In just a few months, voters across the United States will go to the polls to decide who will be the next President of the United States. A new study draws on mathematics to break down how people make decisions like this.

The researchers, including Zachary Kilpatrick, an applied mathematician at CU Boulder, developed mathematical tools known as models to simulate the deliberation process of groups of people with different prejudices. They found that decision makers with strong initial biases were usually the first to make a choice.

“If I want good quality feedback, maybe I should look to people who are a little more deliberate in their decision-making,” said Kilpatrick, co-author of the new study and associate professor in the Department of Applied Mathematics. “I know they’ve done their due diligence in making up their minds.”

The researchers, led by Samatha Linn at the University of Utah, is published their findings August 12 in the journal Physical examination E.

In the team’s models, mathematical decision makersor “agents”, gather information from the outside world until they finally make a choice between two alternatives. That might include getting pizza or Thai food for dinner or coloring the bubble for one candidate versus the other.

The team found that when agents started with a big bias (say, they really wanted pizza), they also made their decisions very quickly—even if those decisions turned out to be contrary to the available evidence (the Thai restaurant got much better reviews). Those with less prejudice, in contrast, often took so long to consider that their original preconceived notions were completely washed away.

The results may not be surprising, depending on your thoughts human nature. But they can help reveal the math behind how the brain works when it needs to make a quick choice in the heat of the moment – ​​and perhaps even more complicated decisions like who to vote for.

“It’s like standing on a street corner and deciding in a split second whether to cross,” he said. “Simulating decision making becomes a little more difficult when it’s something like, ‘Which college should I go to?’

Pour water

To understand how the team’s mathematical agents work, it helps to imagine buckets. Kilpatrick and his colleagues usually begin their decision-making experiments by feeding their agents with information over time, a bit like pouring water into a mop bucket. In some cases, this evidence favors one decision (getting pizza for dinner), and in others the opposite choice (Thai food). When the buckets are filled to the brim, they tip, and the agent makes his decision.

In their experiment, the researchers added a twist to that set-up: They filled some of their buckets halfway before the simulations began. These agents, like many people, were biased.

The team ran millions of simulations including anywhere from 10 to thousands of agents. The researchers were also able to predict the behavior of the most and least biased funds by hand using pencil, paper and some smart guesswork.

A pattern began to emerge: the agents who started with the greatest bias, or were mostly full of water to begin with, were the first to tip—even when the preponderance of evidence suggested they should have chosen otherwise. In contrast, the agents who started with only small biases appeared to take time to weigh all the available evidence and then make the best available decision.

“The slowest agent to make a decision tended to make decisions in a way similar to a completely unbiased agent,” Kilpatrick said. “They pretty much acted like they were starting from scratch.”

Choice of neighborhood

He noted that the study had some limitations. In the team’s experiments, for example, none of the agents knew what the others were doing. Kilpatrick compared it to neighbors staying inside their homes during an election year, without talking about their choices or putting up yard signs. In reality, people often change their decisions based on the actions of their friends and neighbors.

Kilpatrick hopes to run a similar set of experiences there agents can influence each other’s behaviour.

“You can speculate that if you had a large group interconnected, the first agent to make a decision could start a cascade of potentially wrong decisions,” he said.

Still, political pollsters may want to take a look at the team’s results.

“The study can also be applied to group decision-making in human organizations where there is democratic voting, or even when people give their opinions in surveys,” Kilpatrick said. “You might want to watch people carefully if they give quick answers.”