# Hundred Flowers Bloom Model

## Introduction

From a 2021 Frieden lunch on the 2020 working paper, "THE POLITICAL ECONOMICS OF NON-DEMOCRACY," by Georgy Egorov and Konstantin Sonin.

Anyone who wants to is free to write this up into a paper and publish it under their own name, just crediting me with suggesting the idea in a footnote or such.

## The Model

### The Order of Play

Each Subject is Angry with probability theta and just Unhappy with probability 1-theta. Exogenously, if enough subjects are angry, there may be a revoluiton that will unseat the Ruler— the probability of revolution rises in the number o the Angry. He can, however, do two things to reduce the number of subjects who are angry: (1) Make Concessions (which reduces the number to zero) or (2) Shoot some or all of the angry subjects. But initially he cannot tell who is angry.

The Ruler can make Speech Easy or Difficult. If it is Difficult, Subjects can say nothing. If it is Easy, Subjects have a choice between Complain and Praise. After they have spoken, the Ruler has a choice between Making Concessions, Doing Nothing, and Shooting a percentage of the Subjects. Nobody knows theta.

### Payoff Functions

An Angry subject derives utility from himself personally Complaining (from doing his duty, as well as from just enjoying it), especially if the Complaining results in Concessions. All subjects like Concessions, which are made to the subjects generally (lower taxes, for example).

The Ruler does not like to make Concessions or to Shoot subjects, in themselves. Even more, however, he dislikes Revolution.

### The Equilibrium

The equilibrium depends on the form of the Revolution function, I think, but it will likely be in mixed strategies no matter what (unless all Angry subjects Complain or all of them Praise, or the Ruler makes speech Difficult).

• One possibility is that the Ruler makes speech Easy, Angry subjects mix between Complain and Praise, and if enough Complain, the Ruler makes concessions. If, however, only a few complain, the Ruler instead shoots zero, some, or all of them. It might be that he shoots some if they are very few and does nothing if they are moderate in number; that is the case if a few Angry subjects create possibly dangerous tinder, but if there are more, it isn’t that much worse and it is costly to shoot subjects. It miht be that he does nothing if they are few but shoots some or all if they are more numerous (but not so many as to make Concessions a better choice for the ruler); that is the case if a few dissidents are harmless, but if they get more numerous, the probability of revolution rises considerably.
• Another possibility is that the Ruler makes speech Easy, Angry subjects mix between Complain and Praise, and if enough Complain, the Ruler shoots some or all of them. If, however, a moderate number complain, the Ruler makes Concessions. And if only a few complain, he either does Nothing, or again he shoots some or all of them. This equilibrium is the result if when a lot of peope are angry a revolution can be averted only by Shooting, but if a moderate number are, it can be averted by Concessions.
```Now that I’ve written this out, I see it is more intricate than I thought, but that is mainly because the Revolution technology could realistically take many shapes, and that is crucial to the Ruler’s optimal policy. REalistically, in some countries rulers ought to make concessions and in other shoot people, even if the  number of angry subjects is the same in both countries.
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