The Gift of Doubt

> As was nearly always the case with Hirschman’s writing, he made his argument without mathematical formulas or complex models. His subject was economics, but his spirit was literary.

That observation explains what is so unsatisfactory about Exit, Voice, and Loyalty. Hirschman thought that if those in charge reduced ordinary peoples right of Exit, then they would respond with more Voice.

That's half true. Voice = Talk x Listen. When it gets harder to Exit, the trapped Talk more and the trappers Listen less. You could make a slogan out of it. "Halve Exit, double Talk, double Voice."

But Hirschman wasn't a mathematizer. It would not occur to him to factorise Voice into Talk x Listen. Thus he misses the opportunity to look around him and see the usual pattern: Halve Exit, double Talk, quarter Listen, halve Voice.

One also notices that Talk is a function of two variables: Exit and Listen. One Talks because ones Exit is blocked, but also because one thinks or at least hopes that some-one is listening. As Exit is reduced, those who should Listen become less inclined to bother. Those who should Talk are encouraged by the lack of Exit as an alternative, but also discouraged by not being listened to.

Mathematics is the language for these kinds of discussions. There are partial derivatives, of Talk with respect to Exit and Talk with respect to Listen. But Listen is a function of Exit. The basic model is Voice = Talk(Exit, Listen(Exit) x Listen(Exit). The distinction between the partial derivative of Talk with respect to Exit and the total derivative of Talk with respect to Exit (That is Talk(Exit, Listen(Exit)) wrt Exit) is easily made.

In the real world, as Exit rights are extinguished, the talkers complain for a while, until the listeners stop listening and then the talkers lapse into apathetic silence. Those of a mathematical bent can easily cloth such bones in an animating flesh of differential equations. The real world contains real problems and one can engage with them.

Those of a literary bent are not, of course, lost for words. This blinds them to the problem: it is not words that are needed.