Optimal Decisions of a Rational Agent in the Presence of Biased Information Providers (2004.12910v1)

Abstract: We consider information networks whereby multiple biased-information-providers (BIPs), e.g., media outlets/social network users/sensors, share reports of events with rational-information-consumers (RICs). Making the reasonable abstraction that an event can be reported as an answer to a logical statement, we model the input-output behavior of each BIP as a binary channel. For various reasons, some BIPs might share incorrect reports of the event. Moreover, each BIP is: 'biased' if it favors one of the two outcomes while reporting, or 'unbiased' if it favors neither outcome. Such biases occur in information/social networks due to differences in users' characteristics/worldviews. We study the impact of the BIPs' biases on an RIC's choices while deducing the true information. Our work reveals that a "graph-blind" RIC looking for $n$ BIPs among its neighbors, acts peculiarly in order to minimize its probability of making an error while deducing the true information. First, we establish the counter-intuitive fact that the RIC's expected error is minimized by choosing BIPs that are fully-biased against the a-priori likely event. Then, we study the gains that fully-biased BIPs provide over unbiased BIPs when the error rates of their binary channels are equalized, for fair comparison, at some $r>0$. Specifically, the unbiased-to-fully-biased ratio of the RIC's expected error probabilities grows exponentially with the exponent $\frac{n}{2}\ln\left(4\rho_0^2\left(\frac{1}{r}-1\right)\right)$, where $\rho_0$ is the event's prior probability of being $0$. This shows not only that fully-biased BIPs are preferable to unbiased or heterogeneously-biased BIPs, but also that the gains can be substantial for small $r$.