Magnitude-sensitive reaction times reveal non-linear time costs in multi-alternative decision-making

Optimality analysis of value-based decisions in binary and multi-alternative choice settings predicts that reaction times should be sensitive only to differences in stimulus magnitudes, but not to overall absolute stimulus magnitude. Yet experimental work in the binary case has shown magnitude sensitive reaction times, and theory shows that this can be explained by switching from linear to multiplicative time costs, but also by nonlinear subjective utility. Thus disentangling explanations for observed magnitude sensitive reaction times is difficult. Here for the first time we extend the theoretical analysis of geometric time-discounting to ternary choices, and present novel experimental evidence for magnitude-sensitivity in such decisions, in both humans and slime moulds. We consider the optimal policies for all possible combinations of linear and geometric time costs, and linear and nonlinear utility; interestingly, geometric discounting emerges as the predominant explanation for magnitude sensitivity

Examining the generalizability of research findings from archival data

This initiative examined systematically the extent to which a large set of archival research findings generalizes across contexts. We repeated the key analyses for 29 original strategic management effects in the same context (direct reproduction) as well as in 52 novel time periods and geographies; 45% of the reproductions returned results matching the original reports together with 55% of tests in different spans of years and 40% of tests in novel geographies. Some original findings were associated with multiple new tests. Reproducibility was the best predictor of generalizability—for the findings that proved directly reproducible, 84% emerged in other available time periods and 57% emerged in other geographies. Overall, only limited empirical evidence emerged for context sensitivity. In a forecasting survey, independent scientists were able to anticipate which effects would find support in tests in new samples

A Drift Diffusion Model Account of the Semantic Congruity Effect in a Classification Paradigm

The semantic congruity effect refers to the facilitation of judgements (i) when the direction of the comparison of two items coincides with the relative position of the items along the dimension comparison or (ii) when the relative size of a standard and a target stimulus coincides. For example, people are faster in judging 'which is bigger?' for two large items, than judging 'which is smaller?' for two large items (selection paradigm). Also, people are faster in judging a target stimulus as smaller when compared to a small standard, than when compared to a large standard, and vice versa (classification paradigm). We use the Drift Diffusion Model (DDM) to explain the time course of a semantic congruity effect in a classification paradigm. Formal modelling of semantic congruity allows the time course of the decision process to be described, using an established model of decision making. Moreover, although there have been attempts to explain the semantic congruity effect within evidence accumulation models, two possible accounts for the congruity effect have been proposed but their specific predictions have not been compared directly, using a model that could quantitatively account for both; a shift in the starting point of evidence accumulation or a change in the rate at which evidence is accumulated. With our computational investigation we provide evidence for the latter, while controlling for other possible explanations such as a variation in non-decision time or boundary separation, that have not been taken into account in the explanation of this phenomenon

Optimal decision boundaries in the space of possible estimates of option values: Optimal policies for linear time cost (Bayes Risk) rapidly transition from approximately linear subjective utility, and hence weakly magnitude-sensitive, decision boundaries in estimate space (Fig 3, top row for <i>s</i> = 0.25; present figure, top row for <i>s</i> = 0.5, to more step-like subjective utility where immediate ‘choose the best’ decision-boundaries are necessarily magnitude-insensitive (bottom row for <i>s</i> = 0.75, and higher values of <i>s</i>).

Triangles are low dimensional projections of the 3-dimensional evidence estimate space onto a plane moving along the equal value line, at value v [4]. Dynamic programming parameters were: prior mean and variance , and utility function parameters m = 4, s ∈ {0.5, 0.75}. Time steps chosen to illustrate boundary collapse.</p

Mixed-effect regression for reaction times as a function of food quality in the slime moulds study.

Sclerotia identity was included as a random factor. The regression was performed using R (RStudio Version 1.2.1335; function ‘lmer’, package ‘lme4’). Given the typical skewness of reaction times, the dependent variable was transformed (i.e. normalized) using the ‘bestNormalize’ function in R. As the food quality of equal alternatives increased, reaction times significantly decreased. (PDF)</p

Empirical results from the slime mould experiment.

Decreasing latencies to reach a food source as a function of the magnitude of the equal alternatives. X-axis presents the concentration in egg yolk of equal food sources (20, 40, 60, 80 g.L−1). Y-axis presents mean latency to reach a food source, in minutes. Bars show 95% confidence intervals. 50 slime moulds were tested for each magnitude for a total of 200 slime moulds.</p

Linear time costs lead to weakly magnitude-sensitive simulated reaction times across a range of nonlinear subjective utility functions for equal value option sets.

Simulation parameters were: prior mean and variance , observation noise variance , temporal cost c = 0, waiting time tw = 1, and simulation timestep dt = 5 × 10−3. Lines are the mean reaction time for 104 simulations, 95% confidence intervals are shown as red shading (mostly invisible because smaller than the linewidth). Y-axis made consistent with Fig 6 for comparison. Non-decision time was implicitly zero.</p

Fig 7 -

(A) Stimuli example for human psychophysical experiments: Participants were requested to decide as fast and accurately as possible which of the three stimuli was brighter; they were asked to maintain fixation on the cross at the centre of the screen and minimise distraction for the short duration of the experiment. Unknown to participants, conditions of interest were conditions for which the stimuli had equal mean brightness. (B) Photograph showing a slime mould that chose one food alternative among three equal ones. The slime mould was placed in the centre of a petri dish (60 mm ⌀) filled with agar gel (10 g.L−1) at a distance of 2 mm from each food alternative.</p