased relative to a normative ideal, they may still make optimal choices given their limited cognitive resources, or rationally balance the utility of holding accurate beliefs with the belief's intrinsic utility. Across two studies, we develop and test a unified computational account of belief polarization under these proposed mechanisms, showing that people's performance on a belief updating task best fits a limited-resource Bayesian model; external motivations may contribute to divergence (or convergence) by determining what pre-existing information people consider relevant to a situation, rather than by changing how people evaluate new information in isolation.

A Theory of Narrow Thinking

Abstract Unlike in standard models, decision makers often narrowly bracket and make each decision in isolation. I develop a new approach, which I term narrow thinking, to systematically model narrow bracketing. The definition of narrow thinking is that different decisions are based on different, non-nested, information. As a result, the narrow thinker makes each decision with imperfect knowledge of other decisions and faces difficulties coordinating her multiple decisions. The narrow thinker effectively cares less about her other decisions when making each decision. The main application of narrow thinking is to provide a smooth model of mental accounting without requiring the decision maker to have explicit budgets. My approach generates unique predictions about how the degree of mental accounting depends on expenditure shares and cognitive limitations. It also illustrates how narrow bracketing and mental accounting can be explained by the same underlying friction.

The Exception Is the Rule: Underestimating and Overspending on Exceptional Expenses

Abstract Purchases fall along a continuum from ordinary (common or frequent) to exceptional (unusual or infrequent), with many of the largest expenses (e.g., electronics, celebrations) being the most exceptional. Across seven studies, we show that, while people are fairly adept at budgeting and predicting how much they will spend on ordinary items, they both underestimate their spending on exceptional purchases overall and overspend on each individual purchase. Based on the principles of mental accounting and choice bracketing, we show that this discrepancy arises in part because consumers categorize exceptional expenses too narrowly, construing each as a unique occurrence and consequently overspending across a series of discretely exceptional expenses. We conclude by proposing an intervention that diminishes this tendency by helping consumers consider their spending on exceptional items as part of a larger set of purchases.

Adult age differences in monetary decisions with real and hypothetical reward

Abstract Age differences in monetary decisions may emerge because younger and older adults perceive the value of outcomes differently. Yet, age‐differential effects of monetary rewards on decisions are not well understood. Most laboratory studies on aging and decision making have used scenarios in which rewards were merely hypothetical (decisions did not have any real consequences) or in which only small amounts of money were at stake. In the current study, we compared younger adults' (20–29 years) and older adults' (61–82 years) decisions in probabilistic choice problems with real or hypothetical rewards. Decision‐contingent rewards were in a typical range of previous studies (gains of up to ~4.25 USD) or substantially scaled up (gains of up to ~85 USD per participant). Reward type (real vs. hypothetical) affected decision quality, including value maximization, switching between options, and dominance violations (choices of an option that was inferior to another option in all respects). Decision quality was markedly better with real than hypothetical rewards in older adults and correlated with numeracy in both age groups. However, we found no evidence that reward type affected people's risk preferences. Overall, the findings portray a fairly positive picture regarding the use of hypothetical scenarios to assess preferences: With carefully prepared instructions, people from different age groups indicate preferences in hypothetical scenarios that match their decisions with real and much higher rewards. One advantage of using real rewards is that they help to reduce decision noise.

Harnessing naturally occurring data to measure the response of spending to income

Balancing your incomings and outgoings Economic theory predicts that when someone receives money should have little effect on their spending patterns. Gelman et al. constructed a data set of 60 million transactions made by 75,000 people to test this theory. People do seem to go on a mini–spending spree after they get their paychecks or pensions. However, closer inspection reveals that that's mostly explained by the convenience of linking regular payments, such as rent and utilities, to regular income. Unsurprisingly, cash-strapped people are more likely to increase their spending in response to receiving income. Science , this issue p. 212 , How do theoretical predictions of individual fiscal behaviors match up against real-world, real-time data? , This paper presents a new data infrastructure for measuring economic activity. The infrastructure records transactions and account balances, yielding measurements with scope and accuracy that have little precedent in economics. The data are drawn from a diverse population that overrepresents males and younger adults but contains large numbers of underrepresented groups. The data infrastructure permits evaluation of a benchmark theory in economics that predicts that individuals should use a combination of cash management, saving, and borrowing to make the timing of income irrelevant for the timing of spending. As in previous studies and in contrast to the predictions of the theory, there is a response of spending to the arrival of anticipated income. The data also show, however, that this apparent excess sensitivity of spending results largely from the coincident timing of regular income and regular spending. The remaining excess sensitivity is concentrated among individuals with less liquidity.

