Implications of visual attention phenomena for models of preferential choice

We use computational modelling to examine the ability of evidence accumulation models to produce the reaction time distributions and attentional biases found in behavioural and eye-tracking research. We focus upon simulating reaction times and attention in binary choice with particular emphasis upon whether different models can predict the late onset bias (LOB), commonly found in eye movements during choice (sometimes called the gaze cascade). The first finding is that this bias is predicted by models even when attention is entirely random and independent of the choice process. This shows that the LOB is not evidence of a feedback loop between evidence accumulation and attention. Second, we examine models with a relative evidence decision rule and an absolute evidence rule. In the relative models a decision is made once the difference in evidence accumulated for two items reaches a threshold. In the absolute models, a decision is made once one item accumulates a certain amount of evidence, independently of how much is accumulated for a competitor. Our core result is simple – the existence of the late onset gaze bias to the option ultimately chosen, together with a positively skewed reaction time distribution means that the stopping rule must be relative not absolute. A large scale grid search of parameter space shows that absolute threshold models struggle to predict these phenomena even when incorporating evidence decay and assumptions of either mutual inhibition or feed forward inhibition

Benthic Algae of Lake Erie (1865-2006): A Review of Assemblage Composition, Ecology, and Causes and Consequences of Changing Abundance

Author Institution: Department of Natural Resource Ecology and Management, Iowa State UniversityAuthor Institution: Department of Biological Sciences, Bowling Green State UniversityPeer-reviewed literature and published reports were used to summarize knowledge of benthic algal assemblage composition and ecology in Lake Erie, and causes and consequences of temporal variation in algal abundance. Macroalgal assemblages in rocky littoral and soft substrate habitats have been reasonably well described and studied, as has the epiphyte/metaphyte assemblage associated with rocky littoral macroalgae. In contrast, little information exists for non-epiphytic microalgae in littoral habitat. During the period when algal records were reported (1865-2006), the rocky littoral macroalgal assemblage was often dominated by the chlorophyte genera Cladophora and Ulothrix and the rhodophyte Bangia, whereas the charophytes Chara and Nitella were most abundant in littoral soft substrate. In addition to substrate effects, assemblage composition varied as a function of depth, temperature, light levels, and nutrient concentrations. Under certain conditions, macroalgal taxa appeared to outcompete and exclude other taxa from littoral habitat. However, these organisms have also facilitated increased algal diversity by supporting epiphytes/metaphytes. In Lake Erie, significant temporal change in benthic algal abundance has been associated with: 1) eutrophication (prior to 1972), 2) oligotrophication following the Great Lakes Water Quality Agreement (1972-1985), and 3) invasion by Dreissena mussels (1986-2006). Increasingly eutrophic conditions were reflected by high abundance and frequent shoreline fouling by Cladophora, declining charophyte (such as Chara, Nitella) abundance, and invasion of rocky littoral habitat by euryhaline Bangia. Subsequent indicators of oligotrophication included declining Cladophora abundance, and increased diatom abundance in deepwater habitat. Effects of filter-feeding Dreissena (such as increased water clarity, phosphorus excretion) were likely causes for Cladophora resurgence in the 1990s, and likely contributed to return of Chara and Nitella to formerly occupied habitat. Algal assemblages clearly reflect environmental conditions in aquatic ecosystems. To accurately assess present and future conditions in Lake Erie, continued study of all benthic assemblages is recommended, with greater attention directed toward microalgae in littoral habitat than has occurred in the past

Benthic Algae of Lake Erie (1865-2006): A Review of Assemblage Composition, Ecology, and Causes and Consequences of Changing Abundance

Peer-reviewed literature and published reports were used to summarize knowledge of benthic algal assemblage composition and ecology in Lake Erie, and causes and consequences of temporal variation in algal abundance. Macroalgal assemblages in rocky littoral and soft substrate habitats have been reasonably well described and studied, as has the epiphyte/metaphyte assemblage associated with rocky littoral macroalgae. In contrast, little information exists for non-epiphytic microalgae in littoral habitat. During the period when algal records were reported (1865-2006), the rocky littoral macroalgal assemblage was often dominated by the chlorophyte genera Cladophora and Ulothrix and the rhodophyte Bangia, whereas the charophytes Chara and Nitella were most abundant in littoral soft substrate. In addition to substrate effects, assemblage composition varied as a function of depth, temperature, light levels, and nutrient concentrations. Under certain conditions, macroalgal taxa appeared to outcompete and exclude other taxa from littoral habitat. However, these organisms have also facilitated increased algal diversity by supporting epiphytes/metaphytes. In Lake Erie, significant temporal change in benthic algal abundance has been associated with: 1) eutrophication (prior to 1972), 2) oligotrophication following the Great Lakes Water Quality Agreement (1972-1985), and 3) invasion by Dreissena mussels (1986-2006). Increasingly eutrophic conditions were reflected by high abundance and frequent shoreline fouling by Cladophora, declining charophyte (such as Chara, Nitella) abundance, and invasion of rocky littoral habitat by euryhaline Bangia. Subsequent indicators of oligotrophication included declining Cladophora abundance, and increased diatom abundance in deepwater habitat. Effects of filter-feeding Dreissena (such as increased water clarity, phosphorus excretion) were likely causes for Cladophora resurgence in the 1990s, and likely contributed to return of Chara and Nitella to formerly occupied habitat. Algal assemblages clearly reflect environmental conditions in aquatic ecosystems. To accurately assess present and future conditions in Lake Erie, continued study of all benthic assemblages is recommended, with greater attention directed toward microalgae in littoral habitat than has occurred in the past

