Ecological Rationality

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Gerd Gigerenzer - One of the best experts on this subject based on the ideXlab platform.

  • Ecological Rationality fast and frugal heuristics for managerial decision making under uncertainty
    Academy of Management Journal, 2019
    Co-Authors: Shenghua Luan, Jochen Reb, Gerd Gigerenzer
    Abstract:

    Heuristics are often viewed as inferior to “rational” strategies that exhaustively search and process information. Introducing the theoretical perspective of Ecological Rationality, we challenge th...

  • Axiomatic Rationality and Ecological Rationality
    Synthese, 2019
    Co-Authors: Gerd Gigerenzer
    Abstract:

    Axiomatic Rationality is defined in terms of conformity to abstract axioms. Savage (The foundations of statistics, Wiley, New York, 1954 ) limited axiomatic Rationality to small worlds ( S , C ), that is, situations in which the exhaustive and mutually exclusive set of future states S and their consequences C are known. Others have interpreted axiomatic Rationality as a categorical norm for how human beings should reason, arguing in addition that violations would lead to real costs such as money pumps. Yet a review of the literature shows little evidence that violations are actually associated with any measurable costs. Limiting axiomatic Rationality to small worlds, I propose a naturalized version of Rationality for situations of intractability and uncertainty (as opposed to risk), all of which are not in ( S , C ). In these situations, humans can achieve their goals by relying on heuristics that may violate axiomatic Rationality. The study of Ecological Rationality requires formal models of heuristics and an analysis of the structures of environments these can exploit. It lays the foundation of a moderate naturalism in epistemology, providing statements about heuristics we should use in a given situation. Unlike axiomatic Rationality, Ecological Rationality can explain less-is-more effects (when using less information can be expected to generate more accurate predictions), formalize when one should move from ‘is’ to ‘ought,’ and be evaluated by goals beyond coherence, such as predictive accuracy, frugality, and efficiency. Ecological Rationality can be seen as a formalization of means–end instrumentalist Rationality, based on Herbert Simon’s insight that rational behavior is a function of the mind and its environment.

  • The Ecological Rationality of situations: Behavior = f(adaptive toolbox, environment)
    The Oxford Handbook of Psychological Situations, 2019
    Co-Authors: Peter M. Todd, Gerd Gigerenzer
    Abstract:

    The study of situations involves asking how people behave in particular environmental settings, often in terms of their individual personality differences. The Ecological Rationality research program explains people’s behavior in terms of the specific decision-making tools they select and use from their mind’s adaptive toolbox when faced with specific types of environment structure. These two approaches can be integrated to provide a more precise mapping from features of situation structure to decision heuristics used and behavioral outcomes. This chapter presents three examples illustrating research on Ecological Rationality and its foundations, along with initial directions for incorporating it into an integrated situation theory.

  • Emerging Trends in the Social and Behavioral Sciences: An Interdisciplinary, Searchable, and Linkable Resource - Heuristics: Tools for an Uncertain World
    Emerging Trends in the Social and Behavioral Sciences, 2015
    Co-Authors: Hansjörg Neth, Gerd Gigerenzer
    Abstract:

    We distinguish between situations of risk, where all options, consequences, and probabilities are known, and situations of uncertainty, where they are not. Probability theory and statistics are the best tools for deciding under risk but not under uncertainty, which characterizes most relevant problems that humans have to solve. Uncertainty requires simple heuristics that are robust rather than optimal. We propose to think of the mind as an adaptive toolbox and introduce the descriptive study of heuristics, their building blocks, and the core capacities they exploit. The question of which heuristic to select for which class of problems is the topic of the normative study of Ecological Rationality. We discuss earlier views on the nature of heuristics that maintained that heuristics are always less accurate because they ignore information and demand less effort. Contrary to this accuracy–effort trade-off view, heuristics can lead to more accurate inferences—under uncertainty—than strategies that use more information and computation. The study of heuristics opens up a new perspective on the nature of both cognition and Rationality. In a world of uncertainty, Homo sapiens might well be called Homo heuristicus. Keywords: accuracy–effort trade-off; adaptive toolbox; Ecological Rationality; heuristics; satisficing; Herbert A. Simon; uncertainty

  • Ecological Rationality and citizenship education: an
    2014
    Co-Authors: Gerd Gigerenzer, Danilo R. Streck
    Abstract:

