Article

Sympathy and Callousness: The Impact of Deliberative Thought on Donations to Identifiable And Statistical Victims

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Abstract

When donating to charitable causes, people do not value lives consistently. Money is often concentrated on a single victim even though more people would be helped, if resources were dispersed or spent protecting future victims. We examine the impact of deliberating about donation decisions on generosity. In a series of field experiments, we show that teaching or priming people to recognize the discrepancy in giving toward identifiable and statistical victims has perverse effects: individuals give less to identifiable victims but do not increase giving to statistical victims, resulting in an overall reduction in caring and giving. Thus, it appears that, when thinking deliberatively, people discount sympathy towards identifiable victims but fail to generate sympathy toward statistical victims.

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... Prior studies on altruism have revealed that providing information about an anonymous victim or statistical victim (regardless of its magnitude) is not nearly as powerful in eliciting prosocial affect and behavior as a vivid story about a single, identifiable victim (Jenni & Loewenstein, 1997;Small et al., 2007;Small & Loewenstein, 2003). This phenomenon, known as the identifiable victim effect, suggests that even a very weak form of identifiability (e.g., pre-selecting a specific recipient for a prosocial act without providing any personal information about them) is sufficient to increase caring and donations (Small & Loewenstein, 2003). ...
... In all experiments, we hypothesized that participants would be more likely to show prosocial intention and behavior toward the single-identifiable animal victim compared to the other animal victim conditions. Further, as previously mentioned, emotional processes elicited in response to a single-identifiable victim were determined to be a crucial factor in this effect (Kogut & Ritov, 2005a, 2005bSmall et al., 2007;Västfjäll et al., 2014). In light of that, in Experiments 1 and 2, following the assessment of the dependent measure, we asked participants to rate their feelings of sympathy toward the runaway calf/calves and distress in response to the story. ...
... In contrast, in the current work, we found that the average donation (as well as other prosocial acts) to a single-identifiable victim was higher than the average donation to a group of victims (regardless of the identifiability of the group). Thus, consistent with previous findings on a single-identifiable human victim (Kogut & Ritov, 2005a, 2005bSmall et al., 2007;Västfjäll et al., 2014), in the current work, we found not only insensitivity to the number of farm animal victims, but also a greater willingness to help a single-identifiable animal compared to the willingness to assist a group of animals. ...
Article
Diets based on animal products are costly to our health and the planet and often inflict suffering on animals. In this study, we aimed to elicit animal advocacy among omnivores using the identifiable victim effect, a well-documented phenomenon in which presenting an identifiable victim, compared to anonymous or statistical victims, evokes greater caring and helping behavior. We explored whether this finding extends to farm animal victims and particularly among omnivores who may have a material interest in the outcome (i.e., the slaughter of farm animals). Consequently, due to their dietary lifestyle and consumer support of the meat industry, they may be perceived as complicit in the victimization. In Experiment 1, omnivore participants indicated a greater likelihood to sign and share a petition to save an identified runaway calf (presented with a name and a picture) from slaughter than several unidentified runaway calves. In Experiment 2, we extended these findings to actual petition signing, along with reporting support of the petition. In Experiment 3, we further replicated the identifiability effect using real donations to save the runaway calf (calves) from slaughter and demonstrated it is limited to a single-identified victim. Additionally, we found that feelings of sympathy (Experiment 1) and ambivalence towards meat (Experiment 3) mediated the effect, whereas concern, empathy, identification with animals (Experiment 2), and ecological identity (Experiment 3) moderated it. Omnivores who scored high in concern and ecological identity, and low in empathy and identification with animals were more susceptible to the effect. Theoretical and practical implications are discussed.
... Humans are intuitively prosocial and altruistic (Batson & Shaw, 1991;Zaki & Mitchell, 2013). Yet they are often unmoved by widespread problems, a fact that has perplexed psychologists for decades (Slovic, 2010;Slovic et al., 2007;Small et al., 2007). Why don't mass atrocities, famines, and genocides motivate more action? ...
