有偏见信息提供方存在时理性主体的最优决策
Optimal Decisions of a Rational Agent in the Presence of Biased Information Providers
摘要：
我们考虑信息网络，其中多个偏置信息提供者（BIP），例如，媒体出口/社交网络用户/传感器与理性信息消费者（RIC）共享事件报告。作出合理的抽象，一个事件可以报告为一个逻辑语句的答案，我们模型的输入输出行为的每个BIP作为一个二进制通道。出于各种原因，一些BIP可能会分享错误的事件报告。此外，每个BIP是：“有偏见的”，如果它有利于两个结果之一，而报告，或“无偏见的”，如果它有利于任何结果。由于用户特征/世界观的差异，信息/社交网络中会出现这种偏见。我们研究了在推断真实信息的同时，BIP的偏见对RIC选择的影响。我们的工作表明，一个“图盲”的RIC寻找$n$ BIP之间的邻居，行为特殊，以尽量减少其错误的概率，同时推导出真实的信息。首先，我们建立了一个反直觉的事实，即RIC的预期误差最小化，通过选择BIP是完全有偏见的先验可能的事件。然后，我们研究的增益，完全偏置的BIP提供无偏置的BIP时，他们的二进制信道的出错率均衡，公平的比较，在一些$r>0$。具体而言，RIC的预期错误概率的无偏与全偏比率随指数$\frac{n}{2}\ln\left(4ρ_0^2\left(\frac{1}{r}-1\right)\right)$呈指数增长，其中$ρ_0$是事件为$0$的先验概率。这不仅表明完全偏置的BIP优于无偏置或非均匀偏置的BIP，而且还表明对于小的$r$，增益可以是相当大的。
英文摘要：
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 $\frac{n}{2}\ln\left(4ρ_0^2\left(\frac{1}{r}-1\right)\right)$, where $ρ_0$ 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 $r$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
