A big fish or a small pond? Framing effects in percentages Meng Li a,⇑ , Gretchen B. Chapman b a University of Colorado Denver, United States b Department of Psychology, Rutgers University, United States article info Article history: Received 21 March 2012 Accepted 19 July 2013 Accepted by Harris Sondak Keywords: Framing effect Number perception Percentages Judgment and decision making abstract This paper presents three studies that demonstrate people’s preference for a large percentage of a small subset over a small percentage of a large subset, when the net overall quantity is equated. Because the division of a set into subsets is often arbitrary, this preference represents a framing effect. The framing effect is particularly pronounced for large percentages. We propose that the effect has two causes: A par- tial neglect of the subset information, and a non-linear shaped function in the way people perceive percentages. Ó 2013 Elsevier Inc. All rights reserved. Introduction Judgment and decision making research has long demonstrated that people are easily attracted by feelings of certainty—100% probability (certainty effect, Kahneman & Tversky, 1979; Tversky & Kahneman, 1992). Recent research however, has revealed a more general preference for ‘‘100%’’ outside the domain of probability: In Li and Chapman (2009), participants preferred a vaccine described as ‘‘100% effective against 70% of virus strains that cause a specific cancer’’ over one described as ‘‘70% effective against 100% of virus strains that cause the same cancer’’, while both are preferred over vaccines with the same net benefit but that were less than 100% effective toward fewer than 100% of targets. Participants also pre- ferred a 100% discount on a cup of coffee every 10 days, as well as a 10% discount everyday (100% of the days during the year) over other coffee discount programs with in-between amounts and frequencies but the same net savings. This ‘‘100% effect’’ is ironic, because the 100% discount or time coverage are only superficial— they apply to a small subset (i.e., 1 out of every 10 days, or 10% of the price) instead of the whole set. However, people seem to fo- cus on 100% instead of the scope over which the 100% applies. A separate line of research demonstrates that when making probability judgments, children and adults focus on the numerator, and sometimes ignore the denominator. For example, participants viewed 10 out of 13 as a greater chance to win than 9 out of 11 (Reyna & Brainerd, 2008), and a cancer that ‘‘kills 1286 out of 10,000 people’’ (12.86%) as riskier than one that ‘‘kills 24.14 out of 100 people’’ (24.14%) (Yamagishi, 1997). Similarly, a ratio of lar- ger numbers (e.g. 10 in 100) seems larger than the same ratio with smaller numbers (e.g. 1 in 10) (ratio bias, see Pacini & Epstein, 1999). According to Fuzzy Trace Theory (Reyna, 2004; Reyna & Bra- inerd, 1995, 2008), people mainly rely on the gist of information to make judgments, and when they judge risk or probability, extract- ing the gist from both the numerator and denominator becomes difficult because the numerator class (e.g., the number of people who survive a surgery) is included in the denominator class (e.g., the number of people who have the surgery), which creates confu- sion. As a result, people often focus on the salient gist in ratios, that is, the numerator (e.g. how many patients survive the surgery, which relates to the outcome they care about), and ignore the denominator. Arguably, such ‘‘denominator neglect’’ is similar to the 100% ef- fect, which manifests as a focus on the salient 100% and under- weighting of the subset information (e.g., scope of the virus strains targeted by the vaccine). However, the 100% effect cannot be fully explained by a neglect of denominators. Li and Chapman’s study (2009) showed that 100% can be overweighted when it refers to either the discount amount (100% discount) or discount fre- quency (discount everyday—100% of the days), while denominator neglect predicts the neglect of only one dimension (denominator) and overweighting of the other. An additional explanation could be that people perceive percentages in a non-linear fashion, with a convex curvature near 100%. It is unclear what the weighting function for percentages might look like, except that it curves up at 100%. Another distinction between the 100% effect and denom- inator neglect is that in denominator neglect, people are presented with the numerator and denominator information (the ratio of the 0749-5978/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.obhdp.2013.07.003 ⇑ Corresponding author. Address: Department of Health and Behavioral Sciences, University of Colorado Denver, Campus Box 188, PO Box 173364, Denver, CO 80217- 3364, United States. Fax: +1 (303) 556 8501. E-mail address: meng.li@ucdenver.edu (M. Li). Organizational Behavior and Human Decision Processes 122 (2013) 190–199 Contents lists available at ScienceDirect Organizational Behavior and Human Decision Processes journal homepage: www.elsevier.com/locate/obhdp