9,727 research outputs found

    On Regularity, Transitivity, and Ergodic Principle for Quadratic Stochastic Volterra Operators

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    In this paper we showed an equivalence of notions of regularity, transitivity and Ergodic principle for quadratic stochastic Volterra operators acting on the finite dimensional simplex.Comment: 5 page

    Modelling Noise and Imprecision in Individual Decisions

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    When individuals take part in decision experiments, their answers are typically subject to some degree of noise / error / imprecision. There are different ways of modelling this stochastic element in the data, and the interpretation of the data can be altered radically, depending on the assumptions made about the stochastic specification. This paper presents the results of an experiment which gathered data of a kind that has until now been in short supply. These data strongly suggest that the 'usual' (Fechnerian) assumptions about errors are inappropriate for individual decision experiments. Moreover, they provide striking evidence that core preferences display systematic departures from transitivity which cannot be attributed to any 'error' story.Error Imprecision Preferences Transitivity

    Testing for regularity and stochastic transitivity using the structural parameter of nested logit

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    We introduce regularity and stochastic transitivity as necessary and well-behaved conditions respectively, for the consistency of discrete choice preferences with the Random Utility Model (RUM). For the specific case of a three-alternative nested logit (NL) model, we synthesise these conditions in the form of a simple two-part test, and reconcile this test with the conventional zero-one bounds on the structural (‘log sum’) parameter within this model, i.e. 0 0. On the other hand, we show that neither regularity nor stochastic transitivity constrain the upper bound at one. Therefore, if the conventional zero-one bounds are imposed in model estimation, preferences which violate regularity and/or stochastic transitivity may either go undetected (if the ‘true’ structural parameter is less than zero) and/or be unknowingly admitted (if the ‘true’ lower bound is greater than zero), and preferences which comply with regularity and stochastic transitivity may be excluded (if the ‘true’ upper bound is greater than one). Against this background, we show that imposition of the zero-one bounds may compromise model fit, inferences of willingness-to-pay, and forecasts of choice behaviour. Finally, we show that where the ‘true’ structural parameter is negative (thereby violating RUM – at least when choosing the ‘best’ alternative), positive starting values for the structural parameter in estimation may prevent the exposure of regularity and stochastic transitivity failures

    Non-transitivity of the Win Ratio and Area Under the Receiver Operating Characteristics Curve (AUC): a case for evaluating the strength of stochastic comparisons

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    The win ratio (WR) is a novel statistic used in randomized controlled trials that can account for hierarchies within event outcomes. In this paper we report and study the long-run non-transitive behavior of the win ratio and the closely related Area Under the Receiver Operating Characteristics Curve (AUC) and argue that their transitivity cannot be taken for granted. Crucially, traditional within-group statistics (i.e., comparison of means) are always transitive, while the WR can detect non-transitivity. Non-transitivity provides valuable information on the stochastic relationship between two treatment groups, which should be tested and reported. We specify the necessary conditions for transitivity, the sufficient conditions for non-transitivity and demonstrate non-transitivity in a real-life large randomized controlled trial for the WR of time-to-death. Our results can be used to rule out or evaluate possibility of non-transitivity and show the importance of studying the strength of stochastic relationships