# Example 1: Applied Alchemy

Info-gap decision theory is claimed to be radically different from all current theories for decision under uncertainty. The characteristic that is supposed to set it apart from all current theories for decision under uncertainty is its being non-probabilistic, likelihood-free, chance-free, belief-free, etc.

It is hard to overstate what a gross misrepresentation of the state of the art is entailed by this portrayal of info-gap decision theory. The suggestion that info-gap decision theory offers what all current theories for decision under uncertainty fail to offer misrepresents the fact that, models for dealing with a non-probabilistic uncertainty have been staple fare in this area of expertise for decades. Indeed, the most well-known, most widely used paradigm for decision-making under a non-probabilistic uncertainty is Wald’s Maximin model (circa 1940). And if this were not enough, then the irony is that info-gap’s robustness model and info-gap’s decision model for robustness are … simple Maximin models.

Still, ignoring this interesting fact for the moment, consider another interesting fact about info-gap decision theory which attests to the jarring inconsistencies in which info-gap scholars get entangled.

As stated above, info-gap decision theory is claimed to be non-probabilistic, likelihood-free, belief-free, chance-fee, etc. Yet, this does not stop info-gap scholars from attributing the following features and results to info-gap’s robustness model:

However, if they are uncertain about this model and wish to minimize the chance of unacceptably large costs, they can calculate the robustÐoptimal number of surveys with eqn 5.

Rout et al. (2009, p. 785, emphasis added)

The question of course is: how can a chance-free model possibly minimize the chance of unacceptably large costs?

And to make the point that this is not a slip of the tongue, but is rather typical of the explanations given by info-gap scholars to describe the info-gap methodology, consider this statement:

As the horizon of uncertainty $\alpha$ gets larger, the sets $U(\alpha,\tilde{u})$ become more inclusive. The info-gap model expresses the decision maker’s beliefs about uncertain variation of $u$ around $\tilde{u}$.

Davidovitch et al. (2009, p. 4, emphasis added)

The question of course is: how can a model of a belief-free theory possibly express the decision maker’s beliefs?

And another example:

Information-gap (henceforth termed ‘info-gap’) theory was invented to assist decision-making when there are substantial knowledge gaps and when probabilistic models of uncertainty are unreliable (Ben-Haim 2006). In general terms, info-gap theory seeks decisions that are most likely to achieve a minimally acceptable (satisfactory) outcome in the face of uncertainty, termed robust satisficing.

Burgman, Wintle, Thompson, Moilanen, Runge, and Ben-Haim (2008, p. 8; emphasis added).
Reconciling uncertain costs and benefits in Bayes nets for invasive species management
ACERA Endorsed Core Material: Final Report, Project 0601 – 0611, July 2008.

When challenged to explain the manifest inconsistency implied by these claims, info-gap scholars often resort to excuses such as this:

Well … we should perhaps have used different language. But you know what we mean.

To which the most appropriate answer is:

Indeed we do but … in this case your methodology amounts to the practice of Alchemy!