Accumulation is late and brief in preferential choice

Preferential choices are often explained using models within the evidence accumulation framework: value drives the drift rate at which evidence is accumulated until a threshold is reached and an option is chosen. Although rarely stated explicitly, almost all such models assume that decision makers have knowledge at the onset of the choice of all available attributes and options. In reality however, choice information is viewed piece-by-piece, and is often not completely acquired until late in the choice, if at all. Across four eye-tracking experiments, we show that whether the information was acquired early or late is irrelevant in predicting choice: all that matters is whether or not it was acquired at all. Models with potential alternative assumptions were posited and tested, such as 1) accumulation of instantaneously available information or 2) running estimates as information is acquired. These provided poor fits to the data. We are forced to conclude that participants either are clairvoyant, accumulating using information before they have looked at it, or delay accumulating evidence until very late in the choice, so late that the majority of choice time is not time in which evidence is accumulated. Thus, although the evidence accumulation framework may still be useful in measurement models, it cannot account for the details of the processes involved in decision making

Eye movements in strategic choice

In risky and other multiattribute choices, the process of choosing is well described by random walk or drift diffusion models in which evidence is accumulated over time to threshold. In strategic choices, level-k and cognitive hierarchy models have been offered as accounts of the choice process, in which people simulate the choice processes of their opponents or partners. We recorded the eye movements in 2 × 2 symmetric games including dominance-solvable games like prisoner's dilemma and asymmetric coordination games like stag hunt and hawk–dove. The evidence was most consistent with the accumulation of payoff differences over time: we found longer duration choices with more fixations when payoffs differences were more finely balanced, an emerging bias to gaze more at the payoffs for the action ultimately chosen, and that a simple count of transitions between payoffs—whether or not the comparison is strategically informative—was strongly associated with the final choice. The accumulator models do account for these strategic choice process measures, but the level-k and cognitive hierarchy models do not

Eye movements in strategic choice

In risky and other multiattribute choices, the process of choosing is well described by random walk or drift diffusion models in which evidence is accumulated over time to threshold. In strategic choices, level-k and cognitive hierarchy models have been offered as accounts of the choice process, in which people simulate the choice processes of their opponents or partners. We recorded the eye movements in 2 × 2 symmetric games including dominance-solvable games like prisoner's dilemma and asymmetric coordination games like stag hunt and hawk–dove. The evidence was most consistent with the accumulation of payoff differences over time: we found longer duration choices with more fixations when payoffs differences were more finely balanced, an emerging bias to gaze more at the payoffs for the action ultimately chosen, and that a simple count of transitions between payoffs—whether or not the comparison is strategically informative—was strongly associated with the final choice. The accumulator models do account for these strategic choice process measures, but the level-k and cognitive hierarchy models do not

Resummed Photon Spectra for WIMP Annihilation

We construct an effective field theory (EFT) description of the hard photon spectrum for heavy WIMP annihilation. This facilitates precision predictions relevant for line searches, and allows the incorporation of non-trivial energy resolution effects. Our framework combines techniques from non-relativistic EFTs and soft-collinear effective theory (SCET), as well as its multi-scale extensions that have been recently introduced for studying jet substructure. We find a number of interesting features, including the simultaneous presence of SCET$_{\text{I}}$ and SCET$_{\text{II}}$ modes, as well as collinear-soft modes at the electroweak scale. We derive a factorization formula that enables both the resummation of the leading large Sudakov double logarithms that appear in the perturbative spectrum, and the inclusion of Sommerfeld enhancement effects. Consistency of this factorization is demonstrated to leading logarithmic order through explicit calculation. Our final result contains both the exclusive and the inclusive limits, thereby providing a unifying description of these two previously-considered approximations. We estimate the impact on experimental sensitivity, focusing for concreteness on an SU(2)$_{W}$ triplet fermion dark matter - the pure wino - where the strongest constraints are due to a search for gamma-ray lines from the Galactic Center. We find numerically significant corrections compared to previous results, thereby highlighting the importance of accounting for the photon spectrum when interpreting data from current and future indirect detection experiments.Comment: 55+25 pages, 11+2 figures; v3, updated an expression in the appendix to make it applicable at higher order - no impact on the results in this wor

Process tracing, sampling, and drift rate construction

In this chapter, the authors review the idea from a model called decision by sampling and show how they have used process tracing data to constrain the development of this model into a process model of choice. They explain how people counting wins will behave as if the subjective value for an attribute value is given by its rank position against other attribute values. The authors discuss how the sort of tally can be particularly robust and can be considered as optimal and also review evidence for the rank hypothesis in judgment and choice, and also evidence from neuroimaging studies including functional magnetic resonance imaging and single cell recording. They consider the attentional drift diffusion model and deal with a discussion of how the rank hypothesis and drift diffusion can be combined and developed into a new mathematical model of multiattribute choice, with modeling assumptions constrained by process data

A zero attraction effect in naturalistic choice

In the attraction effect, adding a dominated third option to a choice set of two options can reverse the preference for the original two options, and even increase one of the option’s choice share. This constitutes a violation of the axioms of regularity and independence from irrelevant alternatives, which are core properties of any choice model in which the utility of each option is stable across choice sets. Consequently, in the past 20 years, the attraction effect has driven the development of a set of influential models of multiattribute choice. However, Frederick, Lee, and Baskin (2014) have recently claimed that the attraction effect is only limited to options with numerical attributes, and does not hold for choices between naturalistic options (e.g., snacks, movies) — a claim which would severely undermine its theoretical importance. Huber, Payne, and Puto (2014) criticised Frederick et al.’s experiments, laying down a set of criteria that should be met by any experiment wishing to test for the attraction effect in real-world consumer choices. This article presents the first experiment that meets these criteria. The results show a precisely zero attraction effect