... How can we be so callous? One of the bestdocumented explanations of this apathy is that it is a limitation of the human heart (Hsee & Rottenstreich, 2004;Slovic, 2010;Slovic et al., 2007;Small et al., 2007). Here, we offer a complementary answer. ...
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Across 15 studies (N = 2,636), people who considered the prevalence of a problem (e.g., 4.2 million people drive drunk each month) inferred it caused less harm, a phenomenon we dub the big problem paradox. People believed dire problems—ranging from poverty to drunk driving—were less problematic upon learning the number of people they affect (Studies 1–2). Prevalence information caused medical experts to infer medication nonadherence was less dangerous, just as it led women to underestimate their true risk of contracting cancer. The big problem paradox results from an optimistic view of the world. When people believe the world is good, they assume widespread problems have been addressed and, thus, cause less harm (Studies 3–4). The big problem paradox has key implications for motivation and helping behavior (Studies 5–6). Learning the prevalence of medical conditions (i.e., chest pain, suicidal ideation) led people to think a symptomatic individual was less sick and, as a result, to help less—in violation of clinical guidelines. The finding that scale warps judgments and de-motivates action is of particular relevance in the globalized 21st century.
... Found moderate evidence of publication bias, adjusting for which, there was no evidence for the identified victim effect, with adjusted effect down to r = .002 Maier et al. (2023) replication of Small et al. (2007) Identifiability + Singularity A failed replication of Small et al. (2007). No support for identified victim effects Moche and Västfjäll (2021) Identifiability In 3 studies (overall N = 1508) with different samples from different countries, there was no main effect of identifiability on any of the measures Moche et al. (2022) Singularity Weak effects, with just below the alpha threshold for the Israeli sample, and in the Swedish sample, a signal for willingness to contribute was detected but not for actual donations Moche et al. (2023) Singularity Three adults elicited more help than one adult Moche et al. (2024) Identifiability Identified victim effect is contextual and much weaker than originally thought Morvinski and Gordon-Hecker (2023) Singularity Adding a photo has a positive effect on donations, yet results are inconsistent with singularity effect and scope insensitivity Vu et al. (2024) Identifiability No effect of identifiability on altruism on willingness to contribute. ...
... Found moderate evidence of publication bias, adjusting for which, there was no evidence for the identified victim effect, with adjusted effect down to r = .002 Maier et al. (2023) replication of Small et al. (2007) Identifiability + Singularity A failed replication of Small et al. (2007). No support for identified victim effects Moche and Västfjäll (2021) Identifiability In 3 studies (overall N = 1508) with different samples from different countries, there was no main effect of identifiability on any of the measures Moche et al. (2022) Singularity Weak effects, with just below the alpha threshold for the Israeli sample, and in the Swedish sample, a signal for willingness to contribute was detected but not for actual donations Moche et al. (2023) Singularity Three adults elicited more help than one adult Moche et al. (2024) Identifiability Identified victim effect is contextual and much weaker than originally thought Morvinski and Gordon-Hecker (2023) Singularity Adding a photo has a positive effect on donations, yet results are inconsistent with singularity effect and scope insensitivity Vu et al. (2024) Identifiability No effect of identifiability on altruism on willingness to contribute. ...
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The identified victim effect is the phenomenon in which people tend to contribute more to identified than to unidentified victims. Kogut and Ritov (2005a) found that the identified victim effect was limited to a single victim and driven by empathic emotions. In a pre-registered experiment with an online U.S. American MTurk sample on CloudResearch (N = 2003), we conducted a close replication and extension of Experiment 2 from Kogut and Ritov (2005a). The replication findings failed to provide empirical support for the identified single victim effect hypothesis since we found no evidence of differences in willingness to contribute when comparing a single identified victim to a single unidentified victim. (η2p = .00, 90% CI [0.00, 0.00]), and no indication for the target article’s interaction between singularity and identifiability (original: η2p = .062, 90% CI [0.01, 0.15]; replication: η2p = .00, 90% CI [0.00, 0.00]). Extending the replication to conduct a conceptual replication of Kogut and Ritov (2007), we investigated a boundary condition of the effect - group belonging. We found support for an ingroup bias in helping behaviors and indications for empathic emotions and perceived responsibility contributing to this effect. We discuss differences between our study and the target article and implications for the literature on the identified victim effect.
