A Few Bad Apples: Communication in the Presence of Strategic Ideologues

I propose a very simple model of strategic communication. The motivation is to help explain widespread persistent disagreement about objective facts. In the model, there is a message sender and a receiver, and two possible states of the world, left or right. The sender is one of three types: honest, or a leftist or rightist "ideologue." The honest type observes a private signal in {0, 1, ..., N}, with higher values implying stronger support for the right state, and reports the observed value truthfully. Ideologues strategically choose any message from this set to maximize the receiver's belief in their preferred state, ignoring any private information they may have. I show that a small presence of ideologues can have a large effect on communication: while we might expect ideologues to just send extreme messages, in most equilibria ideologues use "strategic understatement," and in many cases actually mix over all non-neutral (non-N/2) messages to mimic honest types and gain credibility. This distorts the interpretation of these messages such that all messages on a side of the spectrum (above or below N/2) have the same effect on receiver beliefs. This coarsened communication is less informative than even the weakest non-neutral messages in the absence of ideologues. I show by example how ideologues can cause large delays in the time required for receiver beliefs to converge to truth.