The object of this study was to determine whether statistical decision theory, or a special application of it, the theory of signal detection, could be of value in accounting for the behaviour of subjects in a perceptual decision-making task. The amount of information in these tasks was varied to see if the theory could predict changes in subject performance. Five subjects were required to distinguish between fifty percent time compressed recordings of the stimulus words "commination" and "comminution” embedded in "white" noise. Under one treatment, compression was gained by discarding many small letter segments while in the other this same compression value was obtained by discarding a few large letter segments. It was hypothesized that large-discard- interval compression would be more detrimental to stimulus intelligibility than small-discard-interval compression. Five other subjects were asked to distinguish between the two noise-embedded stimulus words which had been time-compressed sixty and seventy-four percent. It was predicted that sixty percent compression would be less detrimental to the intelligibility of the stimulus words than seventy-four percent compression. Concurrently, in both groups, an attempt was made to manipulate the degree of cautiousness or decision criteria of all ten subjects. Such manipulation was attempted in order to permit the separation of each subjects' actual sensitivity from each's variable decision criterion. This manipulation involved varying the costs and fines associated with correct and incorrect decisions as well as the probabilities of each stimulus word's occurrence. Large-discard-interval compression was found to be less detrimental to intelligibility, as inferred from subject performance, than small-discard-interval compression. This finding was contrary to the first hypothesis. Sixty percent compression, as predicted, was less detrimental to intelligibility than seventy-four percent compression. It was observed that the theory of signal detection permitted separation of each subjects' sensitivity from his monetary degree of cautiousness. This cautiousness was also found to be accessible to manipulation. It is suggested that since the approach of statistical decision theory detected changes in subject performance in response to varying amounts of information, it can be profitably applied to the study of perception. / Arts, Faculty of / Psychology, Department of / Graduate

This dissertation consists of two parts. Part I contains the statements and proofs of two representation theorems. The first theorem, proved in Chapter 1, generalizes the quasilinear mean of Hardy, Littlewood and Poly by weakening their axiom of quasilinearity. Given two distributions with the same means, quasilinearity requires that mixtures of these distributions with another distribution in the same proportions share the same mean, regardless of the distribution that they are mixed with. We weaken the quasilinearity axiom by allowing the proportions that give rise to the same means to be different, This leads to a more general mean, denoted by M[sub=αФ], which has the form: M[sub=αФ] = Ф⁻¹(ʃ[sub=R] αФF/ʃαdF), where α is continuous and strictly monotone, a is continuous and strictly positive (negative) and F is a probability distribution. The quasilinear mean, denoted by M[sub=Ф], results when the a function is constant. We showed, in addition, that the M[sub=αФ] mean has the intermediate value property, and can be consistent with the stochastic dominance (including higher degree ones) partial order. We also generalized a well known inequality among quasilinear means, via the observation that the M[sub=αФ] mean of a distribution F can be written as the quasilinear mean of a distribution F[sup=α], where F[sup=α] is derived from F via a as the Radon-Nikodym derivative of F[sup=α] with respect to F. We noted that the M[sub=αФ] mean induces an ordering among probability distributions via the maximand, ʃ[sub=R] αФF/ʃαdF, that contains the (expected utility) maximand, ʃ[sub=R] αФF, of the quasilinear mean as a special case. Chapter 2 provides an alternative characterization of the above representation for simple probability measures on a more general outcome set where mean values may not be defined. In this case, axioms are stated directly in terms of properties of the underlying ordering. We retained several standard properties of expected utility, namely weak order, solvability and monotonicity but relaxed the substitutability axiom of Pratt, Raiffa and Schlaifer, which is essentially a restatement of quasi-linearity in the context of an ordering. Part II of the dissertation concerns one specific area of application decision theory. Interpreting the M[sub=αФ](F) mean of Chapter 1 as the certainty equivalent of a monetary lottery F, the corresponding induced binary relation has the natural interpretation as 'strict preference' between lotteries. For non-monetary (finite) lotteries, we apply the representation theorem of Chapter 2. The hypothesis, that a choice agent's preference among lotteries can be represented by a pair of α and Ф functions through the induced ordering, is referred to as alpha utility theory. This is logically equivalent to saying that the choice agent obeys either the mean value (certainty equivalent) axioms or the axioms on his strict preference binary relation. Alpha utility theory is a generalization of expected utility theory in the sense that the expected utility representation is a special case of the alpha utility representation. The motivation for generalizing expected utility comes from difficulties it faced in the description of certain choice phenomena, especially the Allais paradox. These are summarized in Chapter 3. Chapter 4 contains the formal statements of assumptions and the derivations of normative and descriptive implications of alpha utility theory. We stated conditions, taken from Chapter 1, for consistency with stochastic dominance and global risk aversion and derived a generalized Arrow-Pratt index of local risk aversion. We also demonstrated how alpha utility theory can be consistent with those choice phenomena that contradict the implications of expected utility, without violating either stochastic dominance or local risk aversion. The chapter ended with a comparison of alpha utility with two other theories that have attracted attention; namely, Allais' theory and prospect theory. Several other applications of the representation theorems of Part I are considered in the Conclusion of this dissertation. These include the use of the M[sub=αФ] mean as a model of the equally-distributed-equivalent level of income (Atkinson, 1970), and as a measure of asymmetry of a distribution (Canning, 1934). The alpha utility representation can also be used to rank social situations in the sense of Harsanyi (1977). We ended by pointing out an open question regarding conditions for comparative risk aversion and stated an extension of Samuelson's (1967) conjecture that Arrow's impossibility theorem would hold if individuals and society express their preferences by von Neumann-Morgenstern utility functions. / Graduate and Postdoctoral Studies / Graduate

