Flexible Bayesian approach for psychological modeling of decision making

KAZUO SHIGEMASU; AKIKO YOKOYAMA

doi:10.4992/psycholres1954.36.20

心理学的意思決定モデルのためのベイズアプローチの柔軟化

繁桝算男, 横山明子

著者情報

ジャーナルフリー

1994 年 36 巻 1 号 p. 20-28

DOI https://doi.org/10.4992/psycholres1954.36.20

詳細

発行日: 1994/04/20 受付日: 1993/11/16 J-STAGE公開日: 2009/02/24 受理日: 1994/01/08 早期公開日: - 改訂日: -
訂正情報
訂正日: 2009/02/24 訂正理由: - 訂正箇所: 論文抄録訂正内容: Wrong : In this paper, we propose the flexible Bayesian approach to describe the psychological decision making process. That is, by easing the Bayesian Axiom system, we come up with higher order probability and flexible utitiliy assessment. The purpose of this paper is to check whether the flexible Bayesian approach can explain some counter-intuitive examples. Using a questionnaire, we asked the subjects (undergraduate students, n=203) to evaluate the subjective probabilities and the betting preferences in the Ellsberg's Urn Problem and the Three Prisoners Problem. For the Ellsberg's Urn Problem, higher order probability was adequate to explain the paradox, more so than the non-additive representation of uncertainty. For the Three Prisoners Problem, higher order mathematical probability fails to explain the subjects' responses, which are stubbornly against Bayesian probability, but the fuzzy representation of higher order probability by means of the membership function was adequate for the explanation of this paradox.
Right : In this paper, we propose the flexible Bayesian approach to describe the psychological decision making process. That is, by easing the Bayesian Axiom system, we come up with higher order probability and flexible utitiliy assessment. The purpose of this paper is to check whether the flexible Bayesian approach can explain some counter-intuitive examples. Using a questionnaire, we asked the subjects (undergraduate students, n=203) to evaluate the subjective probabilities and the betting preferences in the Ellsberg's Urn Problem and the Three Prisoners Problem. For the Ellsberg's Urn Problem, higher order probability was adequate to explain the paradox, more so than the non-additive representation of uncertainty. For the Three Prisoners Problem, higher order mathematical probability fails to explain the subjr<ts' tesponses, which are stubbornly against Bayesian probability, but the fuzzy representation of higher order probability by means of the membership function was adequate for the explanation of this paradox.

訂正日: 2009/02/24 訂正理由: - 訂正箇所: 所属機関情報訂正内容: Wrong :
1) Department of Education, Faculty of Engineering, Tokkyo Institute of Technology
2) School of Science and Engineering, Teikyo University

Right :
1) Department of Education, Faculty of Engineering, Tokyo Institute of Technology
2) School of Science and Engineering, Teikyo University

訂正日: 2009/02/24 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : Camerer, C., & Weber, M. 1992 Recent development in modeling preferences: Uncertainty and ambiguity. Journal of Risk and Uncertainty, 5, 325-370.
DeGroot, M. H. 1970 Optirnal statistical decisions. New York: MacGraw-Hill.
Ellsberg, D. 1961 Risk, ambiguity, and the Savage axioms. Quarterly Journal of Economics, 75, 643-669.
Good. 1. J. 1965 The estimation of probabilities. An essay on modern Bavesian Methods. Boston: The M. I. T. Press.
Good, I. J. 1971 The probabilistic explication and of information, evidence, surprise, causality, explanation and utility In V. P. Godambe & D. A. Sprott (Eds.), Foundation of statistical inference. Toronto: Holt, Rinehart, and Winston of Canada. Pp. 108-141.
Goldsmith, R. W., & Sahlin, N. 1983 The role of second-order probabilities in decision making. In P. Humphreys, O. Svenson & A. Vari (Eds.), Analysing and aiding decision processes. New York: North-Holland Publising. Pp. 455-466.
Kahneman, D., Knetsch, J. I., & Thaler, R. 1990 Experimental test of the endowment effect and the Coase theorem. Journal of Political Economy, 98. 1325-1348.
Kahneman, D., Solvic. P., & Tversky, A. 1982 Judgement under uncertainty: Heristics and biases. Cambridge: Cambridge University Press.
Kahneman, D., & Tversky, A. 1979 Prospect theory: An analysis of decision under risk. Econometrica, 47, 263-291.
Kahneman, D., & Tversky, A. 1982 The psychology of preference. Scientific American, 264, 160-173.
Lindley, D. V. 1971 Making decisions. London: John Wiley.
Lindley, D. V. 1985 Making decisions. 2nd ed. London: John Wiley.
Mosteller, F. 1965 Fifty challenging problems in probability with solution. Reading, MA: Addison-Wesley.
Rapoport, A., Wallsten, T. S., & Cox, J. A. 1987 Direct and indirect scaling of membership function of probability phrases. Muthl Modelling, 9, 397-417.
Schmaidler, D. 1989 Subjective probability and expected utility without additivity. Econornetrika, 57, 571-587.
Shigemasu, K. 1988 Rationality in probability judgement. Japanese Journal of Behaviormetrics, 16, 39-48. (In Japanese with English summary)
Shigemasu, K., & Sugawara. H. 1991 Measurement of subjective probability by means of membership function. Proceedings of the International Fuzzy Engineering System '91, 175-184.
Shimojo, S., & Ichikawa, S. 1989 Intuitive reasoning about probability: Theoretical and experimental analyses of the “problem of three prisoners”.Cognition, 32, 1-24.
Simonson, I., & Tversky, A. 1992 Choice in context: Tradeoff contrast and extremeness aversion. Journal of Marketing Research, 14, 281-295.
Tversky, A., & Kahneman, D. 1991 Loss aversion in riskless choice: A reference-dependent model. Quarterly Journal of Economics, 107, 1039-1061.
Tversky, A., & Kahneman, D. 1992 Advances in Prospect Theory: Cumulative presentation of uncertainty. Journal of Risk and Uncertainty, 5, 297-323.
Von Neumann, J, & Morgenstern, O. 1947 Theory of games and economic behavior. 2nd ed. Princeton: Princeton University Press.

