Recognising Multidimensional Euclidean Preferences

Euclidean preferences are a widely studied preference model, in which decision makers and alternatives are embedded in d-dimensional Euclidean space. Decision makers prefer those alternatives closer to them. This model, also known as multidimensional unfolding, has applications in economics, psychometrics, marketing, and many other fields. We study the problem of deciding whether a given preference profile is d-Euclidean. For the one-dimensional case, polynomial-time algorithms are known. We show that, in contrast, for every other fixed dimension d > 1, the recognition problem is equivalent to the existential theory of the reals (ETR), and so in particular NP-hard. We further show that some Euclidean preference profiles require exponentially many bits in order to specify any Euclidean embedding, and prove that the domain of d-Euclidean preferences does not admit a finite forbidden minor characterisation for any d > 1. We also study dichotomous preferencesand the behaviour of other metrics, and survey a variety of related work.Comment: 17 page

An Ordinal Model of Risk Based on Mariner’s Judgement

This paper describes a statistical method for learning and estimating the risk posed by other craft in the vicinity of a vessel and an overview of its possible spatial application, simulating how professional mariners perceive and assess such risk and using navigational data obtained from a standard integrated bridge. We propose a non-linear model for risk estimation which attempts to capture mariners' judgement. Questionnaire data has been collected that captures and quantifies mariners’ judgements of risk for craft in the vicinity, where each craft is described by measurements that can be obtained easily from the data already present in the ship's navigational equipment. The dataset has then been used for analysis, training and validating Ordered Probit models in order to obtain a computationally efficient data driven model for estimating the risk probability vector posed by other craft. Finally, we discuss how this risk model can be incorporated into decision making and path finding algorithms.</jats:p

The GIST of Concepts

A unified general theory of human concept learning based on the idea that humans detect invariance patterns in categorical stimuli as a necessary precursor to concept formation is proposed and tested. In GIST (generalized invariance structure theory) invariants are detected via a perturbation mechanism of dimension suppression referred to as dimensional binding. Structural information acquired by this process is stored as a compound memory trace termed an ideotype. Ideotypes inform the subsystems that are responsible for learnability judgments, rule formation, and other types of concept representations. We show that GIST is more general (e.g., it works on continuous, semi-continuous, and binary stimuli) and makes much more accurate predictions than the leading models of concept learning difficulty,such as those based on a complexity reduction principle (e.g., number of mental models,structural invariance, algebraic complexity, and minimal description length) and those based on selective attention and similarity (GCM, ALCOVE, and SUSTAIN). GIST unifies these two key aspects of concept learning and categorization. Empirical evidence from three\ud experiments corroborates the predictions made by the theory and its core model which we propose as a candidate law of human conceptual behavior

Factor Analysis vs. Fuzzy Sets Theory: Assessing the Influence of Different Techniques on Sen's Functioning Approach

This paper explores a couple of specific operational interpretations of Sen's approach in view of assessing the extent to which the results originated by the implementation of Sen's concepts are influenced by the choice of the specific technique. By means of a survey based on a representative sample of Belgian individuals, seven achieved functioning's are identified via each technique and subsequently confronted. To structure the information and to facilitate comparisons, standard multivariate analysis is performed, while at the same time considering in more detail the sub-group of the most deprived individuals. In this way, a substantial accordance - yet no perfect equivalence - is uncovered in the general patterns of functionings' achievements.

Factor Analysis vs Fuzzy Sets Theory: Assessing the Influence of Different Techniques on Sen's Functioning Approach.

This paper explores a couple of specific operational interpretations of Sen's approach in view of assessing the extent to which the results originated by the implementation of Sen's concepts are influenced by the choice of the specific technique. By means of a survey based on a representative sample of Belgian individuals, seven achieved functioning's are identified via each technique and subsequently confronted. To structure the information and to facilitate comparisons, standard multivariate analysis is performed, while at the same time considering in more detail the sub-group of the most deprived individuals. In this way, a substantial accordance - yet no perfect equivalence - is uncovered in the general patterns of functioning's' achievements.

Recent Developments in Reliability Analysis

For many researchers, the literature of reliability coefficients seems bewildering although the methodological problem in which they are embedded is reasonably clear: Since we can never know what it is that we claim to see independent of our seeing it, or, translated into the language of science, since we can not test hypotheses about reality without first generating the observations or data to talk about, the accuracy by which primary data represent an unobserved nature remains unascertainable in principle (Krippendorff, 1991). Yet, to assure that the data that go into scientific inquiries are not accidental, it is important to demonstrate that the data-generating procedures are reproducible under varying circumstances and by several observers. All reliability measures are intended to express the degree to which several observers, several measuring instruments, or several interrogations of the same units of analysis yield the same descriptive accounts, category assignments, quantitative measures or data for short

Multidimensional Scaling Using Majorization: SMACOF in R

In this paper we present the methodology of multidimensional scaling problems (MDS) solved by means of the majorization algorithm. The objective function to be minimized is known as stress and functions which majorize stress are elaborated. This strategy to solve MDS problems is called SMACOF and it is implemented in an R package of the same name which is presented in this article. We extend the basic SMACOF theory in terms of configuration constraints, three-way data, unfolding models, and projection of the resulting configurations onto spheres and other quadratic surfaces. Various examples are presented to show the possibilities of the SMACOF approach offered by the corresponding package.

Autherine Lucy & the University of Alabama Integration at U of A 1952-1956

Located in Tuscaloosa, Alabama, the University of Alabama was chartered in 1820 and is Alabama’s oldest public university. Prior to 1956, the University was segregated; admission was limited to white men and women. On February 3, 1965, Miss Autherine Lucy stepped foot on campus for the first time to attend classes at the University; history was made as she was the first African American present. Lucy’s attendance stirred conflict throughout campus and the state of Alabama. Unbeknownst to many, Lucy’s attendance garnered both national and international attention. The central argument here is that Lucy’s experiences at the University of Alabama adds an important chapter to the struggle against segregation, American higher education, and enhances the global dimensions of the Civil Rights Movement. The case of Autherine Lucy will be used, as it represents an ideal example of how segregation received a substantial amount of international criticism to undermine America’s image abroad as the world’s leading democracy during the Cold War. Amongst many of America’s school segregation cases, Lucy’s was one the first to become an international event. Lucy’s case is especially unique because she is an African American woman. This allows gender to be added as a scope while addressing issues in higher education and where Lucy challenged said issues. Although efforts were made to salvage America’s international image—such as the Supreme Court’s 1954 Brown decision—they were unsuccessful. To a multitude of countries abroad, America and its slogans promising freedom, liberty, and democracy were nothing more than propaganda