    The subject of this interview is the research on Ecological Rationality carried out at the Max-Planck Instuitute for Human Development, in Berlin, and its implications for education, especially for citizenship education. The studies on Ecological Rationality focus on the processes of decision making in a world in which human activity happens in a context of uncertainties, where a complete evaluation of factors is practically impossible. The assumption of the research is that cognitive processes cannot be dissociated from social and cultural realities, and that therefore the identification of the heuristics used in making decisions can be an important instrument for the formation of autonomous thinking. Of special interest from the pedagogical perspective is promoting the development of the capacity to understand and deal with the limits and possibilities of the scientific logic on which educational processes are largely based, and the development of forms of knowing that are as much or more determinant than that one. Gigerenzer emphasizes the role of collective and interdisciplinary work to promote creativity in research and teaching, as well as to make decisions in daily life.

Ralph Hertwig - One of the best experts on this subject based on the ideXlab platform.

  • The interpretation of uncertainty in Ecological Rationality
    Synthese, 2019
    Co-Authors: Anastasia Kozyreva, Ralph Hertwig
    Abstract:

    Despite the ubiquity of uncertainty, scientific attention has focused primarily on probabilistic approaches, which predominantly rely on the assumption that uncertainty can be measured and expressed numerically. At the same time, the increasing amount of research from a range of areas including psychology, economics, and sociology testify that in the real world, people’s understanding of risky and uncertain situations cannot be satisfactorily explained in probabilistic and decision-theoretical terms. In this article, we offer a theoretical overview of an alternative approach to uncertainty developed in the framework of the Ecological Rationality research program. We first trace the origins of the Ecological approach to uncertainty in Simon’s bounded Rationality and Brunswik’s lens model framework and then proceed by outlining a theoretical view of uncertainty that ensues from the Ecological Rationality approach. We argue that the Ecological concept of uncertainty relies on a systemic view of uncertainty that features it as a property of the organism–environment system. We also show how simple heuristics can deal with unmeasurable uncertainty and in what cases ignoring probabilities emerges as a proper response to uncertainty.

  • Ecological Rationality: A Framework for Understanding and Aiding the Aging Decision Maker
    Frontiers in neuroscience, 2012
    Co-Authors: Rui Mata, Ralph Hertwig, Thorsten Pachur, Bettina Von Helversen, Jörg Rieskamp, Lael J. Schooler
    Abstract:

    The notion of Ecological Rationality sees human Rationality as the result of the adaptive fit between the human mind and the environment. Ecological Rationality focuses the study of decision making on two key questions: First, what are the environmental regularities to which people's decision strategies are matched, and how frequently do these regularities occur in natural environments? Second, how well can people adapt their use of specific strategies to particular environmental regularities? Research on aging suggests a number of changes in cognitive function, for instance, deficits in learning and memory that may impact decision-making skills. However, it has been shown that simple strategies can work well in many natural environments, which suggests that age-related deficits in strategy use may not necessarily translate into reduced decision quality. Consequently, we argue that predictions about the impact of aging on decision performance depend not only on how aging affects decision-relevant capacities but also on the decision environment in which decisions are made. In sum, we propose that the concept of the Ecological Rationality is crucial to understanding and aiding the aging decision maker.

  • Ecological Rationality a framework for understanding and aiding the aging decision maker
    Frontiers in Neuroscience, 2012
    Co-Authors: Rui Mata, Ralph Hertwig, Thorsten Pachur, Bettina Von Helversen, Jörg Rieskamp, Lael J. Schooler
    Abstract:

    Ecological Rationality sees human Rationality as the result of the adaptive fit between the human mind and the environment. The concept of Ecological Rationality focuses the study of cognition on two key questions: First, what are the environmental regularities to which people’s decision strategies are matched, and how frequently do these regularities occur in natural environments? Second, how well can people adapt their use of specific strategies to particular environments? Research on aging suggests a number of changes in cognitive function, for instance, deficits in learning and memory that may impact decision-making skills. However, it has been shown that simple strategies can work well in many natural environments, which suggests that age-related deficits in strategy use may not necessarily translate into diminished decision performance. Consequently, we argue that predictions about the impact of aging on decision performance depend not only on how aging affects decision-relevant capacities but also on the decision ecology in which decisions are made. In sum, we propose that the concept of the Ecological Rationality is crucial to understanding and aiding the aging decision maker.

