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

Decision by sampling and rank order effects in value judgement and decision making

This thesis uses the Decision by Sampling model as a basis for examining effects of rank order encoding in value judgement and preferential choice. A range of experiments are reported, and these employ a variety of methodologies including behavioural paradigms, eye tracking and functional MRI. The results show that when there are a relatively small number of values used during an experiment, participants encode utility based upon the rank order of a potential outcome within these values. By introducing different decision contexts where the experienced values have a positive or negative skew, an individual’s utility curve can be made concave and risk averse or convex and risk seeking. These different utility curves can be produced within the same individual and same task simply by providing a contextual cue for each trial. Two fMRI experiments demonstrate the neural systems underlying this phenomenon. The results show that all regions of the reward network encode reward as a function of the reward’s rank order within the current context. No region of the brain was found to encode a reward’s absolute financial value. Other experiments investigated choice and valuation in more complex decision environments. It was found that when the number of experienced values is significantly larger than working memory capacity DbS is a relatively poor predictor of behaviour. The Weighted ADDitive rule proved to be more accurate throughout. However, in multi-attribute choice experiments where one attribute had a manipulated distribution, individuals use and weighting of the attribute value was determined by rank order rather than its numerical value. The specific characteristics of this were found to be incompatible with an exemplar based model of recall and binary comparison to specific items. It was instead found to be compatible with non-exemplar, fuzzy trace theories of decision making which are based upon estimates of the distribution. Eye tracking during multi-attribute choice additionally shows that participants begin to attend more to their preferred choice as they near the point at which they respond. However, they do not attend more to the attributes which they weight more highly in their choices, questioning the validity of previous eye-tracking findings

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

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

Does the butcher-on-the-bus phenomenon require a dual-process explanation? A signal detection analysis

The butcher-on-the-bus is a rhetorical device or hypothetical phenomenon that is often used to illustrate how recognition decisions can be based on different memory processes (Mandler, 1980). The phenomenon describes a scenario in which a person is recognized but the recognition is accompanied by a sense of familiarity or knowing characterized by an absence of contextual details such as the person’s identity. We report two recognition memory experiments that use signal detection analyses to determine whether this phenomenon is evidence for a recollection plus familiarity model of recognition or is better explained by a univariate signal detection model. We conclude that there is an interaction between confidence estimates and remember-know judgments which is not explained fully by either single-process signal detection or traditional dual-process models

Does the Butcher-on-the-Bus Phenomenon Require a Dual-Process Explanation? A Signal Detection Analysis

The butcher-on-the-bus is a rhetorical device or hypothetical phenomenon that is often used to illustrate how recognition decisions can be based on different memory processes (Mandler, 1980). The phenomenon describes a scenario in which a person is recognized but the recognition is accompanied by a sense of familiarity or knowing characterized by an absence of contextual details such as the person’s identity. We report two recognition memory experiments that use signal detection analyses to determine whether this phenomenon is evidence for a recollection plus familiarity model of recognition or is better explained by a univariate signal detection model. We conclude that there is an interaction between confidence estimates and remember-know judgments which is not explained fully by either single-process signal detection or traditional dual-process models

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

Alcohol and the link between national football (soccer) tournaments and domestic abuse - evidence from England

Domestic abuse is increasingly recognised as a serious public health concern worldwide. Previous research has suggested a link between national football (soccer) tournaments and domestic abuse. While hypothesized to be a significant factor, the role alcohol plays in this relationship has not yet been explored quantitatively. In this study, using 10 years' worth of crime data (from 2010 to 2019) from the second largest police force in England (West Midlands Police), we explored the effect of England draws, losses, and wins in national football tournaments on the number of alcohol and non-alcohol-related domestic abuse cases reported to the police. Results from a series of negative binomial regression analyses show that the number of reported alcohol-related domestic abuse cases increases by 47%, 95% confidence interval [26%–71%], following an England football victory. This effect is limited to alcohol-related cases. The estimate translates into a 0.53, 95% CI [0.3–0.8], increase in the daily rate of alcohol-related cases per 100,000 individuals. The England win effect survives various robustness checks (including the re-analysis of a dataset from another geographical area in England), and its time course is strongly consistent with a causal link between England's football victories and an increase in alcohol-related domestic abuse. We also found a comparable increase in the number of other (not classified as domestic abuse) alcohol-related violent crimes on England win days. Further research is required to understand the exact causal pathway between national football tournaments, alcohol consumption, and violent behaviours in domestic settings