Decision accuracy in complex environments is often maximized by small group sizes

Individuals in groups, whether composed of humans or other animal species, often make important decisions collectively, including avoiding predators, selecting a direction in which to migrate and electing political leaders. Theoretical and empirical work suggests that collective decisions can be more accurate than individual decisions, a phenomenon known as the ‘wisdom of crowds’. In these previous studies, it has been assumed that individuals make independent estimates based on a single environmental cue. In the real world, however, most cues exhibit some spatial and temporal correlation, and consequently, the sensory information that near neighbours detect will also be, to some degree, correlated. Furthermore, it may be rare for an environment to contain only a single informative cue, with multiple cues being the norm. We demonstrate, using two simple models, that taking this natural complexity into account considerably alters the relationship between group size and decision-making accuracy. In only a minority of environments do we observe the typical wisdom of crowds phenomenon (whereby collective accuracy increases monotonically with group size). When the wisdom of crowds is not observed, we find that a finite, and often small, group size maximizes decision accuracy. We reveal that, counterintuitively, it is the noise inherent in these small groups that enhances their accuracy, allowing individuals in such groups to avoid the detrimental effects of correlated information while exploiting the benefits of collective decision-making. Our results demonstrate that the conventional view of the wisdom of crowds may not be informative in complex and realistic environments, and that being in small groups can maximize decision accuracy across many contexts.     

Using and communicating uncertainty for the effective control of invasive non-native species

Estimates of quantities needed to plan invasive species control, such as population size, are always uncertain; this is an issue that can become a problem when mishandled in ecological science and its communication. The complexities of incorporating uncertainty into sophisticated decision-support tools may be a barrier to their use by decision makers, leading to decisions being made without due regard to uncertainty and risking misplaced certainty of predicted outcomes. We summarise ways in which uncertainty has been incorporated into and used to advise decisions on the management of invasive non-native species and other problem species, and offer a simple conceptual model for accommodating and using uncertainty at the planning stage. We also demonstrate how frequently uncertainty has been misused and miscommunicated in the wildlife management literature. We contend that uncertainty in estimates of natural quantities must be acknowledged, can inform decisions and can be made to derive decisions, and should not be ignored if invasive species policy is to be delivered effectively. Uncertainty must be communicated thoroughly and correctly by scientists if decision makers are to understand its consequences for planning and resourcing control programmes.     

Metabolic State Alters Economic Decision Making under Risk in Humans

Background

Animals'' attitudes to risk are profoundly influenced by metabolic state (hunger and baseline energy stores). Specifically, animals often express a preference for risky (more variable) food sources when below a metabolic reference point (hungry), and safe (less variable) food sources when sated. Circulating hormones report the status of energy reserves and acute nutrient intake to widespread targets in the central nervous system that regulate feeding behaviour, including brain regions strongly implicated in risk and reward based decision-making in humans. Despite this, physiological influences per se have not been considered previously to influence economic decisions in humans. We hypothesised that baseline metabolic reserves and alterations in metabolic state would systematically modulate decision-making and financial risk-taking in humans.

Methodology/Principal Findings

We used a controlled feeding manipulation and assayed decision-making preferences across different metabolic states following a meal. To elicit risk-preference, we presented a sequence of 200 paired lotteries, subjects'' task being to select their preferred option from each pair. We also measured prandial suppression of circulating acyl-ghrelin (a centrally-acting orexigenic hormone signalling acute nutrient intake), and circulating leptin levels (providing an assay of energy reserves). We show both immediate and delayed effects on risky decision-making following a meal, and that these changes correlate with an individual''s baseline leptin and changes in acyl-ghrelin levels respectively.

Conclusions/Significance

We show that human risk preferences are exquisitely sensitive to current metabolic state, in a direction consistent with ecological models of feeding behaviour but not predicted by normative economic theory. These substantive effects of state changes on economic decisions perhaps reflect shared evolutionarily conserved neurobiological mechanisms. We suggest that this sensitivity in human risk-preference to current metabolic state has significant implications for both real-world economic transactions and for aberrant decision-making in eating disorders and obesity.     

