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This short paper states a new objection against "spectrum arguments" for nontransitive betterness. It is shown that defenders of such arguments must reject one of two very plausible principles. [ABSTRACT FROM AUTHOR]

We propose a regret-based model that allows the separation of attitudes towards transitivity on triples of random variables that are close to each other and attitudes towards transitivity on triples that are far apart. This enables a theoretical reinterpretation of evidence related to intransitive behavior in the laboratory. When viewed through this paper's analysis, the experimental evidence need not imply intransitive behavior for large risky decisions such as investment choices and insurance. [ABSTRACT FROM AUTHOR]

We study the phenomenon of intransitivity in models of dice and voting. First, we follow a recent thread of research for n-sided dice with pairwise ordering induced by the probability, relative to 1/2, that a throw from one die is higher than the other. We build on a recent result of Polymath showing that three dice with i.i.d. faces drawn from the uniform distribution on { 1 , ... , n } and conditioned on the average of faces equal to (n + 1) / 2 are intransitive with asymptotic probability 1/4. We show that if dice faces are drawn from a non-uniform continuous mean zero distribution conditioned on the average of faces equal to 0, then three dice are transitive with high probability. We also extend our results to stationary Gaussian dice, whose faces, for example, can be the fractional Brownian increments with Hurst index H ∈ (0 , 1) . Second, we pose an analogous model in the context of Condorcet voting. We consider n voters who rank k alternatives independently and uniformly at random. The winner between each two alternatives is decided by a majority vote based on the preferences. We show that in this model, if all pairwise elections are close to tied, then the asymptotic probability of obtaining any tournament on the k alternatives is equal to 2 - k (k - 1) / 2 , which markedly differs from known results in the model without conditioning. We also explore the Condorcet voting model where methods other than simple majority are used for pairwise elections. We investigate some natural definitions of "close to tied" for general functions and exhibit an example where the distribution over tournaments is not uniform under those definitions. [ABSTRACT FROM AUTHOR]

Both behavioral and standard neoclassical economists place a heavy emphasis on the consistency of preferences. In particular, transitive preferences are considered a desideratum. This paper attempts to show that consistency at the level of individual choice may be pragmatically irrelevant. Consistently following an environmentally adapted rule can result in intransitive preferences without negative consequences for individual or social goals. I give three examples of this. Social scientists should look at intransitivity of choices as a challenge to offer better explanations rather than as a normative defect. [ABSTRACT FROM AUTHOR]

In hard cases of comparison, people are faced with two options neither of which is conceived of as better, worse, or equally good compared to the other. Most philosophers claim that hard cases (1) can indeed be distinguished from cases in which two options are equally good, and (2) can be characterized by a failure of transitive reasoning. It is a much more controversial matter and at the heart of an ongoing debate, whether the options in hard cases of comparison should be interpreted as incomparable, on par, or roughly equal. So far, however, none of these claims and interpretations have been tested. This paper presents the first empirical investigation on hard cases, intransitive reasoning, and incomparability. Our results reveal that hard cases present real-world dilemmas in which a significant majority of people violate transitivity. After suggesting a way of operationalizing the notion of incomparability, we provide empirical evidence that the options in some hard cases are not considered to be incomparable. Theories of rough equality or parity seem to provide better interpretations of our results. [ABSTRACT FROM AUTHOR]

Recent theoretical advances on learning (mathematics) emphasize the fact that what results from engagement with curriculum materials is not entirely in the control of the students in the way classical theories of knowing and learning suggest. These new theories distinguish themselves by either invoking distributed agency, some of which is attributed to non-human aspects of the environment, or by emphasizing the essential (radical) passivity that characterizes coming to know. In this study, an alternative is offered: making as a modality of growing. This move allows us to capture theoretically that both growers-makers and their materials grow (old) together. The proposed approach troubles existing ones because it shifts our perspective from a transitive relation between students and the curricular objects to an intransitive one, where the becoming of each is described in terms of Deleuzian lines of flight. A case study involving two girls and tangram pieces is described in terms of growing together and becoming-hexagon. Implications are discussed for how researchers can capture the non-agential, non-causal dimensions of coming to know. [ABSTRACT FROM AUTHOR]

Although the thesis that the moral better than relation is transitive seems obviously true, there is a growing literature according to which Parfit's repugnant conclusion and related puzzles reveal that this thesis is false or problematic. This paper begins by presenting several such puzzles and explaining how they can be used in arguments for the intransitivity of better than. It then proposes and defends a plausible alternative picture of the behavior of better than that both resolves the repugnant conclusion and preserves transitivity. On the threshold-based model of lexicality defended here, hedonic episodes whose intensity is above a certain point are lexically greater (in absolute magnitude) than those whose intensity is below it. The final sections argue that this model is independently plausible and can be defended from several important objections. [ABSTRACT FROM AUTHOR]