... We also examined a limited set of demographic variables, leaving out key factors (e.g., variations in recycling rules) that could also have a substantial bearing on recycle/reuse behaviors. Next, although our stimulus message related to plastic waste was adapted from various online sources and revised by two experts in the field, message effects are often tied to message framing (Powell et al., 2015), as well as statistical versus emotionally laden information (Small et al., 2007). Thus, future research should delve deeper into these message attributes. ...
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Although persuasive messages are designed to motivate individuals to engage in intended behaviors, they do not always work. Often, people follow previously established values and ideologies and dismiss persuasive messages. We examine how participants react to a persuasive message related to plastic pollution and how these reactions shape their willingness to recycle and reuse. Results indicate that environmental values and political ideology are associated with message derogation in distinct ways, which, in turn, affect risk perception, self‐efficacy, and intention to recycle and reuse. Further, past behavior moderates the relationship between message derogation and perceived risk, but not the relationship between message derogation and self‐efficacy. These results suggest that pre‐existing values and ideologies play an important role in message derogation, a hitherto under‐researched phenomenon that has key implications for self‐reported behavioral change. Moreover, past behavior could serve as a powerful lever in steering risk perception and behavioral intent.
... This allows for a relatively clean investigation of the relative importance of impact and responsibility considerations, with limited scope for alternative explanations and minimal noise deriving from unaccounted factors. For instance, since all candidates are equally identifiable and there are no overhead costs, neither the identifiable victim effect(Jenni and Loewenstein, 1997;Small and Loewenstein, 2003;Small, Loewenstein and Slovic, 2007) nor overhead aversion(Baron and Szymanska, 2011; Caviola et al., 2014; Gneezy, Keenan and Gneezy, 2014) can account for how the audience members choose between the three candidates. Likewise, since decision makers cannot keep the money for themselves, differences in their tendencies to give can neither be of influence. ...
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We directly compare the influences of impact and responsibility considerations on giving behavior. In moral philosophy, utilitarianism emphasizes the importance of the former, whereas theories of equity and desert argue for the importance of the latter. Our data are from a television show where an audience of one hundred people divides ten thousand euros among three financially distressed candidates, and from independent raters who evaluated various attributes of the candidates and their financial predicaments. We find that the well-being benefit of a donation (“impact”) outweighs the degree to which the candidate had control over the cause of their situation (“responsibility”). Giving increases more with impact than it decreases with responsibility, and the contribution of impact to the fit of our regression models is approximately two-and-a-half times that of responsibility. Additionally, our analysis shows no evidence of discrimination on age, gender, or physical attractiveness.
... Empathy refers to experiencing other people's psychological feelings through self-projection. When individuals treat other people's emotional events as if they were their own emotional events, they produce a greater degree of emotional resonance response [47,[53][54][55][56], thereby inducing a higher level of emotional and motivational significance. Self-other overlap refers to the incorporation of other people's resources, perspectives, and traits into the self-concept [57]. ...
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This study employs event-related potential (ERP) to examine the impact of empathic concern on prosocial decision-making with costs in both gain and loss contexts. In this experiment, participants can choose between two types of lottery tickets and pay lottery money to help the target person gain more money or lose less money. The behavioral results showed that regardless of the context of the decision (financial loss or gain), participants tended to help individuals who had induced high empathic concern. ERP results show that compared to the low-empathic-concern condition, the high-empathic-concern condition induced greater P3 amplitude in the gain context. However, this change in P3 amplitude caused by empathic concern did not occur in the context of loss. These findings indicate that empathic concern has different psychological mechanisms that moderate prosocial behavior in gain and loss contexts.