Adaptive Sampling of Information in Perceptual Decision-Making

In many perceptual and cognitive decision-making problems, humans sample multiple noisy information sources serially, and integrate the sampled information to make an overall decision. We derive the optimal decision procedure for two-alternative choice tasks in which the different options are sampled one at a time, sources vary in the quality of the information they provide, and the available time is fixed. To maximize accuracy, the optimal observer allocates time to sampling different information sources in proportion to their noise levels. We tested human observers in a corresponding perceptual decision-making task. Observers compared the direction of two random dot motion patterns that were triggered only when fixated. Observers allocated more time to the noisier pattern, in a manner that correlated with their sensory uncertainty about the direction of the patterns. There were several differences between the optimal observer predictions and human behaviour. These differences point to a number of other factors, beyond the quality of the currently available sources of information, that influences the sampling strategy.     

Continuous evolution of statistical estimators for optimal decision-making

In many everyday situations, humans must make precise decisions in the presence of uncertain sensory information. For example, when asked to combine information from multiple sources we often assign greater weight to the more reliable information. It has been proposed that statistical-optimality often observed in human perception and decision-making requires that humans have access to the uncertainty of both their senses and their decisions. However, the mechanisms underlying the processes of uncertainty estimation remain largely unexplored. In this paper we introduce a novel visual tracking experiment that requires subjects to continuously report their evolving perception of the mean and uncertainty of noisy visual cues over time. We show that subjects accumulate sensory information over the course of a trial to form a continuous estimate of the mean, hindered only by natural kinematic constraints (sensorimotor latency etc.). Furthermore, subjects have access to a measure of their continuous objective uncertainty, rapidly acquired from sensory information available within a trial, but limited by natural kinematic constraints and a conservative margin for error. Our results provide the first direct evidence of the continuous mean and uncertainty estimation mechanisms in humans that may underlie optimal decision making.     

Collective Learning and Optimal Consensus Decisions in Social Animal Groups

Learning has been studied extensively in the context of isolated individuals. However, many organisms are social and consequently make decisions both individually and as part of a collective. Reaching consensus necessarily means that a single option is chosen by the group, even when there are dissenting opinions. This decision-making process decouples the otherwise direct relationship between animals'' preferences and their experiences (the outcomes of decisions). Instead, because an individual''s learned preferences influence what others experience, and therefore learn about, collective decisions couple the learning processes between social organisms. This introduces a new, and previously unexplored, dynamical relationship between preference, action, experience and learning. Here we model collective learning within animal groups that make consensus decisions. We reveal how learning as part of a collective results in behavior that is fundamentally different from that learned in isolation, allowing grouping organisms to spontaneously (and indirectly) detect correlations between group members'' observations of environmental cues, adjust strategy as a function of changing group size (even if that group size is not known to the individual), and achieve a decision accuracy that is very close to that which is provably optimal, regardless of environmental contingencies. Because these properties make minimal cognitive demands on individuals, collective learning, and the capabilities it affords, may be widespread among group-living organisms. Our work emphasizes the importance and need for theoretical and experimental work that considers the mechanism and consequences of learning in a social context.     

An economic theory of patient decision-making

Patient autonomy, as exercised in the informed consent process, is a central concern in bioethics. The typical bioethicist's analysis of autonomy centers on decisional capacity--finding the line between autonomy and its absence. This approach leaves unexplored the structure of reasoning behind patient treatment decisions. To counter that approach, we present a microeconomic theory of patient decision-making regarding the acceptable level of medical treatment from the patient's perspective. We show that a rational patient's desired treatment level typically departs from the level yielding an absence of symptoms, the level we call ideal. This microeconomic theory demonstrates why patients have good reason not to pursue treatment to the point of absence of physical symptoms. We defend our view against possible objections that it is unrealistic and that it fails to adequately consider harm a patient may suffer by curtailing treatment. Our analysis is fruitful in various ways. It shows why decisions often considered unreasonable might be fully reasonable. It offers a theoretical account of how physician misinformation may adversely affect a patient's decision. It shows how billing costs influence patient decision-making. It indicates that health care professionals' beliefs about the 'unreasonable' attitudes of patients might often be wrong. It provides a better understanding of patient rationality that should help to ensure fuller information as well as increased respect for patient decision-making.     