Right : Camerer, C., & Weber, M. 1992 Recent develop merit in modeling preferences: Uncertainty and ambiguity. Journal of Risk and Uncertainty, 5, 325-370.
DeGroot, M. H. 1970 Optimal statistical decisions. New York: MacGraw-Hill.
Ellsberg, D. 1961 Risk, ambiguity, and the Savage axioms. Quarterly Journal of Economics, 75, 643-669.
Good, I, J. 1965 The estimation of probabilities. An essay on modern Bayesian Methods. Boston: The M.I.T. Press.
Good, I. J. 1971 The probabilistic explication and of information, evidence,.surprise, causality, explanation and utility, In V. P. Godambe & D. A. Sprott (Eds.), Foundation of statistical inference. Toronto: Holt, Rinehart, and Winston of Canada. Pp.108-141.
Goldsmith, R. W., & Sahlin, N. 1983 The role of second-order probabilities in decision making. In P. Humphreys, O. Svenson & A. Vari (Eds.), Analysing and aiding decision processes. New York: North-Holland Publising. Pp.455-466.
Kahneman, D., Knetsch, J. L., & Thaler, R. 1990 Experimental test of the endowment effect and the Coase theorem. Journal of Political Economy, 98, 1325-1348.
Kahneman, D., Solvic. P., & Tversky, A. 1982 Judgement under uncertainty: Heristic.s and biases. Cambridge: Cambridge University Press.
Kahneman, D., & Tversky, A. 1979 Prospect theory: An analysis of decision under risk. Econometric a, 47, 263-291.
Kahneman, D., & Tversky, A. 1982 The psychology of preference. Scientific American, 264, 160-173.
Lindley, D. V. 1971 Making decisions. London: John Wiley.
Lindley, D. V. 1985 Making decisions. 2nd ed. London: John Wiley.
Mosteller, F. 1965 Fifty challenging problems in probability with solution. Reading, MA: Addison-Wesley.
Rapoport, A., Wallsten, T. S., & Cox, J. A. 1987 Direct and indirect scaling of membership function of probability phrases. Muthl Modelling, 9, 397-417.
Schmaidler, D. 1989 Subjective probability and expected utility without additivity. Econometrika, 57, 571-587.
Shigemasu, K. 1988 Rationality in probability judgement. Japanese Journal of Behaviorrnetrics, 16, 39-48.(In Japanese with English summary)
Shigemasu, K., & Sugawara. H. 1991 Measurement of subjective probability by means of membership function. Proceedings of the International Fuzzy Engineering System '9/, 175-184.
Shimojo, S., & Ichikawa, S. 1989 Intuitive reasoning about probability: Theoretical and experimental analyses of the “problem of three prisoners”. Cognition, 32, 1-24.
Simonson, I., & Tversky, A. 1992 Choice in context: Tradeoff contrast and extremeness aversion. Journal of Marketing Research, 14, 281-295.
Tversky, A., & Kahneman, D. 1991 Loss aversion in nskless choice: A reference-dependent model. Quarterly Journal of Economics, 107, I039-1061.
Tversky, A., & Kahneman, D. 1992 Advances in Prospect Theory: Cumulative presentation of uncertainty. Journal of Risk and Uncertainty, 5, 297-323
Von Neumann, J., & Morgenstern, O. 1947 Theory of games and economic behavior. 2nd ed. Princeton: Princeton University Press.