... Taking donation behavior as an example, victim information in an individual (vs. group) frame increases people's giving (Friedrich and McGuire, 2010;Small et al., 2007). ...
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People tend to perceive the same information differently depending on whether it is expressed in an individual or a group frame. It has also been found that the individual (vs. group) frame of expression tends to lead to more charitable giving and greater tolerance of wealth inequality. However, little is known about whether the same resource allocation in social interactions elicits distinct responses depending on proposer type. Using the second-party punishment task, this study examined whether the same allocation from different proposers (individual vs. group) leads to differences in recipient behavior and the neural mechanisms. Behavioral results showed that reaction times were longer in the unfair (vs. fair) condition, and this difference was more pronounced when the proposer was the individual (vs. group). Neural results showed that proposer type (individual vs. group) influenced early automatic processing (indicated by AN1, P2, and central alpha band), middle processing (indicated by MFN and right frontal theta band), and late elaborative processing (indicated by P3 and parietal alpha band) of fairness in resource allocation. These results revealed more attentional resources were captured by the group proposer in the early stage of fairness processing, and more cognitive resources were consumed by processing group-proposed unfair allocations in the late stage, possibly because group proposers are less identifiable than individual proposers. The findings provide behavioral and neural evidence for the effects of “individual/group” framing leading to cognitive differences. They also deliver insights into social governance issues, such as punishing individual and/or group violations.
... Sadness seems to elicit actions to help others, perhaps to repair or regulate emotions (Small & Verrochi, 2009) and can even result in negative responses to appeals for action (cf. Small et al., 2007). ...
Chapter
We use the five level model of emotional leadership at work to the topic of sustainable development. For each level, we review the relevant literature, and provide a summary of the leadership challenge. In the final section we outline specific ways leaders can integrate emotion into the process they already use to lead transformational change.
... It may lead to resource concentration on a few visible beneficiaries, potentially causing an uneven resource distribution . Conversely, leveraging this effect could boost helping willingness and improve fundraising outcomes (Andreoni, 1990;Harbaugh et al., 2007;Small et al., 2007). Thus, indepth research into both the behavioral and neural mechanisms of this effect in online crowdfunding is essential. ...
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The phenomenon known as the “identifiable victim effect” describes how individuals tend to offer more assistance to victims they can identify with than to those who are vague or abstract. The neural underpinnings of this effect, however, remain elusive. Our study utilized functional magnetic resonance imaging to delve into how the “identifiable victim effect” influences prosocial decision‐making, considering different types of helping costs, across two distinct tasks. Participants were instructed to decide whether to help a victim with personal information shown (i.e., the identifiable victim) and an unidentifiable one by costing their money (task 1) or physical effort (task 2). Behaviorally, we observed a pronounced preference in both tasks for aiding identifiable victims over anonymous ones, highlighting a robust “identifiable victim effect.” On a neural level, this effect was associated with heightened activity in brain areas like the bilateral temporoparietal junction (TPJ) when participants confronted anonymous victims, potentially indicating a more intensive mentalizing process for less concrete victims. Additionally, we noted that the TPJ's influence on value judgment processes is mediated through its functional connectivity with the medial prefrontal cortex. These insights contribute significantly to our understanding of the psychological and neural dynamics underlying the identifiable victim effect.
... Reason 1: Just as there are several studies that show that active reflection typically has negative effects on an agent's epistemic states, there are also several studies that indicate that it typically has positive effects (e.g., Gagné and Smith (1962);DeWall, Baumeister, and Masicampo (2008) ;Small, Loewenstein, and Slovic (2007)). ...