Alasdair I. Houston - One of the best experts on this subject based on the ideXlab platform.

  • An evolutionary perspective on information processing.
    Topics in cognitive science, 2014
    Co-Authors: Peter C. Trimmer, Alasdair I. Houston
    Abstract:

    Behavioral ecologists often assume that natural selection will produce organisms that make optimal decisions. In the context of information processing, this means that the behavior of animals will be consistent with models from fields such as signal detection theory and Bayesian decision theory. We discuss work that applies such models to animal behavior and use the case of Bayesian updating to make the distinction between a description of behavior at the level of optimal decisions and a mechanistic account of how decisions are made. The idea of Ecological Rationality is that natural selection shapes an animal's decision mechanisms to suit its environment. As a result, decision-making mechanisms may not perform well outside the context in which they evolved. Although the assumption of Ecological Rationality is plausible, we argue that the exact nature of the relationship between ecology and cognitive mechanism may not be obvious.

  • The Ecological Rationality of state-dependent valuation
    Psychological review, 2011
    Co-Authors: John M. Mcnamara, Pete C. Trimmer, Alasdair I. Houston
    Abstract:

    Laboratory studies on a range of animals have identified a bias that seems to violate basic principles of rational behavior: a preference is shown for feeding options that previously provided food when reserves were low, even though another option had been found to give the same reward with less delay. The bias presents a challenge to normative models of decision making (which only take account of expected rewards and the state of the animal at the decision time). To understand the behavior, we take a broad Ecological perspective and consider how valuation mechanisms evolve when the best action depends upon the environment being faced. We show that in a changing and uncertain environment, state-dependent valuation can be favored by natural selection: Individuals should allow their hunger to affect learning for future decisions. The valuation mechanism that typically evolves produces the kind of behavior seen in standard laboratory tests. By providing an insight into why learning should be affected by the state of an individual, we provide a basis for understanding psychological principles in terms of an animal's ecology.

Peter M. Todd - One of the best experts on this subject based on the ideXlab platform.

  • The Ecological Rationality of situations: Behavior = f(adaptive toolbox, environment)
    The Oxford Handbook of Psychological Situations, 2019
    Co-Authors: Peter M. Todd, Gerd Gigerenzer
    Abstract:

    The study of situations involves asking how people behave in particular environmental settings, often in terms of their individual personality differences. The Ecological Rationality research program explains people’s behavior in terms of the specific decision-making tools they select and use from their mind’s adaptive toolbox when faced with specific types of environment structure. These two approaches can be integrated to provide a more precise mapping from features of situation structure to decision heuristics used and behavioral outcomes. This chapter presents three examples illustrating research on Ecological Rationality and its foundations, along with initial directions for incorporating it into an integrated situation theory.

  • Building the Theory of Ecological Rationality
    Minds and Machines, 2016
    Co-Authors: Peter M. Todd, Henry Brighton
    Abstract:

    While theories of Rationality and decision making typically adopt either a single-powertool perspective or a bag-of-tricks mentality, the research program of Ecological Rationality bridges these with a theoretically-driven account of when different heuristic decision mechanisms will work well. Here we described two ways to study how heuristics match their Ecological setting: The bottom-up approach starts with psychologically plausible building blocks that are combined to create simple heuristics that fit specific environments. The top-down approach starts from the statistical problem facing the organism and a set of principles, such as the bias– variance tradeoff, that can explain when and why heuristics work in uncertain environments, and then shows how effective heuristics can be built by biasing and simplifying more complex models. We conclude with challenges these approaches face in developing a psychologically realistic perspective on human Rationality.

  • Ecological Rationality: Intelligence in the World
    2012
    Co-Authors: Peter M. Todd, Gerd Gigerenzer
    Abstract:

    "More information is always better, and full information is best. More computation is always better, and optimization is best." More-is-better ideals such as these have long shaped our vision of Rationality. Yet humans and other animals typically rely on simple heuristics to solve adaptive problems, focusing on one or a few important cues and ignoring the rest, and shortcutting computation rather than striving for as much as possible. In this book, we argue that in an uncertain world, more information and computation are not always better, and we ask when, and why, less can be more. The answers to these questions constitute the idea of Ecological Rationality: how we are able to achieve intelligence in the world by using simple heuristics matched to the environments we face, exploiting the structures inherent in our physical, biological, social, and cultural surroundings.

