Transitivity has come to be recognized as a promising heuristic tool for uncovering implicit ideologies in a wide range of areas. Though it has been used to explore worldviews in several kinds of discourse, nearly all have relied solely on qualitative analyses. Statistical analysis can offer a fuller understanding of past societies. This study applies a gradient, discourse-based understanding of transitivity, which lends itself nicely to corpus-based analysis, to data from 16th-century New Spain. In colonial Mexico, female behaviors were often strictly circumscribed. This paper uses a quantitative, corpus-based framework to examine how gender inequality is reflected in patterns of transitivity. It is found that female subjects are significantly associated with imperfective contexts, nonfinite constructions, akinesis, and low affectedness of the object—all markers of lower transitivity. Thus, for the most part, in these data, women are represented as inactive, inert, and powerless.

Limited Aggregation is the view that when there are competing moral claims that demand our attention, we should sometimes satisfy the largest aggregate of claims, depending on the strength of the claims in question. In recent years, philosophers such as Patrick Tomlin and Alastair Norcross have argued that Limited Aggregation violates a number of rational choice principles such as Transitivity, Separability, and Contraction Consistency. Current versions of Limited Aggregation are what may be called Comparative Approaches because they involve assessing the relative strengths of various claims. In this paper, we offer a non-comparative version of Limited Aggregation, what we call the Threshold Approach. It states that there is a non-relative threshold that separates various claims. We demonstrate that the Threshold Approach does not violate rational choice principles such as Transitivity, Separability, and Contraction Consistency, and we show that potential concerns regarding such a view are surmountable.

This paper investigates properties of the class of graphs based on exchangeable point processes. We provide asymptotic expressions for the number of edges, number of nodes, and degree distributions, identifying four regimes: (i) a dense regime, (ii) a sparse, almost dense regime, (iii) a sparse regime with power-law behaviour, and (iv) an almost extremely sparse regime. We show that, under mild assumptions, both the global and local clustering coefficients converge to constants which may or may not be the same. We also derive a central limit theorem for subgraph counts and for the number of nodes. Finally, we propose a class of models within this framework where one can separately control the latent structure and the global sparsity/power-law properties of the graph.

In this paper, we prove using elementary techniques that any group of diffeomorphisms acting on the 2-sphere and properly extending the conformal group of Möbius transformations must be at least 4-transitive or, more precisely, arc 4-transitive. As an important consequence, we derive that any such group must always contain an element of positive topological entropy. We also provide a self-contained characterization, in terms of transitivity, of the Möbius transformations within the full group of sphere diffeomorphisms.

We introduce a notion of sensitivity with respect to a continuous real-valued bounded map which provides a sufficient condition for a continuous transformation, acting on a Baire metric space, to exhibit a Baire generic subset of points with historic behavior (also known as irregular points). The applications of this criterion recover, and extend, several known theorems on the genericity of the irregular set, in addition to yielding a number of new results, including information on the irregular set of geodesic flows, in both negative and non-positive curvature, and semigroup actions.

This study focuses on Estonian verb-complement structures, which include oblique (non-canonically marked) complements marked in spatial cases. Not all approaches agree on whether canonical arguments and oblique complements have argument status of the same type, but they do mostly agree that the two types of complement markings are used by different types of verbs. First, oblique case is viewed as always indexing the original semantics of the case (direct semantics), that is osutama ‘point at’ selecting an allative (‘onto’) complement. Second, oblique case usage is seen as referring to a restricted set of syntactic relations (indirect semantics), that is Estonian allative and adessive being used for marking Experiencers. In any case, oblique complement verbs are viewed as more semantically restricted than canonical object verbs. This study tests these two hypotheses in a quantitative corpus approach. In a non-semantically extracted sample of verbs (n = 232), it compares the lexical-semantic transitivity of oblique and canonical complement verbs in order to investigate the degree to which indirect semantic effects differentiate between the two types of verbs. In addition, it outlines direct semantic effects between oblique case frames in terms of semantic roles. Finally, it investigates the way these patterns are related to the cases’ individual grammaticalisation degrees.

Transitivity is the assumption that if a person prefers A to B and B to C, then that person should prefer A to C. This article explores a paradigm in which Birnbaum, Patton and Lott (1999) thought people might be systematically intransitive. Many undergraduates choose C = ($96, .85; $90, .05; $12, .10) over A = ($96, .9; $14, .05; $12, .05), violating dominance. Perhaps people would detect dominance in simpler choices, such as A versus B = ($96, .9; $12, .10) and B versus C, and yet continue to violate it in the choice between A and C, which would violate transitivity. In this study we apply a true and error model to test intransitive preferences predicted by a partially effective editing mechanism. The results replicated previous findings quite well; however, the true and error model indicated that very few, if any, participants exhibited true intransitive preferences. In addition, violations of stochastic dominance showed a strong and systematic decrease in prevalence over time and violated response independence, thus violating key assumptions of standard random preference models for analysis of transitivity.

True and Error Theory (TET) is a modern latent variable modeling approach for analyzing sets of preferences held by people. Individual True and Error Theory (iTET) allows researchers to estimate the proportion of the time an individual truly holds a particular underlying set of preferences without assuming complete response independence in a repeated measures experimental design. iTET is thus suitable for investigating research questions such as whether an individual ever is truly intransitive in their preferences (i.e., they prefer a to b, b to c, and c to a). While current iTET analysis methods provide the means of investigating such questions they require a lot of data to achieve satisfactory power for hypothesis tests of interest. This paper overviews the performance and shortcomings of the current analysis methods in efficiently using data, while providing new analysis methods that offer substantial gains in power and efficiency.

Butler and Pogrebna (2018) devised triples of three-branch gambles theorized to violate transitivity of preference according to a most probable winner model. According to this model, a person chooses the option that has the higher probability to yield a better outcome than the other alternative. They tested 11 triples with 100 participants and found cases that appeared to violate weak stochastic transitivity and the triangle inequality. But tests of weak stochastic transitivity and the triangle inequality do not provide a proper method to compare transitive and intransitive models that allow mixtures of preference patterns and random errors. Those older methods can yield false conclusions regarding transitivity, for example, if different participants have different true preferences or if different choice problems have different rates of error. This paper reanalyzes their data using a true and error (TE) model, which does not require these unrealistic assumptions, and which provides estimates of the incidence of transitive and intransitive behavior in a mixture. Reanalysis indicated that 3 of the 11 triples showed convincing evidence of violations of transitivity in the opposite direction of the predictions of the most probable winner model. Further, these and other triples showed other significant violations of the most probable winner model. Despite some violations of the true and error model, the data of Butler and Pogrebna appear to contradict not only transitive utility models but they also refute the most probable winner model as a descriptive theory of choice behavior.

This paper develops tests of independence and stationarity in choice data collected with small samples. The method builds on the approach of Smith and Batchelder (2008). The technique is intended to distinguish cases where a person is systematically changing “true” preferences (from one group of trials to another) from cases in which a person is following a random preference mixture model with independently and identically distributed sampling in each trial. Preference reversals are counted between all pairs of repetitions. The variance of these preference reversals between all pairs of repetitions is then calculated. The distribution of this statistic is simulated by a Monte Carlo procedure in which the data are randomly permuted and the statistic is recalculated in each simulated sample. A second test computes the correlation between the mean number of preference reversals and the difference between replicates, which is also simulated by Monte Carlo. Data of Regenwetter, Dana, and Davis-Stober (2011) are reanalyzed by this method. Eight of 18 subjects showed significant deviations from the independence assumptions by one or both of these tests, which is significantly more than expected by chance.