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Informationtheoretic Limitations of Formal Systems
 JOURNAL OF THE ACM
, 1974
"... An attempt is made to apply informationtheoretic computational complexity to metamathematics. The paper studies the number of bits of instructions that must be a given to a computer for it to perform finite and infinite tasks, and also the amount of time that it takes the computer to perform these ..."
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An attempt is made to apply informationtheoretic computational complexity to metamathematics. The paper studies the number of bits of instructions that must be a given to a computer for it to perform finite and infinite tasks, and also the amount of time that it takes the computer to perform these tasks. This is applied to measuring the difficulty of proving a given set of theorems, in terms of the number of bits of axioms that are assumed, and the size of the proofs needed to deduce the theorems from the axioms.
OPTIMISM AND PESSIMISM WITH EXPECTED UTILITY By
, 2011
"... Savage (1954) provided a set of axioms on preferences over acts that were equivalent to the existence of an expected utility representation. We show that in addition to this representation, there is a continuum of other “expected utility”representations in which for any act, the probability distribu ..."
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Savage (1954) provided a set of axioms on preferences over acts that were equivalent to the existence of an expected utility representation. We show that in addition to this representation, there is a continuum of other “expected utility”representations in which for any act, the probability distribution over states depends on the corresponding outcomes. We suggest that optimism and pessimism can be captured by the stakedependent probabilities in these alternative representations; e.g., for a pessimist, the probability of every outcome except the worst is distorted down from the Savage probability. Extending the DM’s preferences to be de…ned on both subjective acts and objective lotteries, we show how one may distinguish optimists from pessimists and separate attitude towards uncertainty from curvature of the utility function over monetary prizes.