In a recent research project, scientists designed a simulated voting booth where individuals, referred to as mathematical ‘agents’ with different biases, could engage in decision-making discussions. This investigation aims to provide insights into how the brain functions during decision-making processes.
In just a few months, voters across America will visit polling stations to choose the next U.S. president.
A recent study utilizes mathematical principles to analyze how people make choices in situations like these. The researchers, including Zachary Kilpatrick, an applied mathematician at the University of Colorado Boulder, created mathematical models to replicate the decision-making process of biased groups. They found that individuals with strong initial biases were usually the quickest to make decisions.
“For obtaining quality feedback, I might prefer to consult those who are more thoughtful in their decision-making,” stated Kilpatrick, co-author of the study and associate professor in the Department of Applied Mathematics. “I trust that they have carefully considered their options.”
The research team, led by Samatha Linn from the University of Utah, published their results on August 12 in the journal Physical Review E.
In their models, these mathematical decision-makers, or “agents,” collect data from their surroundings until they ultimately choose between two alternatives. This could be as simple as deciding whether to have pizza or Thai food for dinner or selecting between candidates on a ballot.
The researchers observed that agents with significant initial biases (for example, a strong preference for pizza) tended to make decisions rapidly, even if the choices contradicted the evidence available (such as better reviews for the Thai restaurant). In contrast, those with minor biases often took such prolonged deliberation that their original opinions faded away completely.
The findings may not be surprising, depending on one’s views of human behavior; however, they could illuminate the mathematical aspects of brain function when quick decisions are required, such as voting.
“It’s reminiscent of standing at a street corner and needing to decide in an instant whether to cross,” he explained. “Simulating decision-making can be more complex when dealing with major life choices, like selecting a college.”
Understanding the Process
To grasp how the mathematical agents function, visualizing buckets can be helpful. Kilpatrick and his team typically initiate their decision-making experiments by gradually providing information to their agents, akin to pouring water into a mop bucket. In some cases, this information favors one option (like pizza) and in others the opposite (like Thai food). When the buckets overflow, the agent makes a decision.
During their experiments, the researchers introduced a modification: they partially filled some buckets before starting the simulations, creating biased agents.
The team conducted millions of simulations with groups ranging from 10 to thousands of agents. They also predicted behaviors of the most and least biased agents manually using pen and paper alongside some inventive approximations. A clear trend emerged: agents that began with the greatest bias, or were nearly full, tended to tip over first, even when evidence suggested they should have chosen differently. Conversely, agents with minimal biases deliberated longer to assess all the available data, ultimately leading to more informed decisions.
“The slowest agents made choices that resembled those of completely unbiased agents,” said Kilpatrick. “They essentially acted as if they started from a blank slate.”
Influence of Peers
Kilpatrick acknowledged some limitations of the study. In their experiments, for instance, none of the agents were aware of each other’s choices. He likened it to neighbors keeping to themselves during an election year, refraining from discussing their votes or displaying yard signs. In real life, individuals often adjust their decisions based on the actions of acquaintances.
Kilpatrick aspires to conduct additional experiments in which agents can impact one another’s decisions.
“One might hypothesize that in a large interconnected group, the first agent to decide could trigger a wave of possibly erroneous decisions,” he suggested.
Nonetheless, political pollsters may find value in the study’s outcomes.
“The findings could be relevant for collective decision-making in democratic organizations or even when individuals provide feedback through surveys,” Kilpatrick noted. “It’s worth paying close attention to those who respond quickly.”
