Abstract
Decision-making under partial ignorance and partial knowledge of risk is discussed. The presented approach is unlike traditional approaches, but is not novel. It retains the MEU rule and advocates further determination of probabilities. However, the further determination does not require personal introspection or additional empirical data.
The approach is possible under any inductive theory of rational belief with a parameterized rule of acceptance, wherein the choice of parameter value trades informativeness against freedom from error. With such a rule, it may be possible to identify justifiable determinate probabilities with a judicious choice of parameter value.
I argue that rationality obliges the use of determinate probabilities, if identifiable, and I make a claim about the epistemological priority of some determinate probabilities over others when there is a choice.
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References
Aitchison, J., 1968, ‘Discussion of Professor Dempster's Paper’, Annals of Mathematical Statistics 39.
Carnap, R., 1952, The Continuum of Inductive Methods, U. Chicago Press, Chicago.
Colson, G. and M. Zeleny, 1980: ‘Multicriterion Concept of Risk Under Incomplete Information’, Computers and Operational Research 7.
Diaconis, P. and S. Zabell: 1983, ‘Some Alternatives to Bayes' Rule’, T.R. 205, Dept. of Statistics, Stanford Univ.
Fishburn, P.: 1965, ‘Analysis of Decisions with Incomplete Knowledge of Probabilities’, Operations Research 13.
Franke, G.: 1978, ‘Expected Utility with Ambiguous Probabilities and Irrational Parameters’, Theory and Decision 9, 267–283.
Good, I.: 1950, Probability and the Weighing of Evidence, Hafner, New York.
Good, I.: 1983, Good Thinking: The Foundations of Probability and Its Applications, Minnesota.
Good, I. and A. McMichael: 1984, ‘A Pragmatic Modification of Explicativity for the Acceptance of Hypotheses’, Philosophy of Science 51.
Hurwicz, L.: ‘Some Specification Problems and Applications to Econometric Models’, Econometrica 19.
Isaacs, H.: 1963, ‘Sensitivity of Decisions to Probability Estimation Errors’, Operations Research 11.
Jaynes, E.: 1979, ‘Where Do We Stand on Maximum Entropy’, in Levine and Tribus (eds.), The Maximum Entropy Formalism, MIT, Cambridge.
Kyburg, H.: 1974, The Logical Foundations of Statistical Inference, D. Reidel, Dordrecht.
Kyburg, H.: 1982, ‘The Reference Class’, Philosophy of Science 50.
Kyburg, H.: 1983, Epistemology and Inference, Minnesota.
Kyburg, H.: 1983, (b) ‘Rational Belief’, Behaviour and Brain Sciences 6.
Kyburg, H.: 1984, Theory and Measurement, Cambridge.
Kyburg, H.: 1985, Science and Reason, working manuscript.
Levi, I.: 1963, ‘Corroboration and Rules of Acceptance’, British Journal for the Philosophy of Science 13.
Levi, I.: 1967, Gambling with Truth, Knopf, New York.
Levi, I.: 1976, ‘Acceptance Revisited’, in Bogdan (ed.), Local Induction, D. Reidel, Dordrecht.
Levi, I.: 1980, The Enterprise of Knowledge, MIT, Cambridge.
Levi, I.: 1980, (b) ‘Acceptance as a Basis for Induction’, in Cohen and Hesse (eds.), Applications of Inductive Logic, Oxford.
Levi, I.: 1982, ‘Self-Profile’, in Bogdan (ed.), Henry E. Kyburg, Jr. and Isaac Levi, D. Reidel, Dordrecht.
Levi, I.: 1984, Decisions and Revisions, Cambridge.
Loui, R.: 1986, ‘Interval-based Decisions for Reasoning Systems’, in Lemmer and Kanal (eds.), Proceedings of the First AAAI Workshop on Uncertainty and Probability in Artificial Intelligence, North-Holland.
Loui, R.: 1987, ‘Theory, Measurement, and Computation of Preference’, Ph.D. thesis in preparation, University of Rochester.
Luce, R. and H. Raiffa: 1958, Games and Decisions, Wiley, New York.
Menges, G., and S. Huschens: 1984, ‘The Information Problem in Decision Making’, Theory and Decision 16, 45–58.
Menges, G. and E. Kofler: 1976, ‘Cognitive Decisions under Partial Information’, in Bogdan (ed.), Local Induction, D. Reidel, Dordrecht.
Potter, J. and B. Anderson: 1980, ‘Partial Prior Information and Decisionmaking’, IEEE Systems, Man, and Cybernetics 10.
Savage, L.: 1954, The Foundations of Statistics, Wiley, New York.
Schneller, G., and G. Sphicas: 1983, ‘Decision Making under Uncertainty: Starr's Domain Criterion’, Theory and Decision 15, 321–336.
Seidenfeld, T.: 1983, ‘Decisions with Indeterminate Probabilities: Response to Kyburg’, Behavioral and Brain Sciences 6.
Shafer, G.: 1976, A Mathematical Theory of Evidence, Princeton.
Shafer, G.: 1984, ‘On Zadeh's Counterexample to Dempster's Rule’, unpublished note.
Starr, M.: 1966, ‘A Discussion of Some Normative Criteria for Decision-Making under Uncertainty’, Industrial Management Review 8.
Swain, M. (ed.): 1970, Induction, Acceptance, and Rational Belief, D. Reidel, Dordrecht.
White, C., A. Sage, and W. Scherer: 1982, ‘Decision Support with Partially Identified Parameters’, Large Scale Systems 3.
Wolfenson, M. and T. Fine: ‘Bayes-Like Decision-Making with Upper and Lower Probabilities’, JASA 77.
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Loui, R.P. Decisions with indeterminate probabilities. Theor Decis 21, 283–309 (1986). https://doi.org/10.1007/BF00134099
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DOI: https://doi.org/10.1007/BF00134099