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According to Rettler, there are three types of control that we should consider in relation to the legitimacy of doxastic blame: Intention-based, reason-based, and influence-based control. Rettler argues that among these, influence-based control is the only type of control that is necessary and sufficient for fulfilling the control con-dition required for legitimate doxastic blame. The aim of this short discussion paper is to critically assess Rettler’s view of doxastic con-trol. By doing so, I attempt to defend the reason-responsiveness view from Rettler’s criticism and cast doubt on whether influence-based control has a positive epistemic influence on beliefs.
... For instance, Nordgren and McDonnell (2011) found that people tend to assign higher blame to the agent when the victim is identifiable, as opposed to when the victim is unidentifiable (i.e., faceless). This effect is believed to result from greater sympathy towards personalised victims as compared to "statistical victims" (i.e., faceless masses), which in turn leads to a higher willingness to help identifiable victims (Small et al., 2007;Small & Loewenstein, 2003). In addition, a study by McManus et al. (2020) revealed intriguing dynamics. ...
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Doing harm is a moral violation, but helping a family member is morally obligatory. In this study, participants encountered this ethical dilemma through stories featuring their sibling (i.e., brother) as either the perpetrator or victim in various moral scenarios. Subsequently, they provided their moral judgments (i.e., moral acceptability and perceived transgression) and made decisions (i.e., willingness and difficulty to disclose what the agent did to the police) regarding the perpetrator. The manipulation of family membership was integrated into the moral scenarios, which were crafted based on whether the perpetrator had malicious intent and whether those intentions resulted in a harmful outcome (i.e., intentional harm, failed attempts to harm, accidental harm, and a harmless/baseline). While we initially expected that individuals would exhibit favoritism toward their brother when harmful intent or outcomes were absent, our findings revealed that both agent/victim identities (brother/stranger) and intent-outcome-based moral scenarios had an additive effect on both measures of moral judgment. This suggests that the family-favoring effect was observed across all intent-outcome scenarios, with a slightly more pronounced effect when the brother accidentally harmed a stranger compared to a stranger accidentally harming the brother. Regarding moral decisions, participants demonstrated a willingness to disclose what they witnessed regardless of their familial relationship with the agent or victim, but it was universally perceived as a difficult decision to make. Together, our results underscore the context-specific nature of moral judgments and decisions, emphasizing the significant impact of family members when they are involved as moral characters.
... Stories are told with a goal in mind, and in many cases the goal of storytelling is to evoke empathy. Stories that evoke empathy can be more impactful than facts and data [18]. In storytelling Ramayana, the empathy is usually used to teach morals [19]. ...
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... However, research within the broader pro-social domain highlights the risk with interventions aiming to increase impactful behavior by redirecting the focus to the outcome and at the same time ignoring the role of affective processes in motivation. 42 Thus, using information aimed at decreasing the influence of affect and emotion might reduce overall pro-environmental behavior. Suppose an individual believes that a certain behavior they adopt has a considerable impact on reducing emissions. ...
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We need unparalleled human behavioral changes to mitigate the effects of climate change. However, recent studies suggest that people are not good at identifying mitigative behaviors that are effective in reducing carbon emissions. Thus, even when there is an intention to engage in climate action, people are not necessarily making the most effective choices. This suggests that there is an impact of neglecting in evaluative judgments about mitigative behaviors. Here, using an online survey (N = 555), we show that people have a rather poor understanding of the mitigation potential of human behaviors, and both impact judgments and the likelihood of adoption of mitigative behaviors are largely influenced by emotional processes. These findings have potential implications for how to motivate impactful climate action in the future and point toward the importance to fully understand how affect and emotions influence impact judgments and pro-environmental behavior.
... We believe that this order of the question was a sensible solution to ensure that willingness to help was not influenced by other factors (ratings of cost and benefit), since this was our main dependent variable. This order of the questions is also consistent with work by Rubaltelli et al. (2020) that used a similar experimental task as well as to what is often done in the charitable giving literature when measuring variables that can influence donations, such as empathy or warm glow (see, for instance, Ritov, 2005a, 2005b;Small et al., 2007;Dickert et al., 2011;Rubaltelli and Agnoli, 2012). Further, to gather further support for our methodological decision, we collected additional data with a sample of adults, in which we counterbalanced the order of the questions (see Supplementary Materials). ...
