Info-gap Decision Theory - Classical Decision Theory Perspective

Classical Decision Theory Perspective

Sniedovich raises two objections to info-gap decision theory, from the point of view of classical decision theory, one substantive, one scholarly:

the info-gap uncertainty model is flawed and oversold

Info-gap models uncertainty via a nested family of subsets around a point estimate, and is touted as applicable under situations of "severe uncertainty". Sniedovich argues that under severe uncertainty, one should not start from a point estimate, which is assumed to be seriously flawed: instead the set one should consider is the universe of possibilities, not subsets thereof. Stated alternatively, under severe uncertainty, one should use global decision theory (consider the entire universe), not local decision theory (starting with an estimate and considering deviations from it).

info-gap is maximin

Ben-Haim (2006, p.xii) claims that info-gap is "radically different from all current theories of decision under uncertainty," while Sniedovich argues that info-gap's robustness analysis is precisely maximin analysis of the horizon of uncertainty. By contrast, Ben-Haim states (Ben-Haim 1999, pp. 271–2) that "robust reliability is emphatically not a worst-case analysis".

Sniedovich has challenged the validity of info-gap theory for making decisions under severe uncertainty. He questions the effectiveness of info-gap theory in situations where the best estimate is a poor indication of the true value of . Sniedovich notes that the info-gap robustness function is "local" to the region around, where is likely to be substantially in error. He concludes that therefore the info-gap robustness function is an unreliable assessment of immunity to error.

In the framework of classical decision theory, info-gap's robustness model can be construed as an instance of Wald's Maximin model and its opportuneness model is an instance of the classical Minimin model. Both operate in the neighborhood of an estimate of the parameter of interest whose true value is subject to severe uncertainty and therefore is likely to be substantially wrong. Moreover, the considerations brought to bear upon the decision process itself also originate in the locality of this unreliable estimate, and so may or may not be reflective of the entire range of decisions and uncertainties.