Magnitude Representations Underlie Valuations of Prospects

In his original conception of expected utility, Daniel Bernoulli (1738; 1954) proposed that individuals generally have diminishing marginal utility (DMU). Much in the same way that an additional spoonful of sugar provides a smaller additional taste sensation than the previous spoonful of sugar (i.e., satiation), an additional dollar of wealth provides a proportionally smaller additional utility than the previous dollar. Current conceptualizations of DMU suppose that consumers simply value additional dollars of wealth less. Rather, we suggest that consumers are simply less sensitive to greater numeric magnitudes. In the current article we demonstrate that an individual’s ability to “value” money, goods, and services depends critically upon their ability to perceive differences in the numeric magnitudes of the money, goods, and services. Previous research in numerical cognition has demonstrated that individuals have curvilinear representations of magnitude (Dehaene et al., 2008; Furlong and Opfer, 2009; Siegler and Opfer, 2003; Opfer and Siegler, 2007; Siegler, Thompson, and Opfer, 2009; Birnbaum, 1974; Anobile, Cicchini, and Burr, 2012; Peters et al. 2008). Although an individual may know that 1,000 is 10 times as large as 100, their subjective representation of 1,000 is often much less than 10 times as large as their subjective representation of 100. In the current article, we propose that the extent of DMU may be related to how individuals represent numeric magnitudes. In particular, we suggest that a gain of $1,000 may not be perceived as ten times as beneficial as a gain of $100 because the magnitude of “1,000” is not perceived as ten times as large as the magnitude of “100”. Across three studies, we tested this hypothesized relation in a riskless paradigm, a risky-choice paradigm, and in a consumer judgment paradigm.