  • Environments That Make Us Smart Ecological Rationality
    Current Directions in Psychological Science, 2007
    Co-Authors: Peter M. Todd, Gerd Gigerenzer
    Abstract:

    Traditional views of Rationality posit general-purpose decision mechanisms based on logic or optimization. The study of Ecological Rationality focuses on uncovering the “adaptive toolbox” of domain-specific simple heuristics that real, computationally bounded minds employ, and explaining how these heuristics produce accurate decisions by exploiting the structures of information in the environments in which they are applied. Knowing when and how people use particular heuristics can facilitate the shaping of environments to engender better decisions.

  • testing the Ecological Rationality of base rate neglect
    Simulation of Adaptive Behavior, 2002
    Co-Authors: Peter M. Todd, Adam S Goodie
    Abstract:

    What simple learning rules can allow agents to cope with changing environments? We tested whether a rule that neglects base rates of events in the world -- something that is usually considered irrational -- could be as successful as Bayesian inference that combines base rates and cue accuracies - the usual standard of Rationality-in making cue-based predictions about events in time-varying environments. We focused on environments in which base rates change more frequently than cue accuracies, a condition that, we argue, is common in the real world. Five strategies (Bayesian combination, cue accuracy alone, adjusted cue accuracy, base rates alone, and a Least Mean Square learning rule) were compared across "lifetimes" of 10,000 predictions, in which base rates and cue accuracy independently changed every 10, 50, 100, 500, 1000, or 5000 events. The results confirmed that simple strategies that are typically deemed irrational (base rate neglect and its opposite, conservatism) can rival the typical standard of Rationality, Bayesian combination of information, by producing Ecologically rational decisions in appropriately varying environments.

Hansjörg Neth - One of the best experts on this subject based on the ideXlab platform.

  • Emerging Trends in the Social and Behavioral Sciences: An Interdisciplinary, Searchable, and Linkable Resource - Heuristics: Tools for an Uncertain World
    Emerging Trends in the Social and Behavioral Sciences, 2015
    Co-Authors: Hansjörg Neth, Gerd Gigerenzer
    Abstract:

    We distinguish between situations of risk, where all options, consequences, and probabilities are known, and situations of uncertainty, where they are not. Probability theory and statistics are the best tools for deciding under risk but not under uncertainty, which characterizes most relevant problems that humans have to solve. Uncertainty requires simple heuristics that are robust rather than optimal. We propose to think of the mind as an adaptive toolbox and introduce the descriptive study of heuristics, their building blocks, and the core capacities they exploit. The question of which heuristic to select for which class of problems is the topic of the normative study of Ecological Rationality. We discuss earlier views on the nature of heuristics that maintained that heuristics are always less accurate because they ignore information and demand less effort. Contrary to this accuracy–effort trade-off view, heuristics can lead to more accurate inferences—under uncertainty—than strategies that use more information and computation. The study of heuristics opens up a new perspective on the nature of both cognition and Rationality. In a world of uncertainty, Homo sapiens might well be called Homo heuristicus. Keywords: accuracy–effort trade-off; adaptive toolbox; Ecological Rationality; heuristics; satisficing; Herbert A. Simon; uncertainty

  • foraging for alternatives Ecological Rationality in keeping options viable
    Cognitive Science, 2014
    Co-Authors: Hansjörg Neth, Neele Engelmann, Ralf Mayrhofer
    Abstract:

