Two experiments examined predictions from two separate explanations for previously observed display effects for communicating low-probability risks: foreground:background salience and proportional reasoning. According to foreground:background salience, people's risk perceptions are based on the relative salience of the foreground (number of people harmed) versus the background (number of people at risk), such that calling attention to the background makes the risk seem smaller. Conversely, the proportional reasoning explanation states that what matters is whether the respondent attends to the proportion, which conveys how small the risk is. In Experiment 1, we made the background more salient via color and bolding; in contrast to the foreground:background salience prediction, this manipulation did not influence participants' risk aversion. In Experiment 2, we separately manipulated whether the foreground and the background were displayed graphically or numerically. In keeping with the proportional reasoning hypothesis, there was an interaction whereby participants given formats that displayed the foreground and background in the same modality (graphs or numbers, thereby making the proportion easier to form) saw the probability as smaller and were less risk averse than participants given the information in different modalities. There was also a main effect of displaying the background graphically, providing some support for foreground:background salience. In total, this work suggests that the proportional reasoning account provides a good explanation of many display effects related to communicating low-probability risks, although there is some role for foreground:background salience as well.questions did not influence their response to that question. Next, they filled out a packet containing the rest of the measures listed above and some other items included for exploratory purposes. Figure 4. Experiment 2 risk magnitude information displaying (a) the background information numerically and the foreground information graphically and (b) the background information graphically and the foreground information numerically 480 Journal of Behavioral Decision Making

Graphs are increasingly recommended for improving decision-making and promoting riskavoidant behaviors. Graphs that depict only the number of people affected by a risk ("foreground-only" displays) tend to increase perceived risk and risk aversion (e.g., willingness to get vaccinated), as compared to graphs that also depict the number of people at risk for harm ("foreground+background" displays). However, previous research examining these "foreground-only effects" has focused on relatively low-probability risks (<10%), limiting generalizability to communications about larger risks. In two experiments, we systematically investigated the moderating role of probability size on foreground-only effects, using a wide range of probability sizes (from 0.1% to 40%). Additionally, we examined the moderating role of the size of the risk reduction, that is, the extent to which a protective behavior reduces the risk. Across both experiments, foreground-only effects on perceived risk and risk aversion were weaker for larger probabilities. Experiment 2 also revealed that foreground-only effects were weaker for smaller risk reductions, while foreground-only displays decreased understanding of absolute risk magnitudes independently of probability size. These findings suggest that the greater effectiveness of foreground-only versus foreground+background displays for increasing perceived risk and risk aversion diminishes with larger probability sizes and smaller risk reductions. Moreover, if the goal is to promote understanding of absolute risk magnitudes, foreground+background displays should be used rather than foregroundonly displays regardless of probability size. Our findings also help to refine and extend existing theoretical accounts of foreground-only effects to situations involving a wide range of probability sizes.