訂正日: 2009/02/24 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

訂正日: 2009/02/24 訂正理由: - 訂正箇所: 論文抄録訂正内容: Wrong : In this paper, we propose the flexible Bayesian approach to describe the psychological decision making process. That is, by easing the Bayesian Axiom system, we come up with higher order probability and flexible utitiliy assessment. The purpose of this paper is to check whether the flexible Bayesian approach can explain some counter-intuitive examples. Using a questionnaire, we asked the subjects (undergraduate students, n=203) to evaluate the subjective probabilities and the betting preferences in the Ellsberg's Urn Problem and the Three Prisoners Problem. For the Ellsberg's Urn Problem, higher order probability was adequate to explain the paradox, more so than the non-additive representation of uncertainty. For the Three Prisoners Problem, higher order mathematical probability fails to explain the subjr<ts' tesponses, which are stubbornly against Bayesian probability, but the fuzzy representation of higher order probability by means of the membership function was adequate for the explanation of this paradox.
Right : In this paper, we propose the flexible Bayesian approach to describe the psychological decision making process. That is, by easing the Bayesian Axiom system, we come up with higher order probability and flexible utitiliy assessment. The purpose of this paper is to check whether the flexible Bayesian approach can explain some counter-intuitive examples. Using a questionnaire, we asked the subjects (undergraduate students, n=203) to evaluate the subjective probabilities and the betting preferences in the Ellsberg's Urn Problem and the Three Prisoners Problem. For the Ellsberg's Urn Problem, higher order probability was adequate to explain the paradox, more so than the non-additive representation of uncertainty. For the Three Prisoners Problem, higher order mathematical probability fails to explain the subjects' responses, which are stubbornly against Bayesian probability, but the fuzzy representation of higher order probability by means of the membership function was adequate for the explanation of this paradox.

訂正日: 2009/02/24 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : Camerer, C., & Weber, M. 1992 Recent develop merit in modeling preferences: Uncertainty and ambiguity. Journal of Risk and Uncertainty, 5, 325-370.
DeGroot, M. H. 1970 Optimal statistical decisions. New York: MacGraw-Hill.
Ellsberg, D. 1961 Risk, ambiguity, and the Savage axioms. Quarterly Journal of Economics, 75, 643-669.
Good, I, J. 1965 The estimation of probabilities. An essay on modern Bayesian Methods. Boston: The M.I.T. Press.
Good, I. J. 1971 The probabilistic explication and of information, evidence,.surprise, causality, explanation and utility, In V. P. Godambe & D. A. Sprott (Eds.), Foundation of statistical inference. Toronto: Holt, Rinehart, and Winston of Canada. Pp.108-141.
Goldsmith, R. W., & Sahlin, N. 1983 The role of second-order probabilities in decision making. In P. Humphreys, O. Svenson & A. Vari (Eds.), Analysing and aiding decision processes. New York: North-Holland Publising. Pp.455-466.
Kahneman, D., Knetsch, J. L., & Thaler, R. 1990 Experimental test of the endowment effect and the Coase theorem. Journal of Political Economy, 98, 1325-1348.
Kahneman, D., Solvic. P., & Tversky, A. 1982 Judgement under uncertainty: Heristic.s and biases. Cambridge: Cambridge University Press.
Kahneman, D., & Tversky, A. 1979 Prospect theory: An analysis of decision under risk. Econometric a, 47, 263-291.
Kahneman, D., & Tversky, A. 1982 The psychology of preference. Scientific American, 264, 160-173.
Lindley, D. V. 1971 Making decisions. London: John Wiley.
Lindley, D. V. 1985 Making decisions. 2nd ed. London: John Wiley.
Mosteller, F. 1965 Fifty challenging problems in probability with solution. Reading, MA: Addison-Wesley.
Rapoport, A., Wallsten, T. S., & Cox, J. A. 1987 Direct and indirect scaling of membership function of probability phrases. Muthl Modelling, 9, 397-417.
Schmaidler, D. 1989 Subjective probability and expected utility without additivity. Econometrika, 57, 571-587.
Shigemasu, K. 1988 Rationality in probability judgement. Japanese Journal of Behaviorrnetrics, 16, 39-48.(In Japanese with English summary)
Shigemasu, K., & Sugawara. H. 1991 Measurement of subjective probability by means of membership function. Proceedings of the International Fuzzy Engineering System '9/, 175-184.
Shimojo, S., & Ichikawa, S. 1989 Intuitive reasoning about probability: Theoretical and experimental analyses of the “problem of three prisoners”. Cognition, 32, 1-24.
Simonson, I., & Tversky, A. 1992 Choice in context: Tradeoff contrast and extremeness aversion. Journal of Marketing Research, 14, 281-295.
Tversky, A., & Kahneman, D. 1991 Loss aversion in nskless choice: A reference-dependent model. Quarterly Journal of Economics, 107, I039-1061.
Tversky, A., & Kahneman, D. 1992 Advances in Prospect Theory: Cumulative presentation of uncertainty. Journal of Risk and Uncertainty, 5, 297-323
Von Neumann, J., & Morgenstern, O. 1947 Theory of games and economic behavior. 2nd ed. Princeton: Princeton University Press.