Behavioural and Physiological Effects of Finely Balanced Decision-Making in Chickens

In humans, more difficult decisions result in behavioural and physiological changes suggestive of increased arousal, but little is known about the effect of decision difficulty in other species. A difficult decision can have a number of characteristics; we aimed to monitor how finely balanced decisions, compared to unbalanced ones, affected the behaviour and physiology of chickens. An unbalanced decision was one in which the two options were of unequal net value (1 (Q1) vs. 6 (Q6) pieces of sweetcorn with no cost associated with either option); a finely balanced decision was one in which the options were of equal net value (i.e. hens were "indifferent" to both options). To identify hens'' indifference, a titration procedure was used in which a cost (electromagnetic weight on an access door) was applied to the Q6 option, to find the individual point at which hens chose this option approximately equally to Q1 via a non-weighted door. We then compared behavioural and physiological indicators of arousal (head movements, latency to choose, heart-rate variability and surface body temperature) when chickens made decisions that were unbalanced or finely balanced. Significant physiological (heart-rate variability) and behavioural (latency to pen) differences were found between the finely balanced and balanced conditions, but these were likely to be artefacts of the greater time and effort required to push through the weighted doors. No other behavioural and physiological measures were significantly different between the decision categories. We suggest that more information is needed on when best to monitor likely changes in arousal during decision-making and that future studies should consider decisions defined as difficult in other ways.     

Bayesian adaptive survey protocols for resource management

Transparency in resource management decisions requires a proper accounting of uncertainty at multiple stages of the decision-making process. As information becomes available, periodic review and updating of resource management protocols reduces uncertainty and improves management decisions. One of the most basic steps to mitigating anthropogenic effects on populations is determining if a population of a species occurs in an area that will be affected by human activity. Species are rarely detected with certainty, however, and falsely declaring a species absent can cause improper conservation decisions or even extirpation of populations. We propose a method to design survey protocols for imperfectly detected species that accounts for multiple sources of uncertainty in the detection process, is capable of quantitatively incorporating expert opinion into the decision-making process, allows periodic updates to the protocol, and permits resource managers to weigh the severity of consequences if the species is falsely declared absent. We developed our method using the giant gartersnake (Thamnophis gigas), a threatened species precinctive to the Central Valley of California, as a case study. Survey date was negatively related to the probability of detecting the giant gartersnake, and water temperature was positively related to the probability of detecting the giant gartersnake at a sampled location. Reporting sampling effort, timing and duration of surveys, and water temperatures would allow resource managers to evaluate the probability that the giant gartersnake occurs at sampled sites where it is not detected. This information would also allow periodic updates and quantitative evaluation of changes to the giant gartersnake survey protocol. Because it naturally allows multiple sources of information and is predicated upon the idea of updating information, Bayesian analysis is well-suited to solving the problem of developing efficient sampling protocols for species of conservation concern. © 2011 The Wildlife Society.     

Using Bayesian networks to incorporate uncertainty in habitat suitability index models