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This dissertation examines the question, how moral sensitivity can be promoted with digital games. Moral sensitivity alerts people to ethical problems, i.e., actions that could conflict with ethical norms, standards, values, and principles, or which have the potential to affect others’ wellbeing or the pursuit of their legitimate interests. The dissertation pursues two major research objectives. First, there is a lack of a unified theory on the nature of moral sensitivity, which integrates normative demands with empirical findings from various streams of research. A multitude of different ideas currently coexist on the nature of moral sensitivity. Prior efforts to integrate theories have been purely normative, ignoring contradictory empirical evidence. Empirically informed theories, on the other hand, tend to ignore findings that point to other explanations. The lack of an adequate theory of moral sensitivity stands in the way of systematic efforts to promote moral sensitivity, including through digital games. To fill this gap, this dissertation aims at proposing an empirically founded theory of moral sensitivity. Secondly, there is a lack of empirically informed recommendations on the use of digital games for the promotion of moral sensitivity. The major weaknesses of previous attempts to provide guidance on the promotion of moral sensitivity via digital games consist in (1) a lack of clarity about the goal of moral-sensitivity training, (2) a lack of knowledge on suitable strategies to promote moral sensitivity in general, and (3) a failure to take empirical findings on the effects of digital games on the development moral sensitivity and its components into consideration. This dissertation aims at overcoming these three limitations of previous research in proposing a first evidence-based framework for the promotion of moral sensitivity with digital games. The first part of this dissertation investigates the nature of moral sensitivity from a normative perspective. A critical analysis of the need for moral sensitivity suggests that its function is to alert people to ethical problems accurately, affectively, automatically, and autonomously. This position is elaborated in confrontation with alternative ideas, e.g., the belief that controlled deliberation should be involved in noticing ethical problems. The following examination of ethical demands on a good moral sensitivity from the perspectives of four paradigms of normative ethics suggests that three abilities are required: (1) a recognitional moral sensitivity enables people to notice ethical problems due to a refined understanding of ethical concepts and corresponding attitudes; (2) a sympathetic moral sensitivity enables people to notice ethical problems due to a concern for those who are affected by their actions; (3) a critical moral sensitivity enables people to notice when their sympathetic and recognitional moral sensitivity could be undermined or biased due to factors like conflicts of interest or fatigue. The second part of this dissertation investigates the nature of moral sensitivity from an empirical perspective. Studies were analyzed and synthesized, which can legitimately claim to investigate moral sensitivity based on valid tests of people’s ability to notice ethical problems. The findings support and help to refine the idea that moral sensitivity bears a recognitional, a sympathetic, and a critical component. Moral expertise, i.e., refined knowledge of ethical concepts, is shown to be indispensable for the recognition of subtle ethical problems – particularly when people have competing objectives or face stress. Moral expertise, on its own, appears to be insufficient, however, if it is not combined with appropriate attitudes towards ethical problems, which motivate people to notice them in the first place, and which trigger appropriate emotional responses in people (e.g., guilt at the thought of ignoring someone’s will). Contrarily, many social and emotional competences that have been viewed as helping people to notice ethical problems, e.g., perspective-taking skills, do not appear to be reliable sources of moral sensitivity. What seems to make a big difference, however, is whether people hold sympathetic and unprejudiced attitudes towards the people who are affected by their actions, as a lack of sympathy and demeaning attitudes will inhibit people’s ability to notice when their actions may be immoral. Finally, the evidence culminates in showing how moral sensitivity can be undermined and biased in various ways, e.g., due to stronger empathic reactions to people who are immediately present. To cope with various sources of bias, people also need to cultivate an automatized ability to recognize when their moral perception could be biased. The final third of this dissertation concentrates on the question, how digital games can be used to promote moral sensitivity. Building on the unified theory of moral sensitivity that was established in the prior parts, strategies were identified that are generally effective in promoting moral sensitivity. The most effective approach appears to be experiential learning in combination with feedback on people’s ability to notice ethical problems. Digital games are found to provide an optimal environment for the provision of this kind of training, because they can motivate learners to engage with ethical problems in an interactive manner, provide appropriate feedback, and do all of this in a safe context. Twenty-four game mechanisms are explored in view of their potential to promote recognitional, sympathetic, and critical moral sensitivity, whereby the findings of more than 80 empirical studies are synthesized. Several game mechanisms are found to be highly promising, while there is a lack of empirical information on others, and some mechanisms appear to bear risks, e.g., the use of egoistic temptations. A critical discussion of different ways in dealing with the risk of malicious play, i.e., the performance of unethical actions in games, suggests that digital games could undermine moral sensitivity, if they provide players with reasons to justify malicious play. On the other hand, when bad choices and malicious play are confronted with negative feedback and bad consequences, the possibility to make ethical mistakes appears to be legitimate and highly useful.
