A Note on an Example from Savage
7 Pages Posted: 21 Apr 2012
Date Written: April 2012
In his discussion of minimax decision rules, Savage (1954, p. 170)presents an example purporting to show the inadequacy of a minimaxnegative expected utility rule (referred to by Savage as 'negativeincome') as a decision criterion for statistics and suggests theapplication of a minimax regret rule instead. The crux of Savage'sobjection to minimax applied to negative income is the possibility thata decision maker would choose to ignore available information,regardless of how relevant the information may be. Notably, minimaxregret decision rules do not suffer from this flaw. However, in hisbook, Savage does not explicitly analyze his example. We give here adetailed examination of Savage's example in an effort to understand thefundamental differences between these two seemingly quite similardecision rules. References are given to other papers that have exploredthis issue, and we also briefly consider a third decision rule derivedfrom Gilboa and Schmeidler (1989).
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