Mathematics, Psychology, and Law: The Legal Ramifications of the Exponential Growth Bias

Eyal Zamir – Faculty of Law, Hebrew University of Jerusalem;

Doron Teichman – Faculty of Law, Hebrew University of Jerusalem

-- The COVID-19 pandemic has drawn attention to the fact that many natural and social processes are characterized by exponential growth, meaning that the rate of change is proportional to the quantity (as, for example, in the series 1, 2, 4, 8, 16, 32…). These include phenomena such as the spread of viral diseases, the accumulation of debt or wealth due to compound interest, and some aspects of global warming. However, as many psychological studies have demonstrated since the 1970s, people face difficulty in grasping the notion of exponential growth, and tend to systematically underestimate it—what has come to be known as the exponential growth bias (EGB). For example, in one of the early studies of the EGB, Wagenaar and Sagaria (1975) found that a great majority of people (90%) gave estimates that were less than half the correct answer; and two-thirds gave estimates that were less than 10% of the correct answer. Surprisingly, the EGB has hardly been mentioned—let alone analyzed systematically—in the legal scholarship.

In our recent paper, Mathematics, Psychology, and Law: The Legal Ramifications of The Exponential Growth Bias, we present the basic mathematics of exponential growth and the psychological findings regarding the exponential growth bias. We then describe several contexts in which the EGB adversely affects the choices individuals and policymakers make, and examine legal means to counteract these adverse effects.

A key example discussed in the Article is that of financial decisions involving compound interest, which by their very nature entail an understanding of exponential processes. Individuals who fail to grasp the long-term impact of compound interest tend to borrow too much to finance their present consumption and save too little for their retirement. Such imprudent decisions may significantly diminish individual welfare, and may even have macro-level and global ramifications, as in the case of the 2007-08 subprime mortgage crisis.

While focusing on the EGB does not offer easy and straightforward solutions, it does call for the introduction of new measures. Thus, disclosure duties should focus on the significance of exponential growth in a bid to encourage people to join pension plans early. For instance, retirement savings statements should elucidate in a simple manner the long-term impact of deposits and fees. At other times, new mandatory rules that would minimize the exploitation of the EGB by profit-maximizing entrepreneurs may be adopted. For example, instead of capping interest rates in consumer credit (or in addition to such capping), it may be advisable to mandate that the periods for which the compound interest is calculated must not be shorter than the repayment period(s). For example, no compound interest would be charged in balloon loans as long as the loan is repaid on time, and no daily compound interest should be allowed in credit cards agreement. People’s limited ability to grasp the speed of exponential growth—and consequently the speed at which such processes may come to a halt in closed environment—may also call for the complete ban of some transactions, such as pyramid schemes.

In the sphere of governmental policymaking, the article reviews numerous examples in which policymakers were late to respond to novel exponential phenomena (the COVID-19 pandemic being a key case in point). Consequently, the article argues that intuitive and “holistic” judgments by laypersons (including politicians) should be replaced or complemented by structured decision processes that rely on empirical evidence and on mathematical models. Given the uncertainty characterizing many exponential processes (e.g., the spread of viral diseases and climate change), such decision methods might not be perfect or all wise, yet they are expected to outperform other decision methods that have been tried from time to time.

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