Rebellion

Bifurcations

We have seen that the macro-state of a system consists of all microstates having some property, P. While microstate properties may not be observable, macro-states often do have observable properties.

For example, the microstate space of a water balloon is the position and momentum of every H2O molecule it contains. The macro-state is the temperature. Many microstates produce the same temperature. The macro2-state might be frozen, liquid, or gas.

It is possible that only a small change in the microstate, conceivably a change in a single agent, might cause a change in the macro-state and possibly even a change in the macro2-state. This is called a bifurcation or phase shift. For example, changing the temperature of the water in our balloon from 0 degrees to 1 degree can cause a phase shift from solid to liquid. Changing from 99 degrees to 100 degrees can cause a phase shift from liquid to gas.

When ice melts, the change in macro2-state from solid to liquid is gradual. But in other cases the shift can be sudden.  Adding grains of sand to a sand pile is an example. As the sand pile reaches a certain angle of repose, adding another grain can cause an avalanche.

Tipping Points are examples of phase shifts in Sociology. White flight, market crashes, panics, fads, and rebellions are examples.

Social Unrest

How many abuses does a government have to inflict on its citizens before they rebel?

In rebel.nlogo users control the level of government abuse and repression as well as the tolerance level of the citizens.

Every citizen has fear and anger attributes that are closely tied to government repression and abuse, respectively. Normally citizens march peacefully in the same direction, but when a citizen's anger exceeds his fear by the general tolerance level, he becomes a rebel:

if anger – fear > tolerance [ set rebel? true ]

A rebel turns red and runs around randomly trying to recruit new rebels. This involves incrementing the prospect's anger level. For example, the rebel may hand the prospect an inflammatory leaflet.

The increase in the number of rebels at time t + 1 is proportional to the number of rebels at time t:

num-rebels(t + 1) = num-rebels(t) + c * num-rebels(t)

Solving this equation shows that the rebellion grows at an exponential rate:

num-rebels(t) = num-rebels(0) * ct

The situation is analogous to a chain reaction in physics. All of the atoms in a chunk of uranium are resting peacefully, when an outside agitator slams into one of them like a queue ball slamming into an eight-ball, and sends it careening off wildly in a random direction. This atom will slam into another atom with a probability P, where P depends on the size of the chunk. If the size is above some critical mass, then P is very high and a chain reaction ensues.

In our model the probability P that a rebel will recruit a new rebel is controlled by the levels of repression and abuse. A rebel can increase the anger of a citizen, but only temporarily. Also, if the level of repression is high, then the probability that the police will capture and "reform" a rebel is also high.

In this screen shot we see a society in the peaceful macro-state:

As we gradually increase the level of government abuse, we see sharp jumps in the number of rebels as the society experiences a phase shift to the macro-state of rebellion: