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Predicting risk-sensitivity in humans and lower animals: Risk as variance or coefficient of variation
- Psychological Review
, 2004
"... This article examines the statistical determinants of risk preference. In a meta-analysis of animal risk preference (foraging birds and insects), the coefficient of variation (CV), a measure of risk per unit of return, predicts choices far better than outcome variance, the risk measure of normative ..."
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This article examines the statistical determinants of risk preference. In a meta-analysis of animal risk preference (foraging birds and insects), the coefficient of variation (CV), a measure of risk per unit of return, predicts choices far better than outcome variance, the risk measure of normative models. In a meta-analysis of human risk preference, the superiority of the CV over variance in predicting risk taking is not as strong. Two experiments show that people’s risk sensitivity becomes strongly proportional to the CV when they learn about choice alternatives like other animals, by experiential sampling over time. Experience-based choices differ from choices when outcomes and probabilities are numerically de-scribed. Zipf’s law as an ecological regularity and Weber’s law as a psychological regularity may give rise to the CV as a measure of risk. Decision making under risk and uncertainty is a topic of re-search in disciplines as diverse as psychology, economics, zool-ogy, and entomology. Both the animal and the human risky choice literatures have proposed models that either predict choices in a deterministic fashion or predict risk sensitivity (i.e., the probability of choosing a riskier or less risky option) in a stochastic fashion.
Is more choice always desirable? Evidence and arguments from leks, food selection, and environmental enrichment
- Biological Review
, 2005
"... ABSTRACT Recent studies on humans show that too much choice can make subjects less likely to choose any item. I consider general adaptive and non-adaptive explanations of why such choice aversion, or its converse, might occur in animals. There are three questions: is more choice always preferred, d ..."
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ABSTRACT Recent studies on humans show that too much choice can make subjects less likely to choose any item. I consider general adaptive and non-adaptive explanations of why such choice aversion, or its converse, might occur in animals. There are three questions: is more choice always preferred, does it ever lead to less consumption (or a lower probability of consumption), and may it result in worse items being selected ? A preference for choice is one of the main explanations for lek formation and I draw attention to previously unrecognised parallels with models of human shopping behaviour. There is indeed evidence of female preference for larger leks, although much of the observational data are open to other interpretations. Unfortunately nobody has looked for choice aversion where it is most to be expected, in leks larger than normally occur. Evidence that too much choice of males confuses females is strongest in acoustically advertising frogs, but the widespread decrease of mating skew in larger leks might also have this explanation. A model reanalyses data on skew in black grouse Tetrao tetrix and suggests that considering only a random subset of a large lek may increase the chances of selecting the better males : larger leks are more likely to include better males, but these are less likely to be selected. These opposing effects may lead to an optimum lek size, but only with a sufficient decline in choice accuracy with size. With food choice, very few studies have avoided confounding choice with food quality, by manipulating only flavour. The widespread phenomena of stimulus-specific satiety and novelty seeking imply that monotonous diets are aversive, but no studies test whether animals choose sites where they know food diversity to be greater. Operant experiments that demonstrate mild preferences for free choice concern choice about the means to get food rather than the food itself. In some insect species even moderate choice of diet can be deleterious, and studies on search images and the confusion effect may be evidence of this in vertebrates. Environmental enrichment of captive animals often relies on increasing the options available, but it need not be the choice itself that is beneficial. I consider briefly further areas in biology where choice preference or aversion are potentially important.
Risk-sensitive foraging, fitness, and life histories: Where does reproduction fit into the big picture
, 1996
"... SYNOPSIS. Risk-sensitive foraging may occur whenever feeding success has non-linear effects on fitness. Models of sensitivity to variation in amount of food obtained have concentrated on foraging in order to survive even though feeding during growth, migration, or reproduction can have strong and no ..."
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SYNOPSIS. Risk-sensitive foraging may occur whenever feeding success has non-linear effects on fitness. Models of sensitivity to variation in amount of food obtained have concentrated on foraging in order to survive even though feeding during growth, migration, or reproduction can have strong and non-linear effects on fitness. I illustrate how risk-sensitive foraging for reproduction could differ from risk-sensitive foraging for survival using two simple models. Each model assumes that organisms must accumulate some threshold amount of resources before they can reproduce. In the first model, additional resources above the threshold lead to increased reproductive success. Here variance in feeding success can be advantageous even when the mean gain would allow organisms to reproduce. In the second model, early breeding is superior to late breeding because recruitment rate declines over time. Here a symmetrical distribution in foraging rates results in a skewed distribution of breeding times. Despite this, variance in feeding success may be advantageous even
Great apes’ risk-taking strategies in a decision making task
- PLoS ONE
, 2011
"... We investigate decision-making behaviour in all four non-human great ape species. Apes chose between a safe and a risky option across trials of varying expected values. All species chose the safe option more often with decreasing probability of success. While all species were risk-seeking, orangutan ..."
