This paper discusses random utility representations of the Luce model. Earlier works, such as McFadden, Yellott, and Strauss have discussed random utility representations under the assumption that utilities are additively separable in a deterministic and a random part. Under various conditions, they have established that a separable and independent random utility representation exists if and only if the random terms are type III extreme value distributed. This paper analyzes independent random utility representations without the separability condition and with an infinite (...) universal set of alternatives. Under these assumptions, it turns out that the most general random utility representation of the Luce model is a utility function that is an arbitrary strictly increasing transformation of a separable utility function with extreme value distributed random terms. (shrink)

Subjective probability plays an increasingly important role in many fields concerned with human cognition and behavior. Yet there have been significant criticisms of the idea that probabilities could actually be represented in the mind. This paper presents and elaborates a view of subjective probability as a kind of sampling propensity associated with internally represented generative models. The resulting view answers to some of the most well known criticisms of subjective probability, and is also supported by empirical work in neuroscience and (...) behavioral psychology. The repercussions of the view for how we conceive of many ordinary instances of subjective probability, and how it relates to more traditional conceptions of subjective probability, are discussed in some detail. (shrink)

In both theoretical and applied modeling in behavioral sciences, it is common to choose a mathematical specification of functional form and distribution of unobservables on grounds of analytic convenience without support from explicit theoretical postulates. This article discusses the issue of deriving particular qualitative hypotheses about functional form restrictions in structural models from intuitive theoretical axioms. In particular, we focus on a family of postulates known as dimensional invariance. Subsequently, we discuss how specific qualitative postulates can be reformulated so as (...) to allow for conventional statistical hypothesis testing, and we also derive details of a particular likelihood ratio test procedure. An empirical application of the testing procedure is carried out, based on data from a Stated Preference survey. (shrink)

Mathematicians often conduct aesthetic judgements to evaluate mathematical objects such as equations or proofs. But is there a consensus about which mathematical objects are beautiful? We used a comparative judgement technique to measure aesthetic intuitions among British mathematicians, Chinese mathematicians, and British mathematics undergraduates, with the aim of assessing whether judgements of mathematical beauty are influenced by cultural differences or levels of expertise. We found aesthetic agreement both within and across these demographic groups. We conclude that judgements of mathematical beauty (...) are not strongly influenced by cultural difference, levels of expertise, and types of mathematical objects. Our findings contrast with recent studies that found mathematicians often disagree with each other about mathematical beauty. (shrink)

To investigate cultural lifestyle preferences in different cultural contexts, a forced-choice questionnaire was constructed, based on Thurstone's Law of Comparative Judgement, an almost forgotten statistical method of 1927, which is a useful tool for assessing groups. This study's questionnaire items targeted job and living conditions in the spectrum from traditional to globalised lifestyles. Subjects were indigenous representatives at the UNO in Geneva, and students in Nigeria, Cameroon, South Africa and Germany. The preferences ascertained reflect attitudes on a scale ranging from (...) very traditional to very globalised lifestyles. Although being an uncommon assessment tool, Thurstone's Comparative Judgement indicates to yield highly valid outcomes, as the results of the African university students, though from three different countries, resembled each other, but were complementary to the results of the indigenous representatives, which, in turn, mirrored the Berlin controls' profiles, according to expectations. Findings are discussed in light of the Symbolic Self-Completion Theory. (shrink)

Human adults are thought to possess two dissociable systems to represent numbers: an approximate quantity system akin to a mental number line, and a verbal system capable of representing numbers exactly. Here, we study the interface between these two systems using an estimation task. Observers were asked to estimate the approximate numerosity of dot arrays. We show that, in the absence of calibration, estimates are largely inaccurate: responses increase monotonically with numerosity, but underestimate the actual numerosity. However, insertion of a (...) few inducer trials, in which participants are explicitly (and sometimes misleadingly) told that a given display contains 30 dots, is sufficient to calibrate their estimates on the whole range of stimuli. Based on these empirical results, we develop a model of the mapping between the numerical symbols and the representations of numerosity on the number line. (shrink)

The literature on mathematical explanation contains numerous examples of explanatory, and not so explanatory proofs. In this paper we report results of an empirical study aimed at investigating mathematicians’ notion of explanatoriness, and its relationship to accounts of mathematical explanation. Using a Comparative Judgement approach, we asked 38 mathematicians to assess the explanatory value of several proofs of the same proposition. We found an extremely high level of agreement among mathematicians, and some inconsistencies between their assessments and claims in the (...) literature regarding the explanatoriness of certain types of proofs. (shrink)