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Thesis (Ph. D.)--Virginia Polytechnic Institute, 1963. / Vita. Abstract. Includes bibliographical references (leaves 113-114). Also available via the Internet.

The Bayesian theory has long been the predominate method in dealing with uncertainties in civil engineering practice including water resources engineering. However, it imposes unnecessary restrictive requirements on inferential problems. Concerns thus arise about the effectiveness of using Bayesian theory in dealing with more general inferential problems. The recently developed Dempster-Shafer theory appears to be able to surmount the limitations of Bayesian theory. The new theory was originally proposed as a pure mathematical theory. A reasonable amount of work has been done in trying to adopt this new theory in practice, most of this work being related to inexact inference in expert systems and all of the work still remaining in the fundamental stage. The purpose of this research is first to compare the two theories and second to try to apply Dempster-Shafer theory in solving real problems in water resources engineering. In comparing Bayesian and Dempster-Shafer theory, the equivalent situation between these two theories under a special situation is discussed first. The divergence of results from Dempster-Shafer and Bayesian approaches under more general situations where Bayesian theory is unsatisfactory is then examined. Following this, the conceptual difference between the two theories is argued. Also discussed in the first part of this research is the issue of dealing with evidence including classifying sources of evidence and expressing them through belief functions. In attempting to adopt Dempster-Shafer theory in engineering practice, the Dempster-Shafer decision theory, i.e. the application of Dempster-Shafer theory within the framework of conventional decision theory, is introduced. The application of this new decision theory is demonstrated through a water resources engineering design example. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

by Choi Ka Wai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 54-55). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Matching Process --- p.1 / Chapter 1.2 --- Centralization --- p.2 / Chapter 1.3 --- One-off Approach --- p.3 / Chapter 1.4 --- Our Approach --- p.4 / Chapter 1.5 --- Organization --- p.5 / Chapter 2 --- Decision Theory --- p.6 / Chapter 2.1 --- Ordinal Preference --- p.6 / Chapter 2.1.1 --- Strict Preference and Indifference --- p.6 / Chapter 2.1.2 --- Weak Preference --- p.8 / Chapter 2.2 --- Utility Theory --- p.8 / Chapter 2.3 --- Group Decision Making --- p.9 / Chapter 2.3.1 --- Social Choice Theory --- p.9 / Chapter 2.3.2 --- Bargaining --- p.11 / Chapter 3 --- The Matching Rule --- p.14 / Chapter 3.1 --- The Marriage Model --- p.15 / Chapter 3.2 --- Stability --- p.16

Thesis (Ph. D.)--California Institute of Technology, 2003. Thesis (Ph. D.). PQ #3093487. / Includes bibliographical references. Also available via the World Wide Web. http://www.fluff.info/klemens

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

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