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                  The Law of Requisite Variety
                                                                 Author
The larger the variety of actions available to a control system, F. Heylighen, & C.
the larger the variety of perturbations it is able to            Joslyn,
compensate.
                  ----------------------------                   Date
                                                                 Aug 31, 2001
Control or regulation is most fundamentally formulated as a      (modified)
reduction of variety: perturbations with high variety affect the Aug 1993 (created)
system's internal state, which should be kept as close as
possible to the goal state, and therefore exhibit a low variety.         Home
So in a sense control prevents the transmission of variety from          [up]
environment to system. This is the opposite of information            Metasystem
transmission, where the purpose is to maximally conserve          Transition Theory
variety.                                                                 [up]
                                                                    Principles of
In active (feedforward and/or feedback) regulation, each             Systems and
disturbance D will have to be compensated by an appropriate          Cybernetics
counteraction from the regulator R. If R would react in the same
way to two different disturbances, then the result would be two           Up
different values for the essential variables, and thus imperfect  Prev. [4arr] Next
regulation. This means that if we wish to completely block the           Down
effect of D, the regulator must be able to produce at least as   --------------------
many counteractions as there are disturbances in D. Therefore,
the variety of R must be at least as great as the variety of D.
If we moreover take into account the constant reduction of
variety K due to buffering, the principle can be stated more
precisely as:

V(E)   V(D) - V(R) - K

Ashby has called this principle the law of requisite variety: in
active regulation only variety can destroy variety. It leads to
the somewhat counterintuitive observation that the regulator
must have a sufficiently large variety of actions in order to
ensure a sufficiently small variety of outcomes in the essential
variables E. This principle has important implications for
practical situations: since the variety of perturbations a
system can potentially be confronted with is unlimited, we
should always try maximize its internal variety (or diversity),
so as to be optimally prepared for any foreseeable or
unforeseeable contigency.

Some Comments

Ashby's Law can be seen as an application of the principle of
selective variety. However, a frequently cited stronger
formulation of Ashby's Law, "the variety in the control system
must be equal to or larger than the variety of the perturbations
in order to achieve control", which ignores the constant factor
K, does not hold in general. Indeed, the underlying "only
variety can destroy variety" assumption is in contradiction with
the principle of asymmetric transitions which implies that
spontaneous decrease of variety is possible (which is precisely
what buffering does). For example, a bacterium searching for
food and avoiding poisons has a minimal variety of only two
actions: increase or decrease the rate of random movements. Yet,
it is capable to cope with a quite complex environment, with
many different types of perturbations and opportunities. Its
blind "transitions" are normally sufficient to find a favourable
situation, thus escaping all dangers.

Ashby's law is perhaps the most famous (and some would say the   --------------------
only successful) principle of cybernetics recognized by the           Discussion
whole Cybernetics and Systems Science community. The Law has     --------------------
many forms, but it is very simple and common sensical: a model   
system or controller can only model or control something to the    * Bacteria and the
extent that it has sufficient internal variety to represent it.      strong form of
For example, in order to make a choice between two alternatives,     Ashby's LRV,
the controller must be able to represent at least two                Comment by
possibilities, and thus one distinction. From an alternative         Phanish Puranam
perspective, the quantity of variety that the model system or
controller possesses provides an upper bound for the quantity of    Add comment...
variety that can be controlled or modeled.
                                                                          _
Requisite Variety has had a number of uses over the years , and
there are a number of alternative formulations. Variety can be
quantified according to different distributions, for example
probabilistic entropies and possibilistic nonspecificities.
Under a stochastic formulation, there is a particularly
interesting isomorphism between the LRV, the 2nd Law of
Thermodynamics, and Shannon's 10th Theorem .

See also: Dictionary: LAW OF REQUISITE VARIETY

Reference: Heylighen F. (1992): "[externalli]Principles

of Systems and Cybernetics: an evolutionary perspective", in:
Cybernetics and Systems '92, R. Trappl (ed.), (World Science,
Singapore), p. 3-10.

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