A new post-compulsory Music course known as the Western Australian Certificate of Education (WACE) Music course was recently introduced into Year 11 and 12 in Western Australian (WA) schools. Following a convoluted process of creation, its implementation into classrooms has been problematic. Given criticism levelled at its process of creation and implementation, the researcher questions whether the WACE Music course embodies effective, recognised principles to support the effective teaching and learning of music. This study investigates the principles which should form (...) the basis of an effective, post-compulsory music curriculum, suitable for WA. It involved a literature review which sought to produce a set of principles for teaching and learning frameworks based upon international best practice in music education, and applicable in the unique geographical, historical and multicultural WA context. In addition, the study employed a researcher–designed survey instrument to examine whether Western Australian music teachers perceived these principles to be evident in their practical experiences of the new WACE music course. With the subsequent publishing of a draft Australian National Arts Curriculum, it is an appropriate time to review the principles which should underpin an effective Music curriculum for senior secondary students in the WA context because, without a clear set of guiding principles that are understood by curriculum writers, there is a possibility that following courses could be fundamentally flawed and not serve the best interests of students. (shrink)

Amartya Sen has developed the so-called capability approach to meet the criticism that income alone may be insufficient as a measure of economic inequality. This is because knowledge about people’s income does not tell us what they are able to acquire with that income. For example, people with the same income may not have the same access to health and transportation services, schools and opportunities in the labor market. Recently, there has been growing interest in empirical studies based on the (...) capability approach. Most of these, however, are only loosely related to quantitative behavioral theory, at least in a concrete and empirically operational way. The purpose of this paper is to demonstrate that the theory of random scale models offers a powerful theoretical and empirical framework for representing and accounting for key aspects of Sen’s theory. (shrink)

For over half a century market segments have been considered objective groupings of individuals which marketers identify, understand, and target with advertising messages. The process of market segmentation has, therefore, occupied a position of moral neutrality. An increasingly popular method of segmentation is by consumer personality, with advertisers targeting messages to specific personality types. This paper explores personality segmentation, and presents empirical evidence to support the proposition that personality metrics that are used to assign individuals to segments may, in fact, (...) be manipulable by advertising executions themselves. Quite apart from the implications that this has for the business efficacy of the segmentation process, the ethical implications – particularly as applied to children – are considerable. (shrink)

Recently proposed models of risky choice imply systematic violations of transitivity of preference. This study explored whether people show the predicted intransitivity of the two models proposed to account for the certainty effect in Allais paradoxes. In order to distinguish “true” violations from those produced by “error,” a model was fit in which each choice can have a different error rate and each person can have a different pattern of preferences that need not be transitive. Error rate for a choice (...) is estimated from preference reversals between repeated presentations of the same choice. Results showed that few people repeated intransitive patterns. We can retain the hypothesis that all participants were transitive. (shrink)

During the interwar years psychologists Louis Leon Thurstone and Rensis Likert produced newly standardized forms of questionnaires. Both built on developments in mental testing, including the use of restricted sets of answers and the emergence of statistical techniques, to create questionnaires that employed numerical scaling. This transformation in shape of questionnaires was intimately tied up with both psychologists’ nominal subject of investigation: attitudes. Efforts to render psychology a socially valuable and influential science spurred psychologists to create sophisticated and increasingly precise (...) means of measuring social attitudes. Reducing mental dispositions to mere numbers on a scale, these developments also initiated new relationships between psychology and the public. Rather than engage a wide spectrum of the public directly in the research process, questionnaire research was limited to those within academic circles. Even so, research with questionnaires aimed to comment on attitudes in the public more broadly. The kind of ‘thin description’ afforded by numerical scales, though used to measure individual psychological subjects, afforded psychologists the opportunity to craft their vision of an increasingly attitudinal public, one positioned as best governed with the aid of psychological expertise. (shrink)

Decision-making capacity in children and adolescents in healthcare requires thorough assessment: the minor's maturity, understanding of the decision, risk of the situation and contextual factors needs to be explored. The intention was to design and validate a test—the Maturtest—to assess the maturity of minors in decision-making processes in healthcare. A reasoning test on moral conflicts for adolescents was designed to infer the degree of maturity of minors applied to decision-making regarding their own health. The test was completed by a sample (...) of 441 adolescents aged from twelve to sixteen, with a corresponding analysis of their psychometric skills to measure feasibility, viability, reliability, validity, and sensitivity to change. Psychometric test results showed viability, reliability, validity, and sensitivity to change. High correlation between the test score and the reference method were notable. A high stability was obtained with an intraclass correlation coefficient. The average response time of the test was twenty-three minutes. This test measures the moral maturity of adolescents. It is presented as an objective, useful, valid, reliable tool, easy to fill out, edit and apply in a healthcare context. It helps to assess the maturity of minors faced with a decision. (shrink)

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