How do we model irrationality? In economics, the attempt to reconcile seemingly irrational behavior with assumptions of rationality has gained increasing attention in the wake of the financial crisis, whose speculative bubble was reinforced by what John Cassidy calls “rational irrationality.” But in fact, exercises in modeling irrationality have produced valuable insights in a wide variety of subfields. For instance, the preference falsification theory developed by Timur Kuran (see here for some high praise from the high priest of econ-blogging, Marginal Revolution’s Tyler Cowen) explains why individuals publicly support privately undesirable cultural norms, and how this damages private knowledge and restricts innovation in the long term.
Adopting a similar mode of analysis, let us examine “A Madman’s Diary” (『狂人日記』, Project Gutenberg full text available here), the debut work of the so-called father of modern Chinese literature, Lu Xun (魯迅). In this 1918 short story – as in many others – Lu Xun lambastes the backward traditional values that governed life and thought in early Republican China. The titular “madman” fears that he will be cannibalized by the rest of his village, reading murderous intent in the gazes of his neighbors and the words of his brother. Meanwhile, we infer that he is treated with derision by the rest of the village, and with pity by his borther. The story ends with the memorable line “Save the children…” (“救救孩子”), but we learn in the story’s introduction that the madman has long since been rehabilitated. Of course, the madman symbolizes a fledgling modernity that is eventually quashed, cannibalism the Confucian values that had reigned in China for 4000 years, and the other villagers the passively conservative masses with their malevolent aversion toward change.
How does this relate to our talk of rationally explaining irrationality? With the help of game theory, I contend that the situation in the village – and the backward situation in early Republican China – can be modeled as a case of dual Nash equilibria. Let us derive a payoff matrix for the village in Lu Xun’s tale, with the individual being the horizontal player and the rest of the village being the vertical one. The strategies for the villager are to consider his neighbors to be “Normal” or “Cannibals.” The strategies for the rest of the village are to consider the villager “Normal” or “Insane.” Below is the payoff matrix:
|Rest of village||Normal||Insane|
|Villager||Normal||a, w||b, y|
|Cannibals||c, x||d, z|
It is easy to see that for the villager,
a > b and
d > c
That is, he will consider others to be normal if they treat him normally, but as cannibals if they treat him as if he were insane. Similarly for the rest of the village,
w > x and
z > y
That is, they will consider the villager to be normal if he behaves as if they were normal, but insane if he behaves as if he thought they were cannibals.
We thus have the two Nash equilibria italicized in the payoff matrix above: (Normal, Normal) and (Cannibals, Insane). The situation is mutually self-reinforcing. When the villagers treat you normally, you act normally; when the villagers treat you as if you were insane, you think they are cannibals. Similarly, when you act normally, the villagers treat you normally; when you think the villagers are cannibals, they treat you as if you were insane.
The situation is disturbingly analagous to that of Lu Xun’s real word, early Republican China. Consider the following payoff matrix:
|Individual||Conservative||a, w||b, y|
|Modern||c, x||d, z|
We have the same result of symmetrical Nash equilibria. A conservative individual is treated as normal by society, and therefore embraces society; a modern individual is ostracized because he is modern, and therefore decries society as backward.
Now let us extend the analysis using the concept of evolutionary stability. We will approach the issue by considering a game of two individuals, as drawn up below. First, note that we are in a society in which the predominant strategy of the population holds traditional values – that is, the predominant strategy is currently “Conservative.” This is noted in the matrix with the italicized square for (Conservative, Conservative). Is this universal conservatism evolutionarily stable?
|Conservative||a, a||b, c|
|Modern||c, b||d, d|
It is easy to rank the payoffs, because we know that consensus is always preferred to non-consensus (which leads to conflict):
a > b and
d > c
That is, the situation is a pure coordination game. We can even say d > a – that a modern society is better than a conservative one – for the sake of realism, though we shall see that this does not matter.
Given the existing situation of (Conservative, Conservative) evolutionarily stable? It is easy to see that the answer is yes; (Conservative, Conservative) is indeed evolutionarily stable. A mutant who chooses to be Modern will always be quashed by the Conservative majority; it matters not whether an outcome of (Modern, Modern) is preferable to (Conservative, Conservative) because the proportion of Conservative individuals is so high. Modernism will always be the tenet of a doomed minority.
Hence we learn valuable lesson from our analysis of Lu Xun’s story, and, by proxy, backward traditional China. It is irrational to adopt modern values when those around you hold traditional ones, even if the world would be a better place if everyone adopted modern values; were you to do so, you would be a “madman.”