    Foraging for Alternatives: Ecological Rationality in Keeping Options Viable Hansjorg Neth, Neele Engelmann & Ralf Mayrhofer {hneth|neele.engelmann|rmayrho}@uni-goettingen.de Cognitive and Decision Sciences Georg-Elias-Muller Institute of Psychology University of Gottingen, Germany Abstract Do we invest irrational amounts of effort into keeping options viable, or do we manage available and threatened options in an adaptive fashion? To ask and answer this question, we advo- cate an approach that considers the dynamic properties of deci- sion environments. By linking the exploration-vs.-exploitation dilemma to animal foraging, we show that preserving and abandoning options can both be adaptive. Specifically, peo- ple should stay and abandon options in progressive environ- ments, and leave and seek alternatives in exhaustive environ- ments. We extend a multi-arm bandit problem with threatened options by a manipulation of environmental expectations. Our findings show that people are highly sensitive to environmental assumptions and small payoff differentials. This replicates the original effect, but may explain the apparently irrational ten- dency to keep options open as an Ecologically rational adapta- tion. Keywords: exploration vs. exploitation; multi-arm bandit; multi-tasking; switch costs; animal foraging. Should I stay or should I go now? If I go there will be trouble, and if I stay it will be double. . . The Clash Introduction Having a choice between multiple options confronts us with a dilemma: We desire the availability of options, but keep- ing options open often comes with costs. For instance, the simultaneous pursuit of several careers, research goals, or ro- mantic relationships can reduce the success or satisfaction en- joyed by any particular one. The dilemma between freedom of choice and the costs of preserving options is aggravated by the fact that options tend to deteriorate or disappear when we fail to invest enough effort or resources (e.g., attention, time, or money) into their availability. In an intriguing study, Shin and Ariely (2004) asked whether options are valued differently when they are in dan- ger of disappearing. The availability of multiple options was operationalized by playing a virtual “door game” in which participants first chose one of three doors to enter a room. From then on, participants could either earn a monetary re- ward by pressing a button within the chosen room or select a different door to switch to another room. As the overall bud- get of actions was limited to 100 clicks, switching between rooms incurred the opportunity cost of forgoing one payoff in the current room. In one condition, the three alternative rooms were continuously available. A second condition im- posed an additional threat of disappearing options by gradu- ally shrinking unused doors. On any click within a room or on the door to another room the two unchosen doors would lose 1/15th of their original width. This implies that the access to a room would effectively vanish if it has not been chosen within the 15 most recent clicks. Shin and Ariely’s (2004) main result was that the threat of losing options caused participants to invest additional efforts into their availability. Crucially, the costs of keeping doors open exceeded the potential benefits conveyed by them. Thus, people exhibited a strong and seemingly irrational tendency to keep poor options viable — a phenomenon that the authors attributed to an aversion to the loss of options. An analysis of the original study reveals an extremely de- manding task even when options are constantly available. Sequential decision environments involving payoff functions that must be estimated on the basis of limited experience tran- scend the realms of risky choice and require decision mak- ing under uncertainty (Sims, Neth, Jacobs, & Gray, 2013). Formally, the simultaneous availability of three rooms consti- tutes a multi-armed bandit problem (Banks, Olson, & Porter, 1997) in which participants must trade-off the exploration of unfamiliar choices with the exploitation of familiar ones to maximize the gain from probabilistic payoff functions (see Lee, Zhang, Munro, & Steyvers, 2011; Steyvers, Lee, & Wa- genmakers, 2009; Sutton & Barto, 1998, for formal models). In the present paradigm, this dilemma is aggravated by im- plicit but substantial switch costs that are paid by forgoing one payoff whenever entering another room. A further dif- ficulty of the original study was that the payoffs of all three rooms were sampled randomly from extremely similar payoff distributions. In fact, for the first 3 of 4 experiments the op- tions’ payoffs differed merely in their distributional form and type, but were equal in expected value. By contrast, the avail- ability of three separate doors suggested that people actually had a choice. If participants erroneously expected that the op- tions differed in some relevant aspect, the high similarity and overlap of experienced payoffs rendered the exploration task even more demanding. Thus, the threat of losing options was added to a non-trivial array of challenging task components. In a follow-up study that manipulated the difference between the payoff distributions of nine options, Ejova, Navarro, and Perfors (2009) showed that people are more willing to walk away from inferior options when the discrim- inability between options increases. This suggests that the dysfunctional aversion to option loss occurs mostly in situa- tions that are difficult to explore, whereas people are willing and able to sacrifice options when superior ones are available and identifiable.