Habitat suitability index (HSI) models rarely characterize the uncertainty associated with their estimates of habitat quality despite the fact that uncertainty can have important management implications. The purpose of this paper was to explore the use of Bayesian belief networks (BBNs) for representing and propagating 3 types of uncertainty in HSI models—uncertainty in the suitability index relationships, the parameters of the HSI equation, and measurement of habitat variables (i.e., model inputs). I constructed a BBN–HSI model, based on an existing HSI model, using Netica™ software. I parameterized the BBN's conditional probability tables via Monte Carlo methods, and developed a discretization scheme that met specifications for numerical error. I applied the model to both real and dummy sites in order to demonstrate the utility of the BBN–HSI model for 1) determining whether sites with different habitat types had statistically significant differences in HSI, and 2) making decisions based on rules that reflect different attitudes toward risk—maximum expected value, maximin, and maximax. I also examined effects of uncertainty in the habitat variables on the model's output. Some sites with different habitat types had different values for E[HSI], the expected value of HSI, but habitat suitability was not significantly different based on the overlap of 90% confidence intervals for E[HSI]. The different decision rules resulted in different rankings of sites, and hence, different decisions based on risk. As measurement uncertainty in habitat variables increased, sites with significantly different (α = 0.1) E[HSI] became statistically more similar. Incorporating uncertainty in HSI models enables explicit consideration of risk and more robust habitat management decisions. © 2012 The Wildlife Society.     

Collective Decision-Making in Homing Pigeons: Larger Flocks Take Longer to Decide but Do Not Make Better Decisions

Social animals routinely are challenged to make consensus decisions about movement directions and routes. However, the underlying mechanisms facilitating such decision-making processes are still poorly known. A prominent question is how group members participate in group decisions. We addressed this question by examining how flocks of homing pigeons (Columba livia) decide their homing direction. We released newly formed flocks varying in size and determined the time taken to choose a homing direction (decision-making period) and the accuracy of that choice. We found that the decision-making period increases exponentially with flock size, which is consistent with a participatory decision-making process. We additionally found that there is no effect of flock size on the accuracy of the decisions made, which does not match with current theory for democratic choices of flight directions. Our combined results are better explained by a participatory choice of leaders that subsequently undertake the flock directional decisions. However, this decision-making model would only entirely fit with our results if leaders were chosen based on traits other than their navigational experience. Our study provides rare empirical evidence elucidating decision-making processes in freely moving groups of animals.     

Incorporating uncertainty and social values in managing invasive alien species: a deliberative multi-criteria evaluation approach

The management of Invasive Alien Species (IAS) is stymied by complex social values and severe levels of uncertainty. However, these two challenges are often hidden in the conventional model of management by “value-free” analyses and probability-based estimates of risk. As a result, diverse social values and wide margins of error in risk assessment carry zero weights in the decision-making process, leaving IAS risk decisions to be made in the wake of political pressure and the crisis atmosphere of incursion. We propose to use a Deliberative Multi-Criteria Evaluation (DMCE) to incorporate multiple social values and profound uncertainty into decision-making processes. The DMCE process combines the advantages of conventional multi-criteria decision analysis methods with the benefits of stakeholder participation to provide an analytical structure to assess complex multi-dimensional objectives. It, therefore, offers an opportunity for diverse views to enter the decision-making process, and for the negotiation of consensus positions. The DMCE process can also function as a platform for risk communication in which scientists, stakeholders, and decision-makers can interact and discuss the uncertainty associated with biological invasions. We examine two case studies that demonstrate how DMCE provides scientific rigor and transparency in the decision-making process of invasion risk management. The first case regards pre-border priority ranking for potential invasive species and the second relates to selecting the most desirable policy option for managing a post-border invader.     

Action planning and control under uncertainty emerge through a desirability-driven competition between parallel encoding motor plans

Living in an uncertain world, nearly all of our decisions are made with some degree of uncertainty about the consequences of actions selected. Although a significant progress has been made in understanding how the sensorimotor system incorporates uncertainty into the decision-making process, the preponderance of studies focus on tasks in which selection and action are two separate processes. First people select among alternative options and then initiate an action to implement the choice. However, we often make decisions during ongoing actions in which the value and availability of the alternatives can change with time and previous actions. The current study aims to decipher how the brain deals with uncertainty in decisions that evolve while acting. To address this question, we trained individuals to perform rapid reaching movements towards two potential targets, where the true target location was revealed only after the movement initiation. We found that reaction time and initial approach direction are correlated, where initial movements towards intermediate locations have longer reaction times than movements that aim directly to the target locations. Interestingly, the association between reaction time and approach direction was independent of the target probability. By modeling the task within a recently proposed neurodynamical framework, we showed that action planning and control under uncertainty emerge through a desirability-driven competition between motor plans that are encoded in parallel.     

