A trichotomy of attitudes for decision-making under complete ignorance

We study decision criteria under complete ignorance, that is, when there is no available information regarding plausible probability distributions over the possible outcomes. We characterize the set of criteria satisfying quasi-transitivity, Savage's independence, duplication, a strong version of dominance and scale invariance. Only three criteria satisfy these requirements. These criteria are the well-known protective criterion, its dual criterion which we call hazardous, and a neutral criterion which is the composition of both (a decision is strictly preferred according to this criterion to another one if both the protective and the hazardous criteria strictly prefer the former).

[1]  Eric Maskin.  Decision-Making Under Ignorance with Implications for Social Choice , 1979 .

[2]  Jean-Yves Jaffray,et al.  Approximations of rational criteria under complete ignorance and the independence axiom , 1983 .

[3]  M. J. Driscoll,et al.  Risk and Uncertainty in Economics: Essays in Honour of James L. Ford , 1994 .

[4]  J. Jaffray,et al.  Rational Behavior under Complete Ignorance , 1980 .

[5]  J. Jaffray.  Linear utility theory for belief functions , 1989 .

[6]  J. Jaffray,et al.  Decision making with belief functions: Compatibility and incompatibility with the sure-thing principle , 1993 .

[7]  Howard Raiffa,et al.  Games and Decisions: Introduction and Critical Survey. , 1958 .

[8]  Claude Toulet.  Complete ignorance and independence axiom: Optimism, pessimism, indecisiveness , 1986 .

[9]  J. Milnor.  Games Against Nature , 1951 .

[10]  L. J. Savage,et al.  The Foundations of Statistics , 1955 .

[11]  Paolo Ghirardato,et al.  Coping with ignorance: unforeseen contingencies and non-additive uncertainty , 2001 .

[12]  Peter C. Fishburn,et al.  Even-chance lotteries in social choice theory , 1972 .

[13]  D. Schmeidler.  Subjective Probability and Expected Utility without Additivity , 1989 .

[14]  I. Gilboa,et al.  Maxmin Expected Utility with Non-Unique Prior , 1989 .

[15]  Massimo Marinacci,et al.  Differentiating ambiguity and ambiguity attitude , 2004, J. Econ. Theory.

[16]  Walter Bossert,et al.  Uncertainty aversion in nonprobabilistic decision models , 1997 .

[17]  Matthew O. Jackson,et al.  Maximin, leximin, and the protective criterion: Characterizations and comparisons , 1988 .

[18]  H. Raiffa,et al.  Games and Decisions: Introduction and Critical Survey. , 1958 .

[19]  T. Bewley.  Knightian Decision Theory, Part II. Intertemporal Problems , 1987 .

[20]  C. Tisdell,et al.  Uncertainty and Expectations in Economics - Carter,cf and Ford,jl , 1972 .

[21]  Kenneth J. Arrow,et al.  Studies in Resource Allocation Processes: Appendix: An optimality criterion for decision-making under ignorance , 1977 .