How to spot a liar using a classic mathematical trick

When we think about why people act the way they do, we usually turn to psychology. Understanding the inner workings of the human mind is essential for explaining behavior. However, to truly “characterize how people’s behavior changes over time, I believe psychology alone is insufficient — and that additional mathematical idea needs to be brought forward.” By using numbers and logic, we can see patterns that the naked eye might miss.

The Science of Making Choices

A new model, recently “published in Frontiers in Psychology, is inspired by the work of the 19th-century American mathematician Norbert Wiener.” This model looks at how our opinions shift when we have to choose between different options. Often, these shifts happen because we only have “limited information, which we analyze before making decisions that determine our behavioral patterns.”

To get a clear picture of these patterns, we use the “mathematics of information processing.” Think of the human mind like a computer that assigns a “likelihood it assigns to different alternatives — which product to buy, which school to send your child to, which candidate to vote for in an election, and so on.”

As we learn more, our confusion starts to fade. For example, “by reading customer reviews, we become more certain about which product to buy.” This process of updating our thoughts based on new facts is described by a “mathematical formula worked out by the 18th-century English scholar Thomas Bayes.” This formula shows how a “rational mind makes decisions by assessing various uncertain alternatives.”

Predicting the Future with Data

When we combine these old theories with modern “mathematics of information (specifically signal processing),” we get a powerful tool for understanding society. This method has already been used in several interesting ways:

• Stock Markets: Predicting how “market participants respond to new information, which leads to changes in stock prices.”

• Nature: Observing how “a flower processes information about the location of the sun and turns its head towards it.”

• Politics: Calculating the “actual probability of a given candidate winning a future election based on today’s poll statistics.”

By modeling how information flows, we can even predict how “fake news” might sway a public vote. It shows us that “one of the key traits of the Bayes updating is that every alternative, whether it is the right one or not, can strongly influence the way we behave.”

Conviction and Bias

Our brains react differently depending on how sure we are. If we have no “preconceived idea,” we tend to look at all options equally. This is a state of high uncertainty. However, if “someone has a very strong conviction on one of the alternatives, then whatever the information says, their position will hardly change for a long time — it is a pleasant state of high certainty.”

This often leads to “confirmation bias,” where we only listen to things that prove we are right. While some see this as “irrational behavior,” math suggests it is actually a “perfectly rational feature compatible with the Bayes logic — a rational mind simply wants high certainty.”

Spotting the “Rational Liar”

The most exciting part of this research is its ability to distinguish between a “genuine misunderstanding” and a deliberate lie.

• The Person Who is Mistaken: If someone is simply wrong, their “perception will slowly shift towards the truth” as they get more information. Even if they are stubborn, their “view will very slowly converge from this false alternative to the true one.”

• The Liar: A person who “knows the truth but refuses to accept it — is a liar” acts differently. They will “rapidly choose one of the false alternatives and confidently assert this to be the truth.” When that lie is exposed, they don’t move toward the truth; instead, they “very quickly and assertively, they will pick another false alternative.”

Because of this, a “rational (in the sense of someone following the Bayes logic) liar will behave in a rather erratic manner, which can ultimately help us spot them.” While we can’t read minds, the math shows that such behavior is “statistically very unlikely” to come from a simple mistake.

Using this “information-based approach,” we can better understand how to “analyze and counter, in particular, the negative ramifications of disinformation.”