Links between ecology and ecophilosophy,ethics and the requirements of environmental management

Abstract This paper concerns the ways that our philosophical attitudes to the environment can influence the appropriateness of methodologies for solving environmental problems. Sometimes a public perception is expressed that science takes scant regard of the concerns of the people affected. Is it possible for scientists and managers to respond to such concerns and still fulfil the logical and methodological rigour that their discipline demands? I believe we have to address fundamental issues of definitions and meaning before useful debate can occur among parties interested in environmental decision-making. Delving into the ideas behind our everyday practices of environmental management should promote re-evaluation of our beliefs, attitudes and concerns about nature. I examine environmental science from both ethical and managerial perspectives. I explore how our assumptions and attitudes might influence ecology, in particular issues raised by environmental impacts and conservation. The major points argued here are:

• 1 Any legal requirements of environmental investigations must be met, but perhaps we should act more in line with the spirit of legislation.
• 2 The managerial imperatives of environmental investigations need to be examined closely because of widely perceived problems with the use of science in impact assessment. We must change either our methods of assessment or the regulations and administration of environmental impact assessment (EIA).
• 3 Science is not paramount in the processes of environmental decision-making. We need to be aware of how psychosocial factors affect the ultimately political decisions about environmental problems.
• 4 Philosophy and ethics offer a range of perspectives that may benefit ecology. Scientists need to be aware of these just as they should be of their own leanings about how we treat nature.
• 5 Scientists need to translate social concerns or demands about the environment into properly defined scientific questions, and then study them as a matter of urgency.
• 6 Ecology needs to guide ecophilosophers and environmental ethicists as to how nature works, why we expect variability in ecosystems, what is naturalness, and other issues where a scientific understanding of nature has progressed beyond the point where these observers of ecology have so far taken inspiration.

     

Setting an optimal α that minimizes errors in null hypothesis significance tests

Null hypothesis significance testing has been under attack in recent years, partly owing to the arbitrary nature of setting α (the decision-making threshold and probability of Type I error) at a constant value, usually 0.05. If the goal of null hypothesis testing is to present conclusions in which we have the highest possible confidence, then the only logical decision-making threshold is the value that minimizes the probability (or occasionally, cost) of making errors. Setting α to minimize the combination of Type I and Type II error at a critical effect size can easily be accomplished for traditional statistical tests by calculating the α associated with the minimum average of α and β at the critical effect size. This technique also has the flexibility to incorporate prior probabilities of null and alternate hypotheses and/or relative costs of Type I and Type II errors, if known. Using an optimal α results in stronger scientific inferences because it estimates and minimizes both Type I errors and relevant Type II errors for a test. It also results in greater transparency concerning assumptions about relevant effect size(s) and the relative costs of Type I and II errors. By contrast, the use of α = 0.05 results in arbitrary decisions about what effect sizes will likely be considered significant, if real, and results in arbitrary amounts of Type II error for meaningful potential effect sizes. We cannot identify a rationale for continuing to arbitrarily use α = 0.05 for null hypothesis significance tests in any field, when it is possible to determine an optimal α.     

Outlier Responses Reflect Sensitivity to Statistical Structure in the Human Brain

