This thesis addresses the problem of combining the prior density functions, f[sub=1],…,f[subn], of n individuals. In the first of two parts, various systems of axioms are developed which characterize successively the linear opinion pool, A(f[sub=1],...,f[sub=n]) = Σ[sup=n; sub= i=1] w[sub=i] f[sub=i] , and the logarithmic opinion pool, G(f[sub=1],…,f[sub=n]) = π[sup=n; sub= i=1] f[sup=α(i); sub=i] / ʃ π[sup=n; sub= i=1] dμ. It is first shown that A is the only pooling operator, T(f[sub=1],…,f[sub=n]), which is expressible as T(f[sub=1],…,f[sub=n]) (θ) = H(f[sub=1](θ),...,f[sub=n](θ), θ) for some function H which is continuous in its first n variables and satisfies H(0,...,0,θ) = 0 for μ- almost all θ. The regularity condition on H may be dispensed with if H does not depend on θ. This result leads to an impossibility theorem involving Madansky's axiom of External Bayesianity. Other consequences of this axiom of group rationality are also examined in some detail and yield a characterization of G as the only Externally Bayesian pooling operator of the form T(f[sub=1],…,f[sub=n])(θ) = H(f[sub=1],(θ),...,f[sub=n](θ))/ ʃH(f[sub=1],…,f[sub=n])dμ for some H:(0, ∞) —>(0, ∞). To prove this n result, it is necessary to introduce a "richness" condition on the underlying space of events, (θ,μ). Next, each opinion f[sub=i] is regarded as containing some "information" about θ and we look for a pooling operator whose expected information content is a maximum. The operator so obtained depends on the definition which is chosen; for example, Kullback-Leibler's definition entails the linear opinion pool, A. In the second part of the dissertation, it is argued that the domain of pooling operators should extend beyond densities. The notion of propensity function is introduced and examples are given which motivate this generalization; these include the well-known problem of combining P-values. A theorem of Aczel is adapted to derive a large class of pooling formulas which encompasses both A and G. A final characterization of G is given via the interpretation of betting odds, and the parallel between our approach and Nash's solution to the "bargaining problem" is discussed. / Science, Faculty of / Mathematics, Department of / Graduate

The strong normative expectation that dictates we should help our elderly parents is a largely unrecognised evolutionary puzzle. Why do we invest so heavily in our parents when they are long past their reproductive years? Adult children looking after their own offspring often face a double burden of care, and choosing to help aging parents is often in conflict with the primary evolutionary task of parenthood - your own genetic posterity by ensuring your children become parents themselves. Despite the large altruism literature, no one has yet addressed this particular issue. This thesis investigates this theoretical paradox and adds to the sparse empirical work on kin and nonkin-directed altruism. As a test of the two most popular Inclusive Fitness evolutionary explanations of altruistic behaviours; Kin Selection (Hamilton, 1964) and Reciprocal Altruism (Trivers, 1971), this study takes a side-wise look at helping attitudes and behaviours across multiple types of relationships. A Choice Model experiment assessed 453 people from all Australian states stratified by age (145 16-24 year olds; 162 25-54 year olds, and 146 over 55 year olds). Participants responded to sixteen hypothetical situations where they could choose to help only one person from two persons requiring their help. The scenarios contained ten variables (relationship type; sex, type of help; history of reciprocation etc.) that were systematically varied. Data was analysed using Hierarchical Bayesian estimation methods, and after factoring out our general tendency toward a species wide cooperation, found broad support for Inclusive Fitness principles. Generally, there was a clear pattern of helping behaviour that saw friends as of at least equal importance to more distant relatives (cousins etc). Elderly parents are helped for no better reason than they are needy and this is an unequivocal demonstration of our species’ primary social imperative - cooperation - a clear inference that adult children are looking for the rewards that cooperation brings. This research also provides interesting insights into the nature of extended family dynamics as a sequelae of our rapid social evolution. / Doctor of Philosophy (PhD)

Thesis (Ph. D.)--Indiana University of Pennsylvania. / Includes bibliographical references.

No description available.

Thesis (Ed.D.)--University of Tulsa, 1976. / Bibliography: leaves 52-54.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1991. / Vita. Abstract. Includes bibliographical references (leaves 90-94). Also available via the Internet.

Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 169-183). Also available via the Internet.

Thesis (Ph. D.)--University of Washington, 1998. / Vita. Includes bibliographical references (leaves [86]-90).

Thesis (Ph. D.)--University of Washington, 1997. / Vita. Includes bibliographical references (leaves [212]-293).

published_or_final_version / Public Administration / Master / Master of Public Administration