How fake news can turn against its spreader

Abstract

When different information sources on a given topic are combined, they interact in a nontrivial manner for a rational receiver of these information sources. Suppose that there are two information sources, one is genuine and the other contains disinformation. It is shown that under the conditions that the signal-to-noise ratio of the genuine information source is sufficiently large, and that the noise terms in the two information sources are positively correlated, the effect of disinformation is reversed from its original intent. That is, the effect of disinformation on a receiver of both information sources, who is unaware of the existence of disinformation, is to generate an opposite interpretation. While the condition in which this phenomenon occurs cannot always be ensured, when it is satisfied, the effect provides an effective way of countering the impacts of disinformation.

Figures (2)

• Figure 1: Perceptions skewed by disinformation. On the left panel the prior probabilities $\{p_k\}$, here taken to be uniform, for the random variable $X$ representing five possible alternatives, are plotted in the form of a histogram. Having sampled the value of $\xi=\sigma X+\epsilon$, where the signal-to-noise ratio is taken to be $\sigma=0.5$ and $\epsilon$ is a zero-mean normal variable with standard deviation $1$, the prior transforms into posterior $\{\pi_k(\xi)\}$ (the second panel). However, if the message $\xi$ is contaminated with disinformation with $f>0$, whose existence is unknown to the receiver, then the posterior view is skewed to the right (the third panel); whereas if $f<0$ then it is skewed to the left.
• Figure 2: Sample paths showing the reversal of the impact of disinformation. On the left panel the posterior probabilities $\{\pi_k\}$ are plotted when $X$ represents five alternatives, in the absence of disinformation. When the second information source contains disinformation of the form $f^2_t = \mu (t-\tau) {\mathds 1}\{t>\tau\}$ that is released at time $\tau$, the intension is to skew the preference of the receiver towards $\pi_5$ if $\mu>0$. Similarly, if $\mu<0$ then the intension is to skew the probabilities towards $\pi_1$. However, when $\sigma_2<\rho\sigma_1$, the impact of disinformation is reversed, as shown in the middle panel for $\mu>0$ depicting how the histories on the left panel would have been affected by the presence of disinformation, enhancing $\pi_1$ rather than $\pi_5$. Similarly, the right panel shows the effect for $\mu<0$, enhancing $\pi_5$ rather than $\pi_1$.