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# The mathematics of human behavior can identify the influence of fake news on election results

A researcher combines psychological theories of human behavior and the field of information science to reach insights. These findings have implications for the way to combat wrong information distributed on the net

By   Dorja C. Brody Professor of Mathematics, University of Surrey, UK

Understanding the human mind and behavior is at the core of the discipline of psychology. But to characterize how people's behavior changes over time, I believe that psychology alone is not enough and that additional mathematical ideas should be promoted.

my new model, Published in the journal Frontiers in Psychology, draws inspiration from the work of the 19th century American mathematician, Norbert Wiener. At its core is the way in which we change our perceptions over time when we are tasked with choosing from a set of alternatives. Such changes often arise because of limited information, which we analyze before making decisions that determine our behavior patterns.

To understand these patterns, we require the mathematics of information processing. Here, a person's state of mind is represented by the likelihood he assigns to different alternatives – which product to buy; which school to send your child to; which candidate to vote for in the elections; And so on.

As we collect piecemeal information, we become less uncertain – for example, by reading customer reviews we become more certain about which product to buy. This mental update is expressed in a mathematical formula formulated by the 18th century English scholar, Thomas Bayes. It actually gives a possible explanation for the way a rational mind makes decisions by evaluating various and uncertain alternatives.

The equation shows the flow of information over time, t. X is a random variable representing different probabilities corresponding to different alternatives. If we assume that the information is revealed at a constant rate σ, and that the noise obscuring the information is B ((described by a theory called Brownian motion, which is random), then the equation can give us the flow of information. Image courtesy of the author

When combining this concept with the mathematics of information (esp Signal Processing), which dates back to the 40s, it can help us understand the behavior of people, or society, guided by how information is processed over time. Only recently have my colleagues and I realized how useful this approach can be.

So far, we have successfully applied it to model the The behavior of financial markets (market participants react to new information, which leads to changes in stock prices), and The behavior of green plants (A flower processes information about the position of the sun and turns its head towards it).

I also showed that it can be used to model the dynamics of public opinion polling statistics related to elections or referendums, and suggest Formula which gives the true probability of a particular candidate winning a future election, based on today's polling statistics and how information will be released in the future.

In this new "information-based" approach, the behavior of a person - or a group of people - over time is inferred by modeling the flow of information. so, For example, you can ask what will happen to an election result (probability of the result in percentages) if there is "fake news" of a given magnitude and frequency in circulation.

But perhaps most unexpected are the deep insights we can glean into the human decision-making process. We now understand, for example, that one of the key features of Bayesian revision is that any alternative, whether it is correct or not, can have a profound effect on how we behave.

If we don't have a preconceived idea, we are attracted to all these alternatives regardless of their type, and we will not choose one for a long time without more information. This is where the uncertainty is greatest, and a rational mind would want to reduce the uncertainty so that a choice can be made.

But if someone has a very strong belief in one of the alternatives, then no matter what the information says, their position will hardly change for a long time - it's a pleasant state of high certainty.

Such behavior is related to the concept of "confirmation bias" - interpreting information as confirming your opinions even when it actually contradicts them. This is seen in psychology as contrary to Bayesian logic, and represents irrational behavior. But we show that this is, in fact, a perfectly rational property consistent with Bayesian logic—a rational mind simply wants high certainty.

## The rational liar

The attitude can even describe the behavior of a pathological liar. Can mathematics distinguish between a lie and a real misunderstanding? It seems that the answer is "yes", at least with a high level of confidence.

If a person really thinks that an alternative that we know to be true is very improbable - that is, he does not understand - then in an environment where partial information about the truth is gradually revealed, his perception will slowly move towards the truth. Even if he has a strong belief in a false alternative, his view will slowly converge from the false alternative to the true one.

However, if a person knows the truth but refuses to accept it - he is a liar - then according to the model, his behavior is quite different: he will quickly choose one of the false alternatives and confidently claim that it is the truth. (In fact, they may almost believe any false alternative chosen at random.) Then, as the truth gradually emerges and this position becomes untenable, they will very quickly and assertively choose another false alternative.

Hence, rational liars (in the sense of people who follow Bayesian logic) will behave quite erratically, which can eventually help us identify them. But they will have such strong faith that they can convince those who have limited knowledge of the truth.

For those who have known a consistent liar, this behavior may seem familiar. Of course, without access to someone's mind, you can never be 100% sure. But mathematical models show that the possibility that such behavior is due to a genuine misunderstanding is statistically very unlikely.

This information-based approach is very effective in predicting the statistics of people's future behavior in response to the disclosure of information - or disinformation, for that matter. It can provide us with a tool to analyze and deal with, in particular, the negative consequences of disinformation.

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