  • CogSci - Foraging for Alternatives: Ecological Rationality in Keeping Options Viable
    Cognitive Science, 2014
    Co-Authors: Hansjörg Neth, Neele Engelmann, Ralf Mayrhofer
    Abstract:

    Foraging for Alternatives: Ecological Rationality in Keeping Options Viable Hansjorg Neth, Neele Engelmann & Ralf Mayrhofer {hneth|neele.engelmann|rmayrho}@uni-goettingen.de Cognitive and Decision Sciences Georg-Elias-Muller Institute of Psychology University of Gottingen, Germany Abstract Do we invest irrational amounts of effort into keeping options viable, or do we manage available and threatened options in an adaptive fashion? To ask and answer this question, we advo- cate an approach that considers the dynamic properties of deci- sion environments. By linking the exploration-vs.-exploitation dilemma to animal foraging, we show that preserving and abandoning options can both be adaptive. Specifically, peo- ple should stay and abandon options in progressive environ- ments, and leave and seek alternatives in exhaustive environ- ments. We extend a multi-arm bandit problem with threatened options by a manipulation of environmental expectations. Our findings show that people are highly sensitive to environmental assumptions and small payoff differentials. This replicates the original effect, but may explain the apparently irrational ten- dency to keep options open as an Ecologically rational adapta- tion. Keywords: exploration vs. exploitation; multi-arm bandit; multi-tasking; switch costs; animal foraging. Should I stay or should I go now? If I go there will be trouble, and if I stay it will be double. . . The Clash Introduction Having a choice between multiple options confronts us with a dilemma: We desire the availability of options, but keep- ing options open often comes with costs. For instance, the simultaneous pursuit of several careers, research goals, or ro- mantic relationships can reduce the success or satisfaction en- joyed by any particular one. The dilemma between freedom of choice and the costs of preserving options is aggravated by the fact that options tend to deteriorate or disappear when we fail to invest enough effort or resources (e.g., attention, time, or money) into their availability. In an intriguing study, Shin and Ariely (2004) asked whether options are valued differently when they are in dan- ger of disappearing. The availability of multiple options was operationalized by playing a virtual “door game” in which participants first chose one of three doors to enter a room. From then on, participants could either earn a monetary re- ward by pressing a button within the chosen room or select a different door to switch to another room. As the overall bud- get of actions was limited to 100 clicks, switching between rooms incurred the opportunity cost of forgoing one payoff in the current room. In one condition, the three alternative rooms were continuously available. A second condition im- posed an additional threat of disappearing options by gradu- ally shrinking unused doors. On any click within a room or on the door to another room the two unchosen doors would lose 1/15th of their original width. This implies that the access to a room would effectively vanish if it has not been chosen within the 15 most recent clicks. Shin and Ariely’s (2004) main result was that the threat of losing options caused participants to invest additional efforts into their availability. Crucially, the costs of keeping doors open exceeded the potential benefits conveyed by them. Thus, people exhibited a strong and seemingly irrational tendency to keep poor options viable — a phenomenon that the authors attributed to an aversion to the loss of options. An analysis of the original study reveals an extremely de- manding task even when options are constantly available. Sequential decision environments involving payoff functions that must be estimated on the basis of limited experience tran- scend the realms of risky choice and require decision mak- ing under uncertainty (Sims, Neth, Jacobs, & Gray, 2013). Formally, the simultaneous availability of three rooms consti- tutes a multi-armed bandit problem (Banks, Olson, & Porter, 1997) in which participants must trade-off the exploration of unfamiliar choices with the exploitation of familiar ones to maximize the gain from probabilistic payoff functions (see Lee, Zhang, Munro, & Steyvers, 2011; Steyvers, Lee, & Wa- genmakers, 2009; Sutton & Barto, 1998, for formal models). In the present paradigm, this dilemma is aggravated by im- plicit but substantial switch costs that are paid by forgoing one payoff whenever entering another room. A further dif- ficulty of the original study was that the payoffs of all three rooms were sampled randomly from extremely similar payoff distributions. In fact, for the first 3 of 4 experiments the op- tions’ payoffs differed merely in their distributional form and type, but were equal in expected value. By contrast, the avail- ability of three separate doors suggested that people actually had a choice. If participants erroneously expected that the op- tions differed in some relevant aspect, the high similarity and overlap of experienced payoffs rendered the exploration task even more demanding. Thus, the threat of losing options was added to a non-trivial array of challenging task components. In a follow-up study that manipulated the difference between the payoff distributions of nine options, Ejova, Navarro, and Perfors (2009) showed that people are more willing to walk away from inferior options when the discrim- inability between options increases. This suggests that the dysfunctional aversion to option loss occurs mostly in situa- tions that are difficult to explore, whereas people are willing and able to sacrifice options when superior ones are available and identifiable.