Risk Theater

Visualizing a More Informed Public

UMass Amherst computer scientists, in collaboration with researchers at Microsoft and Sigma Computing, are designing better data visualizations to help people make sense of risks and probabilities.

Is it safe to attend a concert or eat at a restaurant during COVID-19? Is it important to cast a vote for my preferred candidate? Do I need to evacuate my family to stay safe from a forecasted hurricane? Will the potential benefits of getting surgery outweigh the risks?

Every day, humans are faced with dozens of decisions—some mundane, others potentially life-altering. In an ideal world, we make these decisions with an informed understanding of the risks, or probabilities of the various possible outcomes. Yet, research has shown that people can be easily overwhelmed by this type of numerical information and struggle to grasp its meaning.

Cindy Ya Xiong, professor in the Manning College of Information & Computer Sciences
Cindy Xiong

Researchers and practitioners in the field of data visualization attempt to improve numerical comprehension by designing visual representations of probability. These visualizations have become increasingly ubiquitous in recent years in the news and social media, with many major news organizations now employing dedicated data visualization teams. Still, the media’s use of graphics sometimes misses the mark—like The New York Times’ 2016 “Election Needle,” a speedometer-like graphic which failed to adequately convey uncertainty in its Election Night prediction of a Hillary Clinton win.

Cindy Xiong, assistant professor in the University of Massachusetts Amherst’s Manning College of Information & Computer Sciences, wants to help people make more informed decisions by optimizing data visualization. Xiong, Ali Sarvghad, research assistant professor in the Manning College of Information & Computer Sciences, and collaborators Jake Hofman and Dan Goldstein at Microsoft Research and Çağatay Demiralp at Sigma Computing recently won a Best Paper Honorable Mention award at CHI, the premier venue for human-computer interaction research, for a publication on this research at the intersection of computer science and human cognitive psychology.

Carefully designed visualizations can supplement numerical descriptions and enhance people’s understanding of risks and uncertainty.

Cindy Xiong

From Election Needles to Risk Theaters

Risk and probability can be communicated in myriad ways. For example, a pharmaceutical company may state that there is a 25 percent chance of a drug producing an allergic reaction, or alternatively, that such a reaction occurs in 1 in 4 people. According to Xiong, research shows that people are best able to comprehend numerical information when prompted to imagine a concrete scenario. Thus, they can more easily picture 1 of 4 people having an allergic reaction, versus the more abstract notion of 25 percent.

“Carefully designed visualizations can supplement numerical descriptions and enhance people’s understanding of risks and uncertainty,” Xiong explained.

One effective method to help people understand probabilities are icon arrays—arrangements of shapes shaded different colors to depict the likelihood of various outcomes. For example, she said, “To communicate the risk of getting an allergic reaction, we can visualize 100 squares in a grid, where each square represents a patient and their colors represent whether they have had an allergic reaction or not. 25 shaded squares illustrates 1 out of 4 people having an allergic reaction.”

Icon arrays can also take more creative forms to help people experience the randomness in outcomes. Research has suggested that “risk theaters,” grids shaped and arranged to look like a theater map with seats colored differently to convey different outcomes, are particularly effective.

“Imagine receiving a ticket for a random seat in a theater. Sitting in a red seat represents the outcome where Candidate A wins, whereas sitting in a blue seat represents the outcome where Candidate B wins,” said Xiong. “This elicits an emotional reaction that helps people understand both the probability and the associated uncertainty."

Risk Theater
A risk theater, with the color of seats depicting different possible outcomes.


Conveying uncertainty—something easily lost in graphics like election needles and bar charts—is critical because it helps people gauge how much risk they’re willing to take when making important decisions, like whether to evacuate their family in the face of a nearby wildfire or a forecasted hurricane. Without grasping the uncertainty inherent in these situations, people tend to incorrectly understand probabilities as binary–an outcome will happen, or not.

In the real world, such determinations are rarely simple and often involve several nested risk calculations. Imagine, for example, deciding whether to attend a concert during COVID-19. You might consider factors such as how crowded the venue is likely to be, the COVID positivity rates in your region, how many people are likely to wear masks, and your own personal risk factors for having a bad outcome if you become infected.

“There are so many different components, all with their own uncertainties,” Xiong said. “It’s so complicated. That’s why it’s so important to help people understand it so they can take the appropriate action.”

Optimizing the Theater

In their recent research that was published and recognized at CHI, Xiong and collaborators sought to reduce this complexity in order to systematically investigate how icon array design affects viewers’ perceptions of probability.

The researchers used a simple black-and-white, 10-by-10 array of square icons, and theorized that any viewer bias observed with this simplistic model would only be exaggerated with more complex designs. They surveyed existing literature for different ways icon arrays are typically arranged and tested six different conditions.

Six different styles of icon arrays

More than one thousand participants took part in this work. They were shown a series of icon arrays for one second each, and prompted to estimate the proportion of black icons in the array using a slider from zero to 100. The study found that overall, participants were fairly accurate in estimating the proportion of black icons in the Top, Row, and Diagonal conditions, and less accurate in the Central, Edge, and Random conditions. The researchers conducted multiple variations on the study, such as varying the size and brightness of the grids, making them confident in the generalizability of their findings.



Illuminating the Mysteries of the Human Brain

Xiong has noticed a recent shift in the media’s graphical depictions of probability, with more frequent use of icon array varieties, such as bee swarms. She stressed the importance of transferring the knowledge gained from the latest research into the real world, and she contributes to this effort by regularly collaborating with researchers at companies like Adobe and Tableau Research and presenting her research at computer science conferences. She hoped her research results can be used by industry workers and data journalists to communicate data more clearly to the general public.

Beyond improving data visualizations, this research may shed new light on human cognitive processes. Xiong explained that there is an ongoing debate in psychology over whether humans are able to perceive numerosity—how many things are in a given space—or if they can only detect area and density, allowing them to infer numerosity.

“As a computer scientist, I believe that computers may allow us to model what goes on in the human brain, and thus help uncover the mechanisms of visual perception,” she said.

Ultimately, this may allow researchers to model with computers some of the amazing abilities of the human brain—like how fast we can recognize objects in the world and how efficiently we can learn new concepts—and reverse engineer these abilities to uncover the underlying cognitive and perceptual mechanisms in play. These models could help to improve technologies through emulating human behaviors, such as self-driving cars that can detect obstacles in unpredictable road conditions as well as humans can.

This story was first published in May 2022.