Right : Camerer, C., & Weber, M. 1992 Recent development in modeling preferences: Uncertainty and ambiguity. Journal of Risk and Uncertainty, 5, 325-370.
DeGroot, M. H. 1970 Optimal statistical decisions. New York: MacGraw-Hill.
Ellsberg, D. 1961 Risk, ambiguity, and the Savage axioms. Quarterly Journal of Economics, 75, 643-669.
Good, I, J. 1965 The estimation of probabilities. An essay on modern Bayesian Methods. Boston: The M.I.T. Press.
Good, I. J. 1971 The probabilistic explication and of information, evidence, surprise, causality, explanation and utility, In V. P. Godambe & D. A. Sprott (Eds.), Foundation of statistical inference. Toronto: Holt, Rinehart, and Winston of Canada. Pp. 108-141.
Goldsmith, R. W., & Sahlin, N. 1983 The role of second-order probabilities in decision making. In P. Humphreys, O. Svenson & A. Vari (Eds.), Analysing and aiding decision processes. New York: North-Holland Publising. Pp. 455-466.
Kahneman, D., Knetsch, J. L., & Thaler, R. 1990 Experimental test of the endowment effect and the Coase theorem. Journal of Political Economy, 98, 1325-1348.
Kahneman, D., Solvic. P., & Tversky, A. 1982 Judgement under uncertainty: Heristics and biases. Cambridge: Cambridge University Press.
Kahneman, D., & Tversky, A. 1979 Prospect theory: An analysis of decision under risk. Econometrica, 47, 263-291.
Kahneman, D., & Tversky, A. 1982 The psychology of preference. Scientific American, 264, 160-173.
Lindley, D. V. 1971 Making decisions. London: John Wiley.
Lindley, D. V. 1985 Making decisions. 2nd ed. London: John Wiley.
Mosteller, F. 1965 Fifty challenging problems in probability with solution. Reading, MA: Addison-Wesley.
Rapoport, A., Wallsten, T. S., & Cox, J. A. 1987 Direct and indirect scaling of membership function of probability phrases. Muthl Modelling, 9, 397-417.
Schmaidler, D. 1989 Subjective probability and expected utility without additivity. Econometrika, 57, 571-587.
Shigemasu, K. 1988 Rationality in probability judgement. Japanese Journal of Behaviormetrics, 16, 39-48.(In Japanese with English summary)
Shigemasu, K., & Sugawara. H. 1991 Measurement of subjective probability by means of membership function. Proceedings of the International Fuzzy Engineering System '91, 175-184.
Shimojo, S., & Ichikawa, S. 1989 Intuitive reasoning about probability: Theoretical and experimental analyses of the “problem of three prisoners”. Cognition, 32, 1-24.
Simonson, I., & Tversky, A. 1992 Choice in context: Tradeoff contrast and extremeness aversion. Journal of Marketing Research, 14, 281-295.
Tversky, A., & Kahneman, D. 1991 Loss aversion in riskless choice: A reference-dependent model. Quarterly Journal of Economics, 107, 1039-1061.
Tversky, A., & Kahneman, D. 1992 Advances in Prospect Theory: Cumulative presentation of uncertainty. Journal of Risk and Uncertainty, 5, 297-323.
Von Neumann, J., & Morgenstern, O. 1947 Theory of games and economic behavior. 2nd ed. Princeton: Princeton University Press.

抄録

In this paper, we propose the flexible Bayesian approach to describe the psychological decision making process. That is, by easing the Bayesian Axiom system, we come up with higher order probability and flexible utitiliy assessment. The purpose of this paper is to check whether the flexible Bayesian approach can explain some counter-intuitive examples. Using a questionnaire, we asked the subjects (undergraduate students, n=203) to evaluate the subjective probabilities and the betting preferences in the Ellsberg's Urn Problem and the Three Prisoners Problem. For the Ellsberg's Urn Problem, higher order probability was adequate to explain the paradox, more so than the non-additive representation of uncertainty. For the Three Prisoners Problem, higher order mathematical probability fails to explain the subjects' responses, which are stubbornly against Bayesian probability, but the fuzzy representation of higher order probability by means of the membership function was adequate for the explanation of this paradox.

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