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This paper investigates the random utility representation of best-worst choice probabilities (picking the best and the worst alternative from an offered set). Doignon (2023) presented a complete characterization of the best-worst-choice polytope on four alternatives. Moreover, using polytope methods he showed that the Block-Marschak inequalities for best-worst choices are not sufficient for a random utility representation of best-worst choices for sets of four or more alternatives. Following the approach of Falmagne (1978), we construct a probability measure on the set of rankings for a set of four alternatives implying a random utility representation., Comment: 12 pages

This is a chapter for the third volume of the New Handbook of Mathematical Psychology. It presented mathematical foundations of Fechnerian Scaling, a method of metrizing stimulus spaces based on subjective measures of dissimilarity., Comment: 90 pages

This paper investigates best-worst choice probabilities (picking the best and the worst alternative from an offered set). It is shown that non-negativity of best-worst Block-Marschak polynomials is necessary and sufficient for the existence of a random utility representation. The representation theorem is obtained by extending proof techniques employed by Falmagne (1978) for a corresponding result on best choices (picking the best alternative from an offered set).

This paper presents an introduction to the stochastic concepts of \emph{coupling} and \emph{copula}. Coupling means the construction of a joint distribution of two or more random variables that need not be defined on one and the same probability space, whereas a copula is a function that joins a multivariate distribution to its one-dimensional margins. Their role in stochastic modeling is illustrated by examples from multisensory perception. Pointers to more advanced and recent treatments are provided.

A single neuron is categorized as"multisensory" if there is a statistically significant difference between the response evoked by an audio-visual stimulus combination and that evoked by the most effective of its components individually. Crossmodal enhancement is commonly expressed as a proportion of the strongest unisensory response. However, being responsive to multiple sensory modalities does not guarantee that a neuron has actually engaged in integrating its multiple sensory inputs, rather than simply responding to the most salient stimulus. Here, we propose an alternative index measuring by how much the crossmodal response surpasses the level obtainable by optimally combining the unisensory responses. Optimality is defined by probability summation combining the unisensory responses under maximal negative stochastic dependence. The new index is analogous to measuring crossmodal enhancement by the amount of violation of the "race model inequality", which is widely used in reaction time studies of multisensory integration. Neurons previously labeled as "multisensory" may lose that property since the new index tends to be smaller than the traditional one. This is exemplified with a data set collected from single SC neurons. The new easy-to-compute index does not require any specific distributional assumption. It is sensitive to the variability in the data, in contrast to the traditional index which, by definition, only depends on the means of the uni- and crossmodal response distributions., Comment: 10 pages

A new theoretical analysis of the stop-signal model is proposed. Within the concepts of crude- and net-hazard functions, the nonobservable control-latency distribution can be estimated from observable reaction times. This result allows a test of the Logan and Cowan model (1984) without simplifying assumptions. (SLD)