The evaluation of numerical magnitudes in decision making

The evaluation of numerical magnitudes is critical to decision making and implicitly forms the core of many important theories of choice (e.g., Kahneman & Tversky Reference Kahneman and Tversky1979). For example, an individual faced with multiple job offers needs to compare (among other things) their salaries and assign a subjective value or “utility” to each of these monetary amounts before she can make a proper decision. Similarly, in deciding whether to purchase a good, how much of the good to purchase, or how much we are willing to pay for that good, we must be able to assign subjective “disutilities” to the monetary costs of paying for our purchases, to see whether they outweigh the benefits we expect to receive from those purchases. It turns out that subjective evaluations of monetary gains and losses resemble those for numbers and most perceptual magnitudes: People are much more sensitive to differences between small financial gains (or losses) than they are to the same differences between larger gains (or losses) (Kahneman & Tversky Reference Kahneman and Tversky1979; Tversky & Kahneman Reference Tversky and Kahneman1992).

This problem of assigning subjective values (or utilities) to numerical decision outcomes applies to many different types of choice attributes, and not just monetary ones like salaries and prices. For example, a restaurant patron may wish to evaluate the number of calories associated with each item on the menu, whereas a policy maker considering measures to increase road safety needs to evaluate their potential reductions in human fatalities. As with financial gains and losses, subjective evaluations of non-monetary outcomes tend to exhibit diminishing sensitivity (e.g., Olivola Reference Olivola2015; Slovic Reference Slovic2007). Moreover, the role of numerical magnitude evaluation in decision making extends beyond assigning (dis)utilities to the outcomes themselves, as one also needs to consider their likelihoods of occurrence and when (in time) they are expected to occur. Specifically, uncertain or delayed outcomes need to be discounted relative to certain and immediate ones. Research suggests that numerical probabilities are typically transformed non-linearly into an intuitive sense of likelihood (Prelec Reference Prelec1998; Tversky & Kahneman Reference Tversky and Kahneman1992; Wu & Gonzalez Reference Wu and Gonzalez1996). Similarly, research suggests that people tend to evaluate time delays in a non-linear fashion (Frederick et al. Reference Frederick, Loewenstein and O'Donoghue2002; Olivola & Wang Reference Olivola and Wang2016; Read Reference Read, Koehler and Harvey2004).

Recent theoretical and empirical developments

Although there have been continuous efforts by decision-making researchers to map the relationships between choice-relevant numerical magnitudes and their subjective values or weights, most of this research has operated separately from the field of numerical cognition, and very little of it has examined why or how the observed mappings occur (Olivola & Chater Reference Olivola, Chater and Jones2017). Fortunately, the last decade has witnessed a growing interest in understanding how the evaluation of numerical magnitudes relates to decision making, and this has led to several important insights and theoretical advances. We have learned, for example, that individual differences in symbolic-number mapping predict how people value monetary outcomes (Schley & Peters Reference Schley and Peters2014), and that individual differences in subjective perceptions of temporal distance (i.e., how “far away” a given time delay seems) predict how patient people will be when making intertemporal trade-offs (Kim & Zauberman Reference Kim and Zauberman2009; Zauberman et al. Reference Zauberman, Kim, Malkoc and Bettman2009). Some researchers have also proposed a novel theory of decision making that explicitly attempts to explain the magnitude evaluation process that underlies outcome valuation, probability weighting, and time discounting (Stewart Reference Stewart2009; Stewart et al. Reference Stewart, Chater and Brown2006; see also Kornienko Reference Kornienko2013). According to this “decision by sampling” theory, people evaluate monetary and non-monetary outcomes, probabilities, and time delays by comparing them with other relevant values stored in memory. For example, an individual would determine the value of a particular financial gain (e.g., receiving $100) by comparing it with a sample of other financial gains that she has previously experienced or observed. Depending on the composition of her memory sample, the target numerical magnitude being evaluated will either seem large (if it ranks higher than most comparison values), small (if it ranks lower than most), or of medium size (if it ranks close to the median value). It turns out that this theory successfully explains a wide variety of core phenomena in decision making, such as reflective risk preferences (Stewart & Simpson Reference Stewart, Simpson, Chater and Oaksford2008; Stewart et al. Reference Stewart, Chater and Brown2006), loss aversion (Olivola & Sagara Reference Olivola and Sagara2009; Stewart et al. Reference Stewart, Chater and Brown2006; Walasek & Stewart Reference Walasek and Stewart2015), non-linear probability weighting (Stewart et al. Reference Stewart, Chater and Brown2006), hyperbolic discounting (Stewart et al. Reference Stewart, Chater and Brown2006), and the diminishing sensitivity to human fatalities (Olivola & Sagara Reference Olivola and Sagara2009; Olivola et al. Reference Olivola, Rheinberger and Hammitt2017). In doing so, it explicitly connects the process of magnitude evaluation to many important preference patterns.

Evaluations of choice-relevant magnitudes are neither innate nor stable

The research we have discussed also highlights the malleability of choice-relevant magnitude evaluations and thereby casts doubt on the idea that decisions are driven by an innate, universal, and stable sense of number or value. Individuals differ in their perceptions of numbers and time delays, and these differences reliably predict their risk and time preferences (Kim & Zauberman Reference Kim and Zauberman2009; Schley & Peters Reference Schley and Peters2014; Zauberman et al. Reference Zauberman, Kim, Malkoc and Bettman2009). Some of these individual differences are likely the result of variations in people's experiences (Ungemach et al. Reference Ungemach, Stewart and Reimers2011), which in turn reflect differing environments (Olivola & Sagara Reference Olivola and Sagara2009). Consequently, individuals from different countries may perceive and respond very differently to similar outcome magnitudes (Olivola & Sagara Reference Olivola and Sagara2009). In fact, choice-relevant magnitude evaluations can even vary within individuals if the distribution of comparison values changes (Olivola & Sagara Reference Olivola and Sagara2009; Ungemach et al. Reference Ungemach, Stewart and Reimers2011; Walasek & Stewart Reference Walasek and Stewart2015). In sum, these decision-making findings suggest a highly individual- and context-dependent evaluation of numerical magnitudes, rather than a universal and stable “number sense.”