The Law of Requisite Variety

It has been a plea ever since the days of the psalmist:

Lord, how much longer are the wicked
how much longer are the wicked to triumph?

(Psalm 94:3)

and the prophet:

Why is it that the wicked live so prosperously?
Why do scoundrels enjoy peace?

(Jeremiah 12:1b)

Citations adapted from the Jerusalem Bible

In system terms, there is a simple answer. For present purposes, ignore the fashionable usage of "wicked" as a term of approbation."Good" people are bound by rules as to what is acceptable and what not; "wicked" people are bound by no such rules. In the short term at least, "wicked" people have no constraints and hence greater freedom of action, and the "Law of Requisite Variety" suggests that those components of a system which have the greatest flexibility and freedom are therefore the most powerful.

The law was formulated by W Ross Ashby in 1956, in a seminal theoretical work called "Introduction to Cybernetics" (ch. 11), which set out the cybernetic principles which would need to be embodied in any artificial intelligence project, despite there being little technological infrastructure at the time for its implementation.

He starts from the consideration of a simple game, in which player R has to make choices from a row of symbols presented by player D. It takes little mathematical knowledge, but a certain amount of patience with symbolic notation, to realise that D has the upper hand if the line of symbols presented do not contain the one R is trying to select.

The closest Ashby comes to a real-world example at this point is one of his exercises:

A guest is coming to dinner, but the butler (real-world?) does not know who. He knows only that it may be Mr A, who drinks only sherry or wine, Mrs B who drinks only gin or brandy, or Mr C who drinks only red wine, brandy, or sherry. In the cellar he finds he has only whisky, gin, and sherry. Can he find something acceptable to the guest, whoever comes?

(from Ashby, 1956; 11.4 ex. 4)

(My cynical annotation.) The guests are playing D, the butler R. He can get by, but if a hypothetical Ms D turns up, who drinks only wine or brandy, he can't cope and will be out on his ear, as indeed he should be: what kind of butler has no wine in the cellar?

Putting it "picturesquely", in Ashby's terms:

"Only variety in R can force down the variety due to D; only variety can destroy variety"

An abstract and abstruse point indeed: but put it back into the real world and its implications are indeed frightening.

  • "It's the only language they understand."
  • "You have to fight fire with fire."

This is the rhetoric of vigilantism and the lynch-mob, and it stems from a recognition that as long as the "good guys" are constrained by the rule of law, they do not have the same power as the "bad guys". The problem is that when the "good guys" are no longer so constrained, it is impossible to tell them from the "bad guys".

I don't want to get political, but the parallels are obvious: following this argument the "war on terrorism" cannot be won on the basis of the rule of law and respect for human rights. But if those are jettisoned, aren't democratic authorities "as bad as" the terrorists? Camp X-ray must spring to mind.

Indeed, the "bad guys" can even play this game to their advantage. Make the "good guys" come "down to their level", and they expose the raw violence allegedly at the heart of the most liberal and democratic state. If you are a terrorist (guerilla, freedom fighter, etc.) this is a brilliant tactic to undermine the moral authority of a state (and of course you have no moral compunction against employing it).

Learning and Teaching?

What has this got to do with learning and teaching? It's a pretty trivial arena in which to apply it, when the peace of the world is at stake, isn't it? Perhaps, but it is implicit in issues of class management.

In the short term, the disruptive student can always "win", because she or he has more options than the teacher. He can swear at you. He might even assault you. She can walk out. She can turn over the desks and disrupt the class...

You the teacher on the other hand, are constrained by regulations and codes of practice. You cannot "fight fire with fire". You have paltry and seemingly ineffectual sanctions which make you look weak and powerless.

  • "Go and stand outside the head of department's office!"
  • Why should she?
  • "If you continue with this behaviour, you will be excluded!"
  • Big deal! I didn't want to be here in the first place!

The situation, then, is hopeless. Isn't it? See "Disruptive students"

The power of "w"

W? In game theory, "w" stands for "the probability of this situation occurring again", and it makes all the difference. In time. Game theory ain't trivial; it is a serious branch of mathematics.

Why should a trader not swindle his customers? Because he wants them to come back and deal again. If they are tourists, they may be fair game; but locals are a different matter.

  • The classic illustration is the "Prisoner's Dilemma" (Axelrod, 1984; Poundstone, 1992)

In other words, if you have an investment in the system, you are more likely to play by its rules.

The "system"—whatever it is—is more likely to win in the end, because beyond the micro-situation of the rule-bound teacher and the recalcitrant student, the "system" has other sanctions. They range from economic sanctions (getting a job) through penal sanctions to nuclear weapons. Whichever way you look at it, in the long term the "system" has the requisite variety—and there is no way the stroppy adolescent can avoid interacting with it.

But does he know that (yet)? No. He doesn't do long term.

  • But it is more than that. His behaviour is prima facie evidence of his alienation or "disaffection" from the system. There are plenty of young people like him who feel the same way, but who are nevertheless sufficiently involved in the system not to act it out. (Or in his terms, "lack the f...ing guts" to do so.)

He is not going to change until he has some investment. In simple terms he has to get a greater payoff from involvement (even "conformity") than from using his temporary requisite variety options.

  • The crudest solution is to mobilise fear. That is what the criminal justice system is about. It does not work very well, particularly within communities (systems) which are overall isolated or alienated from the whole.

  • The next crudest is bribery. This is a complicated issue because it suggests that he "wins", and so it is also unfair to those who do not push the issue as far.

There is no simple solution. Ashby's analysis may be sophisticated, but the solutions are banal. The strategies of individuals in moment-to-moment situations are often vitiated by wider considerations. We end up cajoling, nagging, threatening or seducing wild children or "free spirits" back into the fold.

What we may be able to do is to forestall disaffection in the first place (easier said than done, of course); and to show at the moment-to-moment level that "playing the game" really does pay off for everyone. It is never going to be easy.

References

ASHBY, W R (1956) Introduction to Cybernetics London; Wiley (chapter 11)

AXELROD, R (1984) The Evolution of Co-operation New York; Basic Books (UK Penguin edition 1990)

BINMORE K (2007) Game Theory; a very short introduction Oxford, OUP (Very Short Introductions Series)

POUNDSTONE W (1992) Prisoner's Dilemma: John von Neumann, Game Theory and the Puzzle of the Bomb New York; Doubleday (UK edition; Oxford University Press, 1993)

To reference this page copy and paste the text below:

Atherton J S (2013) Doceo; [On-line: UK] retrieved from

Original material by James Atherton: last up-dated overall 10 February 2013

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