How to detect a liar using a classic math trick

When we try to understand why people act the way they do, psychology is usually the first place we look. Learning how the human mind functions helps explain decisions, reactions, and behaviors. Yet psychology alone may not fully explain how behavior changes over time. Incorporating mathematical reasoning can reveal patterns that are not immediately obvious. When logical analysis and numerical models are combined with psychological insight, we gain a clearer picture of how people form opinions and make choices.

The Science of Decision-Making

A recent model described in Frontiers in Psychology takes inspiration from the work of mathematician Norbert Wiener. The model focuses on how people adjust their opinions when faced with several possible choices. Often these shifts happen because we must decide with incomplete information, weighing what we know before selecting the option that guides our behavior.

To analyze these changes, researchers use mathematical concepts related to information processing. In some ways, the human mind can be viewed as a system that compares possibilities and assigns likelihoods to each one. This occurs in everyday decisions—choosing which product to buy, deciding where a child should go to school, or selecting a political candidate.

As we collect additional information, our uncertainty typically decreases. For example, reading reviews from other buyers may help us feel more confident about which product to purchase. The process of updating beliefs when new evidence appears can be explained by a mathematical principle created by the 18th-century scholar Thomas Bayes. His formula describes how a rational thinker revises conclusions when dealing with uncertain outcomes.

Using Data to Predict Behavior

By combining these earlier ideas with modern information mathematics—especially signal processing—researchers gain a powerful tool for studying patterns in social behavior. This method has already been used in several areas:

• Financial markets: Examining how investors respond to new information and how those reactions affect stock prices.
• Nature: Studying how plants, such as flowers, interpret sunlight and turn toward it.
• Politics: Estimating the probability that a candidate will win an election using polling data.

Tracking how information spreads can also help scientists anticipate how misleading stories or false claims might shape public opinion. A key aspect of Bayesian reasoning is that every possible outcome—accurate or inaccurate—can influence how individuals respond and make decisions.

Certainty, Beliefs, and Bias

Our reaction to new information often depends on how strongly we already believe something. When we start without a firm opinion, we are more likely to consider different possibilities evenly. This reflects a state of high uncertainty. However, if someone strongly supports one idea, new information may have only a small effect on their perspective, creating a stable sense of certainty.

This behavior can produce confirmation bias, where people favor information that agrees with what they already believe. While this may seem irrational, mathematical models show that it can still fit within Bayesian logic: individuals naturally move toward explanations that make their understanding feel more certain.

Recognizing the “Rational Liar”

One fascinating outcome of this research is the possibility of distinguishing between honest mistakes and deliberate deception.

Someone who is mistaken:
When a person simply holds incorrect information, their beliefs usually shift gradually toward the truth as they receive new evidence. Even if they resist at first, their views slowly evolve over time.

Someone who is lying:
A person who already knows the truth but intentionally rejects it often behaves differently. They may confidently commit to a specific false claim. If that claim is disproven, instead of adjusting toward the correct explanation, they may quickly switch to another incorrect story.

Because of this pattern, someone intentionally spreading false information may appear inconsistent or erratic, making their behavior easier to detect. Mathematical analysis suggests that such sudden shifts are statistically unlikely to result from simple misunderstanding.

By using this information-based approach, researchers hope to better understand how beliefs develop, spread, and change—and how society can more effectively recognize and respond to the damaging effects of misinformation.