Working Papers

When Risk is More (vs. Less) Probable: The Impact of Denominator Magnitude on Probability Judgment

Consumers often have trouble making sense of uncertain information that is communicated in ratio terms (e.g., 1 in 100 chances of developing an illness) and are therefore prone to making biased judgments. Particularly, two seemingly conflicting effects that bias consumers’ probability judgment have been documented in the literature. One is the 1-in-X effect, which refers to people’s overestimation of risk when it is communicated in the 1-in-X format, as opposed to the X-in-N format. For instance, people rated the risk of contracting Malaria higher when the chances were communicated as 1-in-13 rather than 10-in-130. In the case of the 1-in-X bias, the ratio with the smaller numerator is rated higher than the ratio with the larger numerator. On the other hand, ratio bias, or the denominator neglect, refers to people’s tendency to evaluate ratios that are represented by larger numerators as more likely than ratios represented by smaller numerators. For instance, when cancer was described as killing “1,286 out of 10,000 people”, it was perceived as riskier than when it was described as killing “24.14 out of 100 people”. This happens because people focus on the numerator (1,286 is larger than 24.14) at the expense of factoring in the denominator. In this research, we propose that the size of the denominator used in the ratio will determine whether people will make a probabilistic judgment that is consistent with the 1-in-X bias or one that is consistent with the denominator neglect bias. In so doing, we propose and demonstrate a U-shaped relationship between denominator magnitude and the perceived outcome likelihood. Specifically, holding the ratio size constant, when two ratios have relatively small denominators (i.e., numbers that are fairly easily comprehensible for human mind), the ratio with smaller denominator will be perceived as more likely than the ratio with larger denominator. 

When are Fresh Starts (De)Motivating?

In this research, we examine the effect of employing fresh starts during the goal pursuit process on goal achievement. We are designing a longitudinal real-behavior study with Fordham students where the students will be asked to track their discretionary expenses over the course of one month. Students will be told that the goal is for them to never go above a certain budget in their discretionary expenses. Everyday, students will input their discretionary expenses. If they spend more (less) than the threshold, their balance will be negative (positive). If they remain exactly at the threshold, the balance will be 0. In the control condition, participants will not be able to zero out their balance at any point except by actually spending less on discretionary items. Students in treatment conditions 1, 2, and 3 will, however, have the option to zero out their negative balance every three, seven, and 15 days, respectively (this will mimic a fresh-start opportunity that varies in frequency). Our goal is to compare the balances at the end of the month-long experiment and see which group of students have performed better (i.e., by staying within the budget or even saving money).

Undeserving of Help: How People Form Judgments of Low-Income Individuals’ Spending on Hedonic Activities

“I see this kind of thing all the time. Where if a poor person (say, on welfare), gets anything remotely enjoyable, that people shame them for it. It's like poor people aren't allowed to enjoy themselves in any way, or have anything nice. They expect their clothes to be practically rags, and anything like a phone or a video game is treated as if they're spending their money in a bad way. These people could always save money for these kinds of things. Food isn't exactly something you can wait on and save money for… It's like enjoying anything, having fun is something poor people can't do. If you have anything more than food and shelter, then you're just a leech who's taking advantage.” – from the “Unpopular Opinion Thread” on Reddit.

In this research, we propose that while spending money on product categories that are higher in hedonic value generally requires more rationalization and justification, people find it less rational when low-income people spend money on hedonic activities than when high-income people do so, even if the purchase is made with the low-income people’s hard earned money. We further examine the downstream consequence of such evaluations. Prior research has shown that there is a generally negative perception of low-income individuals and welfare recipients that portrays them as lazy, dishonest, and demotivated, with little interest in self-improvement. Consistent with this, we find that people are more likely to penalize low-income individuals when they spend money on hedonic choices. Specifically, people are less likely to hire a qualified low-income candidate who spent money on hedonic options than the high-income counterpart. Additionally, people are less likely to support government assistance programs that intend to financially help low-income people when they consider the possibility of the low-income’s spending on hedonic (versus utilitarian) purchase categories. Last, we find that making the importance of addressing “wants” and “desires” in addition to “needs” and “necessities” mitigates this effect.