An herbivorous cichlid fish Cichlasoma ( Theraps) nicaraguense has been reported to perform brood care for the fry of a piscivorous cichlid Cichlasoma ( Nandopsis) dovii in a Nicaraguan lake. It was suggested that interspecific brood care (IBC) evolved to propagate C. dovii as a predator of another herbivorous fish Neetroplus nematopus, which is superior to C. nicaraguense in competition for breeding territory. However, it is still unclear how IBC is maintained in the face of cheaters that do not provide IBC. In this study, to elucidate the conditions for maintenance of IBC, we developed a spatially structured model, assuming a trade-off between reproduction and IBC (i.e., intra- and interspecific competition) and behavioral plasticity in IBC. The model predicted the following maintenance conditions: the probability of expressing (or suppressing) IBC in response to competitor invasion (or exclusion) is low, or, if the probability is high, then IBC is less effective for exclusion of competitors. Furthermore, we also predicted that IBC can be maintained without spatial structure if it is plastic behavior. Our model contributes to understanding of maintenance of IBC by providing empirically testable predictions. We discuss how this model is applicable to more general relationships, such as those in competitive or mutualistic systems. [ABSTRACT FROM AUTHOR]

Semiorders may form the simplest class of ordered sets with a not necessarily transitive indifference relation. Their generalization has given birth to many other classes of ordered sets, each of them characterized by an interval representation, by the properties of its relations or by forbidden configurations. In this paper, we are interested in preference structures having an interval representation. For this purpose, we propose a general framework which makes use of n-point intervals and allows a systematic analysis of such structures. The case of 3-point intervals shows us that our framework generalizes the classification of Fishburn by defining new structures. Especially we define three classes of ordered sets having a non-transitive indifference relation. A simple generalization of these structures provides three ordered sets that we call “ d-weak orders”, “ d-interval orders” and “triangle orders”. We prove that these structures have an interval representation. We also establish some links between the relational and the forbidden mode by generalizing the definition of a Ferrers relation. [ABSTRACT FROM AUTHOR]

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Decision makers are often assumed to assign stable fitness-based values to foraging options. Under this assumption, the tendency to prefer the more valuable of two simultaneously available options should be transitive. For example, if option a is preferred when paired with b, and b is preferred when paired with c, then a should be preferred when paired with c. According to the principle of strong stochastic transitivity, the preference for a over c should be at least as strong as the stronger of the other two preferences (i.e., p( a, c)≥max[ p( a, b), p( b, c)]). Gray jays ( Perisoreus canadensis) collecting food for storage violated this principle, and failed to support even weaker forms of transitivity. All subjects preferred option a (one raisin, 28 cm into a tube) over b (two raisins, 42 cm), and b over c (three raisins, 56 cm), but none of the subjects preferred a over c. Such paradoxical preferences are often interpreted as evidence for simple heuristics rather than complex decision mechanisms. According to bounded rationality, intransitive choice is a suboptimal byproduct of heuristics that usually perform well in real-world situations. Alternatively, intransitive choice could be a byproduct of selection favoring a complex decision process involving context-dependent assessment of each the fitness-related value of each option. From this perspective, the decision maker's subjective valuation of each option is not fixed, but rather depends on the context (i.e., the specific pairing of options). In the experiment, the subjective value of option a was apparently lower in option set { a, c} than in { a, b}. A model of context-dependent choice is used to explore conditions under which adaptive choice based on a complex decision process can lead to intransitivity. [ABSTRACT FROM AUTHOR]

Normative theories suggest that inconsistencies be pointed out to the Decision Maker who is thus given the chance to modify his/her judgments. In this paper, we suggest that the inconsistencies problem be transferred from the Decision Maker to the Analyst. With the Mixture of Maximal Quasi Orders, rather than pointing out incoherences for the Decision Maker to change, these inconsistencies may be used as new source of information to model his/her preferences. [ABSTRACT FROM AUTHOR]

This paper tests a novel implication of the original version of prospect theory (Kahneman and Tversky, 1979): that choices may systematically violate transitivity. Some have interpreted this implication as a weakness, viewing it as an anomaly generated by the ‘editing phase’ of prospect theory which can be rendered redundant by an appropriate re-specification of the preference function. Although there is some existing evidence that transitivity fails descriptively, the particular form of non-transitivity implied by prospect theory is quite distinctive and hence presents an ideal opportunity to expose that theory to test. An experiment is reported which reveals strong evidence of the predicted intransitivity. It is argued that the existence of this new form of non-transitive behaviour presents a fresh theoretical challenge to those seeking descriptively adequate theories of choice behaviour, and a particular challenge to those who seek explanations within the conventional economic paradigm of utility maximisation. [ABSTRACT FROM AUTHOR]

Following an introduction to the merits of pairwise comparison methods, we present various ordering algorithms for complete binary preferential structures. These procedures generalize the well-known numbering algorithm to the intransitive case. A new form of independence of irrelevant alternatives is presented. Moreover, various other criteria and characterizations for these algorithms are presented. Aside from solving ranking problems and making explicit value criteria and structures of human preference, our algorithms are applicable to subjects such as task-sequencing and artificial intelligence projects. [ABSTRACT FROM AUTHOR]