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We investigate decision-making behaviour in all four non-human great ape species. Apes chose between a safe and a risky option across trials of varying expected values. All species chose the safe option more often with decreasing probability of success. While all species were risk-seeking, orangutans and chimpanzees chose the risky option more often than gorillas and bonobos. Hence all four species ’ preferences were ordered in a manner consistent with normative dictates of expected value, but varied predictably in their willingness to take risks.
Is a bird in the hand worth two in the future? The neuroeconomics of intertemporal decision-making
, 2008
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Choice processes in multialternative decision making
, 2007
"... We study how the mechanisms of choice influence preferences when animals face more than 2 alternatives simultaneously. Choice mechanisms can be hierarchical (if alternatives are assigned to categories by their similarity and choice is between categories) or simultaneous (if options enter the choice ..."
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We study how the mechanisms of choice influence preferences when animals face more than 2 alternatives simultaneously. Choice mechanisms can be hierarchical (if alternatives are assigned to categories by their similarity and choice is between categories) or simultaneous (if options enter the choice process individually, each with its own value). The latter, although simpler, can lead to counterintuitive outcomes because expressed preference between options depends not only on the kinds of options present but also on the number of exemplars within each kind, so that decision makers have a higher probability of picking an option of a given class when exemplars in this class are common. Higher preference for commoner options has indeed been shown in humans, and if present in animals, it would affect many choice domains, including prey and mate choice. We studied the problem using starlings making risk-sensitive choices. Subjects chose between a risky option and 1 (in binary choices) or 2 (in trinary choices) fixed options that were identifiable as distinct but were identical in reward rate and had no variance. Preference between the risky and each fixed option was unaltered between binary and trinary contexts, but subjects chose a higher proportion of the fixed kind when this was represented by 2 rather than 1 distinct food sources. This means subjects were objectively risk prone in binary and risk averse in trinary contexts. These results fit accounts based on learning principles, but contradict the expectations of functional models of choice, including risk-sensitivity theory. Key words: choice, decision making, foraging, learning, rationality, risk sensitivity. [Behav Ecol] We study the process by which animals make choices in
Metabolic State Alters Economic Decision Making under Risk
- in Humans.” PLoS ONE 5(6):e11090.doi:10.1371/journal.pone.0011090 Tooby, John & Leda Cosmides.
, 2010
"... Abstract 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) fo ..."
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Abstract 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 risktaking in humans.
Variable Risk Control via Stochastic Optimization
"... We present new global and local policy search algorithms suitable for problems with policy-dependent cost variance (or risk), a property present in many robot control tasks. These algorithms exploit new techniques in nonparameteric heteroscedastic regression to directly model the policy-dependent di ..."
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We present new global and local policy search algorithms suitable for problems with policy-dependent cost variance (or risk), a property present in many robot control tasks. These algorithms exploit new techniques in nonparameteric heteroscedastic regression to directly model the policy-dependent distribution of cost. For local search, the learned cost model can be used as a critic for performing risk-sensitive gradient descent. Alternatively, decision-theoretic criteria can be applied to globally select policies to balance exploration and exploitation in a principled way, or to perform greedy minimization with respect to various risk-sensitive criteria. This separation of learning and policy selection permits variable risk control, where risk sensitivity can be flexibly adjusted and appropriate policies can be selected at runtime without relearning. We describe experiments in dynamic stabilization and manipulation with a mobile manipulator that demonstrate learning of flexible, risk-sensitive policies in very few trials. 1
Hyperbolically discounted temporal difference learning. Neural Comput
- Science
, 2010
"... Hyperbolic discounting of future outcomes is widely observed to underlie choice behavior in animals. Additionally, recent studies (Kobayashi & Schultz, 2008) have reported that hyperbolic discounting is observed even in neural systems underlying choice. However, the most prevalent models of tem ..."
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Hyperbolic discounting of future outcomes is widely observed to underlie choice behavior in animals. Additionally, recent studies (Kobayashi & Schultz, 2008) have reported that hyperbolic discounting is observed even in neural systems underlying choice. However, the most prevalent models of temporal discounting, such as temporal difference learning, assume that future outcomes are discounted exponentially. Exponential discounting has been preferred largely because it can be expressed recursively, whereas hyperbolic discounting has heretofore been thought not to have a recursive definition. In this letter, we define a learning algorithm, hyperbolically discounted temporal difference (HDTD) learning, which constitutes a recursive formulation of the hyperbolic model.
