I don’t believe this paper is well-known by economists, but it has been hugely influential for management and media studies. The theory in this paper is qualitative in the same way economic theory is, but is not mathematical. In this post, I’ll try to reinterpret the main ideas mathematically.
Firms face two primary types of uncertainty. First, the outside environment is uncertain. Second, the internal environment is uncertain. When speech is vague, a manager may misinterpret what the true state of the world is, or subordinates may misinterpret the goals of the organization. When speech is precise, it can be very costly to interpret. Indeed, precise speech about unclear goals is basically worthless: two subordinates may precisely state the answer to two different problems, both of which are different from what the manager wanted to know.
Choice of media, then, can vary. Sometimes speech within an organization is very formal: quantitative models, memos, etc. Sometimes it is informal: face-to-face meetings, informal legends, company lore. The informal speech is able to discuss a broader set of ideas, but with greater ambiguity. The formal speech can present specific ideas exactly, but nothing more. This tradeoff roughly implies the following: when the purpose of a discussion is equivocal or unclear, informal speech should be used to “get us on the same page”. When a discussion involves something routine, precise speech can be used. This has a number of implications: for example, informal communication will be most common at the goal setting stage, or when two different departments are beginning to work together on a task, but formal communication will be most common within a division or after goals have been agreed upon by all parties or when the external environment has less uncertainty.
Clearly, the intersection of language and economics is far more general. For example, equivocality is often introduced on purpose: people speak vaguely, for example, in order than common knowledge does not develop. An example, after a first date: “Would you like to come up to my apartment for some coffee?” Further, vague and precise speech are more than simply vague or precise, but rather are vague and precise in particular ways. Poetry is quoted rather than a meaningless stream of words, for example. Neither the authors or I have much to say on these extensions, but it is definitely an open field right now for some interested researcher.
How might you model the ideas of the present paper mathematically? (Of course, you might ask why these ideas should be modeled mathematically anyway, but I have discussed many times here why social science theory ought be formal, and to the extent that it’s formal, the tools of mathematical logic allow the cleanest possible transmission of ideas and derivation of unexpected consequences, so I won’t rehash those arguments here. Indeed, the whole “should we be formal” discussion seems a bit too meta in the context of this post…) Let the relevant true state be a number in [0,1]^n. Let transmission of the exact state be increasing in its dimension, perhaps linearly. Let transmission of imprecise information be increasing less than linearly, perhaps logarithmically. Imprecise states are interpreted by the receiver with error (something like the truncated exponential version of a normal distribution to ensure we stay in [0,1]^n). Loss functions of the final decision made by the receiver depend on distance from the true state. What should a manager do? Well, on simple decisions where the relevant state is only a point on the line segment [0,1], getting the exact state is cheap, so subordinates should send the manager fairly precise information like a statistical estimate in a memo. On complex decisions, where the relevant state is a point in the 100-dimension [0,1] hypercube, learning the true state will be very expensive (it may require the manager to read a 1000 page quantitative report, for instance), but learning an approximate state will be relatively cheap (it may involve some face-to-face conversations). Once the model is formalized like this, then we can answer questions like “Should management communicate via a hierarchy or not?” I have some plans for work along these lines, using some ideas about transmitting counterfactuals given a set of information partitions, and would definitely appreciate comments concerning how to model this type of media richness.