5: Behavioural biases in personal finance

Behavioural economics merges psychology and economics to explore systematic deviations in financial decision-making from traditional economic models. This chapter examines key biases such as mental accounting, present bias, planning fallacy, and misunderstanding of risk, which influence spending, saving, investing, and insuring decisions. Demonstrating the interplay of cognitive biases and heuristics highlights why individuals make suboptimal choices despite financial literacy and resource capacity. Strategies like goal-setting, commitment devices, and education interventions are evaluated, focusing on their limitations and potential for addressing these biases. The chapter concludes by emphasising the need for systemic changes, such as policy-level interventions and financial regulation, to complement behavioural interventions and address structural barriers to better financial decisions. Future research directions are suggested, including tailoring interventions, exploring technology's role, and integrating systemic solutions to support sustainable financial well-being.

Temporal Reframing and Participation in a Savings Program: A Field Experiment

This study explores whether framing savings in more or less granular formats can increase sign-ups for a recurring deposit program in a FinTech environment. , A growing number of American workers are now freelancers and thus, responsible for their own retirement savings, yet they face psychological hurdles that hamper them from saving enough money for the long term. Although prior theory-derived interventions have been successful in addressing some of these obstacles, encouraging participation in saving programs is a challenging endeavor for policy makers and consumers alike. In a field setting, we test whether framing savings in more or less granular formats (for example, saving daily versus monthly) can encourage continued saving behavior through increasing the take up of a recurring deposit program. Among thousands of new users of a financial technology app, we find that framing deposits in daily amounts as opposed to monthly amounts quadruples the number of consumers who enroll. Furthermore, framing deposits in more granular terms reduced the participation gap between lower- and higher-income consumers: three times as many consumers in the highest rather than lowest income bracket participated in the program when it was framed as a $150 monthly deposit, but this difference in participation was eliminated when deposits were framed as $5 per day.

Algorithm appreciation: People prefer algorithmic to human judgment

Even though computational algorithms often outperform human judgment, received wisdom suggests that people may be skeptical of relying on them (Dawes, 1979). Counter to this notion, results from six experiments show that lay people adhere more to advice when they think it comes from an algorithm than from a person. People showed this effect, what we call algorithm appreciation, when making numeric estimates about a visual stimulus (Experiment 1A) and forecasts about the popularity of songs and romantic attraction (Experiments 1B and 1C). Yet, researchers predicted the opposite result (Experiment 1D). Algorithm appreciation persisted when advice appeared jointly or separately (Experiment 2). However, algorithm appreciation waned when: people chose between an algorithm’s estimate and their own (versus an external advisor’s; Experiment 3) and they had expertise in forecasting (Experiment 4). Paradoxically, experienced professionals, who make forecasts on a regular basis, relied less on algorithmic advice than lay people did, which hurt their accuracy. These results shed light on the important question of when people rely on algorithmic advice over advice from people and have implications for the use of “big data” and algorithmic advice it generates.

The Unaccountability Machine: Why Big Systems Make Terrible Decisions—and How the World Lost Its Mind

Longlisted for the 2024 Financial Times Book of the Year. How life and the economy became a black box—a collection of systems no one understands, producing outcomes no one likes.   Passengers get bumped from flights. Phone menus disconnect. Automated financial trades produce market collapse. Of all the challenges in modern life, some of the most vexing come from our relationships with automation: a large system does us wrong, and there’s nothing we can do about it. The problem, economist Dan Davies shows, is accountability sinks: systems in which decisions are delegated to a complex rule book or set of standard procedures, making it impossible to identify the source of mistakes when they happen. In our increasingly unhuman world—lives dominated by algorithms, artificial intelligence, and large organizations—these accountability sinks produce more than just aggravation. They make life and economy unknowable—a black box for no reason. In The Unaccountability Machine, Davies lays bare how markets, institutions, and even governments systematically generate outcomes that no one—not even those involved in making them—seems to want. Since the earliest days of the computer age, theorists have foreseen the dangers of complex systems without personal accountability. In response, British business scholar Stafford Beer developed an accountability-first approach to management called “cybernetics,” which might have taken off had his biggest client (the Chilean government) not fallen to a bloody coup in 1973. With his signature blend of economic and journalistic rigor, Davies examines what’s gone wrong since Beer, including what might have been had the world embraced cybernetics when it had the chance. The Unaccountability Machine is a revelatory and resonant account of how modern life became predisposed to dysfunction.