A detailed theoretical analysis is presented of what five utility representations – subjective expected utility (SEU), rank-dependent (cumulative or Choquet) utility (RDU), gains decomposition utility (GDU), rank weighted utility (RWU), and a configural-weight model (TAX) that we show to be equivalent to RWU – say about a series of independence properties, many of which were suggested by M. H. Birnbaum and his coauthors. The goal is to clarify what implications to draw about the descriptive aspects of the representations from data (...) concerning these properties. The upshot is a sharp rejection of SEU and RDU and no clear choice between GDU and TAX, but a list of 8 properties is given that should receive more attention to discriminate between the latter two models. (shrink)
Discrete choice experiments—selecting the best and/or worst from a set of options—are increasingly used to provide more efficient and valid measurement of attitudes or preferences than conventional methods such as Likert scales. Discrete choice data have traditionally been analyzed with random utility models that have good measurement properties but provide limited insight into cognitive processes. We extend a well-established cognitive model, which has successfully explained both choices and response times for simple decision tasks, to complex, multi-attribute discrete choice data. The (...) fits, and parameters, of the extended model for two sets of choice data (involving patient preferences for dermatology appointments, and consumer attitudes toward mobile phones) agree with those of standard choice models. The extended model also accounts for choice and response time data in a perceptual judgment task designed in a manner analogous to best–worst discrete choice experiments. We conclude that several research fields might benefit from discrete choice experiments, and that the particular accumulator-based models of decision making used in response time research can also provide process-level instantiations for random utility models. (shrink)
The present theory leads to a set of subjective weights such that the utility of an uncertain alternative (gamble) is partitioned into three terms involving those weights—a conventional subjectively weighted utility function over pure consequences, a subjectively weighted value function over events, and a subjectively weighted function of the subjective weights. Under several assumptions, this becomes one of several standard utility representations, plus a weighted value function over events, plus an entropy term of the weights. In the finitely additive case, (...) the latter is the Shannon entropy; in all other cases it is entropy of degree not 1. The primary mathematical tool is the theory of inset entropy. (shrink)
One aspect of the utility of gambling may evidence itself in failures of idempotence, i.e., when all chance outcomes give rise to the same consequence the `gamble' may not be indifferent to its common consequence. Under the assumption of segregation, such gambles can be expressed as the joint receipt of the common consequence and what we call `an element of chance', namely, the same gamble with the common consequence replaced by the status quo. Generalizing, any gamble is indifferent to the (...) joint receipt of its element of chance and a certain consequence, which is called the `kernel equivalent' of the gamble. Under idempotence, the kernel equivalent equals the certainty equivalent. Conditions are reported (Theorem 4) that are sufficient for the kernel equivalents to have the kind of utility representation first discussed by Luce and Fishburn (1991), including being idempotent. This utility representation of the kernel equivalents together with the derived form of utility over joint receipts yields a utility representation of the original structure. Possible forms for the utility of an element of chance are developed. (shrink)
Suppose that the axioms of conjoint measurement hold for quantities having two independent components and that the axioms of extensive measurement hold for each of these components separately. In a recent paper, Luce shows that if a certain axiom relates the two measurement systems, then the conjoint measure on each component is a power function of the extensive measure on that component. Luce supposes that each component set contains all "rational fractions" of each element in that set; in this note (...) we present an alternative form of the axiom relating the measurement systems that enables us to prove Luce's result without requiring that such "rational fractions" exist. (shrink)
Suppose that entities composed of two distinct components can be qualitatively ordered in two ways, such that each ordering relation satisfies the axioms of conjoint measurement. Without further assumptions nothing can be said about the relation between the pair of numerical scales constructed for each component. Axioms are stated that relate the two measurement theories, and that are sufficient to establish that the two conjoint scales on each component are linearly related.
This article presents Paul Ricœur’s hermeneutic of the productive imagination as a methodological tool for understanding the innovative social function of texts that in exceeding their semantic meaning, iconically augment reality. Through the reasoning of Rastafari elder Mortimo Planno’s unpublished text, Rastafarian: The Earth’s Most Strangest Man, and the religious and biblical signification from the music of his most famous postulate, Bob Marley, this article applies Paul Ricœur’s schema of the religious productive imagination to conceptualize the metaphoric transfer from (...) text to life of verbal and iconic images of Rastafari’s hermeneutic of word, sound and power. This transformation is accomplished through what Ricœur terms the phenomenology of the iconic augmentation of reality. Understanding this semantic innovation is critical to understanding the capacity of the religious imagination to transform reality as a proclamation of hope in the midst of despair. (shrink)
In Use and Abuse Revisited: Response to Pluhar and Varner, Kathryn Paxton George misunderstands the point of my essay, In Defense of the Vegan Ideal: Rhetoric and Bias in the Nutrition Literature. I did not claim that the nutrition literature unambiguously confirms that vegans are not at significantly greater risk of deficiencies than omnivores. Rather than settling any empirical controversy, my aim was to show how the literature can give the casual reader a skewed impression of what is known (...) about the risks of a vegan diet. In this brief rejoinder, I illustrate how two essays by nutritionists in the same volume as George's and my essays, and a referee's report on my manuscript which was authored by a nutritionist, confirm the soundness of this basic insight. (shrink)