We constantly look for patterns in the environment that allow us to learn its key regularities. These regularities are fundamental in enabling us to make predictions about what is likely to happen next. The physiological study of regularity extraction has focused primarily on repetitive sequence-based rules within the sensory environment, or on stimulus-outcome associations in the context of reward-based decision-making. Here we ask whether we implicitly encode non-sequential stochastic regularities, and detect violations therein. We addressed this question using a novel experimental design and both behavioural and magnetoencephalographic (MEG) metrics associated with responses to pure-tone sounds with frequencies sampled from a Gaussian distribution. We observed that sounds in the tail of the distribution evoked a larger response than those that fell at the centre. This response resembled the mismatch negativity (MMN) evoked by surprising or unlikely events in traditional oddball paradigms. Crucially, responses to physically identical outliers were greater when the distribution was narrower. These results show that humans implicitly keep track of the uncertainty induced by apparently random distributions of sensory events. Source reconstruction suggested that the statistical-context-sensitive responses arose in a temporo-parietal network, areas that have been associated with attention orientation to unexpected events. Our results demonstrate a very early neurophysiological marker of the brain''s ability to implicitly encode complex statistical structure in the environment. We suggest that this sensitivity provides a computational basis for our ability to make perceptual inferences in noisy environments and to make decisions in an uncertain world.     

Dissecting the links between reward and loss,decision-making,and self-reported affect using a computational approach

Links between affective states and risk-taking are often characterised using summary statistics from serial decision-making tasks. However, our understanding of these links, and the utility of decision-making as a marker of affect, needs to accommodate the fact that ongoing (e.g., within-task) experience of rewarding and punishing decision outcomes may alter future decisions and affective states. To date, the interplay between affect, ongoing reward and punisher experience, and decision-making has received little detailed investigation. Here, we examined the relationships between reward and loss experience, affect, and decision-making in humans using a novel judgement bias task analysed with a novel computational model. We demonstrated the influence of within-task favourability on decision-making, with more risk-averse/‘pessimistic’ decisions following more positive previous outcomes and a greater current average earning rate. Additionally, individuals reporting more negative affect tended to exhibit greater risk-seeking decision-making, and, based on our model, estimated time more poorly. We also found that individuals reported more positive affective valence during periods of the task when prediction errors and offered decision outcomes were more positive. Our results thus provide new evidence that (short-term) within-task rewarding and punishing experiences determine both future decision-making and subjectively experienced affective states.     

Old World monkeys are more similar to humans than New World monkeys when playing a coordination game

There is much debate about how humans' decision-making compares with that of other primates. One way to explore this is to compare species' performance using identical methodologies in games with strategical interactions. We presented a computerized Assurance Game, which was either functionally simultaneous or sequential, to investigate how humans, rhesus monkeys and capuchin monkeys used information in decision-making. All species coordinated via sequential play on the payoff-dominant Nash equilibrium, indicating that information about the partner's choice improved decisions. Furthermore, some humans and rhesus monkeys found the payoff-dominant Nash equilibrium in the simultaneous game, even when it was the first condition presented. Thus, Old World primates solved the task without any external cues to their partner's choice. Finally, when not explicitly prohibited, humans spontaneously used language to coordinate on the payoff-dominant Nash equilibrium, indicating an alternative mechanism for converting a simultaneous move game into a sequential move game. This phylogenetic distribution implies that no single mechanism drives coordination decisions across the primates, while humans' ability to spontaneously use language to change the structure of the game emphasizes that multiple mechanisms may be used even within the same species. These results provide insight into the evolution of decision-making strategies across the primates.     

Relating Pupil Dilation and Metacognitive Confidence during Auditory Decision-Making

The sources of evidence contributing to metacognitive assessments of confidence in decision-making remain unclear. Previous research has shown that pupil dilation is related to the signaling of uncertainty in a variety of decision tasks. Here we ask whether pupil dilation is also related to metacognitive estimates of confidence. Specifically, we measure the relationship between pupil dilation and confidence during an auditory decision task using a general linear model approach to take into account delays in the pupillary response. We found that pupil dilation responses track the inverse of confidence before but not after a decision is made, even when controlling for stimulus difficulty. In support of an additional post-decisional contribution to the accuracy of confidence judgments, we found that participants with better metacognitive ability – that is, more accurate appraisal of their own decisions – showed a tighter relationship between post-decisional pupil dilation and confidence. Together our findings show that a physiological index of uncertainty, pupil dilation, predicts both confidence and metacognitive accuracy for auditory decisions.