Prior-free Blackwell

Abstract This paper develops a prior-free model of data-driven decision making in which the decision maker observes the entire distribution of signals generated by a known experiment under an unknown distribution of the state variable and evaluates actions according to their worst-case payoff over the set of state distributions consistent with that observation. We propose a ranking of experiments in which E is robustly more informative than $$E'$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>E</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:math> if the value of the decision maker’s problem after observing E is always at least as high as the value of the decision maker’s problem after observing $$E'.$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>E</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mo>.</mml:mo> </mml:mrow> </mml:math> This comparison, which is strictly weaker than Blackwell’s classical order, holds if and only if the null space of E is contained in the null space of $$E'.$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>E</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mo>.</mml:mo> </mml:mrow> </mml:math>