Voodoo decision theories

Apparently some readers seem to have difficulties in finding my definition of the key term Voodoo Decision Theory on this site. Take note then that this term is discussed/explained on the Voodoo Science page. For your convenience, here is a copy of this page:

The terms “voodoo economics”, “voodoo mathematics”, “voodoo statistics”, “voodoo ecology” and so on, seem to have been coined with the same object in mind. To put across the idea captured in point 4 of the definition given in the old ENCARTA dictionary (color added):

Voodoo n

  1. A religion practiced throughout Caribbean countries, especially Haiti, that is a combination of Roman Catholic rituals and animistic beliefs of Dahomean enslaved laborers, involving magic communication with ancestors.
  2. Somebody who practices voodoo.
  3. A charm, spell, or fetish regarded by those who practice voodoo as having magical powers.
  4. A belief, theory, or method that lacks sufficient evidence or proof.

It should be pointed out, therefore, that the term “voodoo theory” is used in this blog to convey the thinking summed up in point 4 of the above definition. Hence, in this discussion a voodoo theory designates a theory that lacks sufficient evidence or proof, and/or is based on utterly unrealistic and/or contradictory assumptions, spurious correlations, and so on.

I should point out, though, that the term "Voodoo Decision Theory" is not my coinage (what a pity!):

The behavior of Kropotkin’s cooperators is something like that of decision makers using the Jeffrey expected utility model in the Max and Moritz situation. Are ground squirrels and vampires using voodoo decision theory?

Brian Skyrms (1996, p. 51)
Evolution of the Social Contract
Cambridge University Press.

To illustrate a voodoo decision theory in action, consider this.

Example

Suppose that your task is to determine how a given function, f=f(x), behaves on the interval X=[-1000,1000]. For instance, assume that the issue is the constraint f(x) ≥ 0. That is, assume that you want to know how robust this constraint is over the interval X=[-1000,1000].

Also, assume that evaluating function f on X is difficult and/or costly.

Then, a voodoo decision theory would come to the rescue as follows: instead of examining the constraint f(x) ≥ 0 over X, it would prescribe testing it only over a small subset of X, say X’=[-1,1].

Now suppose that the constraint f(x) ≥ 0 performs well on X’=[-1,1]. What can we say about the performance of this constraint on X=[-1000,1000]?

No Man’s Land No Man’s Land
[-1,1]

Well, if you espouse voodoo decision theory, you would argue that the performance of f(x) ≥ 0 on X’=[-1,1] provides a good indication of the performance of f(x) ≥ 0 on X=[-1000,1000], and therefore the constraint f(x) ≥ 0 performs well on X. In other words, you would argue that the performance on X=[-1,1] is representative of the performance on X=[-1000,1000].

You can save a lot of $$$$$$$ this way: instead of evaluating the performance of a system over the required large space, you quickly evaluate its performance only on a relatively small subset of the required space.

However, seeing through the nonsensical argument made by voodoo decision theory, you would argue that this is absurd because:

  • X’=[-1,1] constitutes a tiny part of X=[-1000,1000], in fact only 0.1 percent of it.
  • All the points in X’ are in the same neighborhood.
  • Therefore X’ is not representative of X insofar as the performance of f(x) ≥ 0 is concerned.
  • Therefore, hardly anything can be deduced about the performance of f(x) ≥ 0 on X from the performance of f(x) ≥ 0 on X’.
  • All we can say is that f(x) ≥ 0 performs well on X’.

Got the drift?

Of course, some readers may question the significance of this example, arguing that it is hyperbolic. After all, who would so much as contemplate suggesting that X=[-1,1] is representative of X=[-1000,1000] with regard to the constraint f(x) ≥ 0 (unless f has some very unique properties)?

My answer to this is that — as we shall see — this example is not an exaggeration. It is implicit in the type of argument used by experienced senior analysts in academia and business/industry (eg. banks) to justify the application of the methodology that they propose/develop (see the discussion on the No Man’s Land syndrome associated with info-gap decision theory).

Viva la Voodoo!

Moshe

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