Tuesday, 8 October 2013

A Revolutionary Model


As another application of an Ising type system in 'social physics' I am going to look at the paper, Peer to Peer and Mass Communication Effect on Revolution Dynamics, if you want more details you can read it, I have nothing to do with the authors and my mistakes are my own. The essential idea is again to simplify people down to binary agents with two possible choices, join the revolution or stay with the status quo. The agents have a predetermined conservatism and they can be influenced by their immediate neighbours. In addition the revolutionary agents have a youtube channel, a 50 megawatt broadcasting tower or a guy handing out leaflets. They have some way to make their influence felt by all the other agents simultaneously.

As an Ising system conservatism is something like a local coupling constant, the neighbour interaction is the usual ising interaction and the mass communication is like a global field, but created by the spins themselves. These analogies are far from exact however and as usual the best way to find out what the model does is to simulate it. We start with an initial state where most people are in the status quo and there are a few randomly distributed revolutionaries. Like the Schelling model but unlike the Ising model we don't allow people to change their minds and go back to the status quo. We could use the standard Metropolis accept reject but it wouldn't modify the conclusions much, as it is you can think of this as the Metropolis algorithm running at zero temperature.

Let $R = N_{rev}/N$ be the ratio of revolutionaries to the total population, initially $R = 0.1$. The parameter $a$ controls the power the mass communication has to influence people: given R let $H(R) = a R^b$ this is the 'media field'. I just follow the paper and set $b = 0.2$ so $a$ controls the strength of the mass media. $J$ controls the influence of the local environment, given an agent $i$ let $H(i) = J \sum_j S_j$ where the sum is over neighbours of $i$, in this case up down left and right. The final parameter $c$ controls the conservatism. Let $h_i$ be the conservatism of the agent $i$. Low $h_i$ means the agent doesn't much like the status quo while an agent with large $h_i$ is very attached to it. The $h_i$'s are randomly distributed at the start of the simulation (whenever you click the random button or move the $c$ slider) according to $P(h_i < h) = h^c$ for $h \in [0,1]$. For low c this gives a wide distribution of people with varied opinions about the current establishment. For large $c$, everyone is about equally conservative. Finally an agent joins the revolution if at any time, \[ h_i + H(i) < H\]

There are several regimes. Let's take $c = 2$ first. When nearest neighbours have little influence, $J \approx 0$ and the effects of mass media are also relatively small $a < 1$, we see an inhomogeneous distribution, much like a high temperature Ising model. There is no clustering of revolutionaries with revolutionaries and conservatives with conservatives. This is probably a dangerous situation in a real society, maybe this is a civil war phase. As the power of the media increases there is total revolution. For moderate $a$, say $0.3$ and moderate $J$, say $0.25$, we start to see clustering. Now that the influence of neighbours becomes as important as the influence of the media we start to see small clusters of conservatives swallowed up by the revolution, but larger clusters surviving. Perhaps we end up with two independent nations in this phase. Unsurprisingly if you increase the conservatism it requires stronger media influence and stronger neighbour coupling to get total revolutions. There also appears to be no phase where there are large numbers of revolutionaries and large clusters of conservatives coexisting. So no civil wars and no new nations, maybe not surprising considering a high $c$ nation is a nation where everyone is almost equally conservative.

People keep finding new applications for this old model which seems apt to describe situations where there is clustering, as here and in the Schelling model, or where there is a change of phase as here in the total revolution case and in the original Ising model at $T_c$. Where there is a binary choice; spin up or down, move or stay, revolt or don't, an Ising like model seems to often reproduce much of the interesting behaviour.

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