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Distinctions have been proposed between systems of reasoning for centuries. This article distills properties shared by many of these distinctions and characterizes the resulting systems in light of recent findings and theoretical developments. One system is associative because its computations reflect similarity structure and relations of temporal contiguity. The other is "rule based" because it operates on symbolic structures that have logical content and variables and because its computations have the properties that are normally assigned to rules. The systems serve complementary functions and can simultaneously generate different solutions to a reasoning problem. The rule-based system can suppress the associative system but not completely inhibit it. The article reviews evidence in favor of the distinction and its characterization.
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The Muskat problem models the evolution of the interface given by two different fluids in porous media. The Rayleigh-Taylor condition is natural to reach the linear stability of the Muskat problem. We show that the Rayleigh-Taylor condition may hold initially but break down in finite time. As a consequence of the method used, we prove the existence of water waves turning.
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The Muskat problem models the dynamics of the interface between two incompressible immiscible fluids with different constant densities. In this work we prove three results. First we prove an L2(R)L^2(\R) maximum principle, in the form of a new ``log'' conservation law \eqref{ln} which is satisfied by the equation \eqref{ec1d} for the interface. Our second result is a proof of global existence of Lipschitz continuous solutions for initial data that satisfy f0L<\|f_0\|_{L^\infty}<\infty and xf0L<1\|\partial_x f_0\|_{L^\infty}<1. We take advantage of the fact that the bound xf0L<1\|\partial_x f_0\|_{L^\infty}<1 is propagated by solutions, which grants strong compactness properties in comparison to the log conservation law. Lastly, we prove a global existence result for unique strong solutions if the initial data is smaller than an explicitly computable constant, for instance f11/5\| f\|_1 \le 1/5. Previous results of this sort used a small constant ϵ1\epsilon \ll1 which was not explicit. Comment: 31 pages
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We consider in this paper the Muskat problem in a periodic geometry and incorporate capillary as well as gravity effects in the modelling. The problem re-writes as an abstract evolution equation and we use this property to prove well-posedness of the problem and to establish exponential stability of some flat equilibrium. Using bifurcation theory we also find finger shaped steady-states which are all unstable.
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In this work we consider weak solutions of the incompressible 2-D porous media equation. By using the approach of De Lellis-Sz\'ekelyhidi we prove non-uniqueness for solutions in LL^\infty in space and time.
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This article examines how consumer decision making is influenced by automatically evoked task-induced affect and by cognitions that are generated in a more controlled manner on exposure to alternatives in a choice task. Across two experiments respondents chose between two alternatives: one (chocolate cake) associated with more intense positive affect but less favorable cognitions, compared to a second (fruit salad) associated with less favorable affect but more favorable cognitions. Findings from the two experiments suggest that if processing resources are limited, spontaneously evoked affective reactions rather than cognitions tend to have a greater impact on choice. As a result, the consumer is more likely to choose the alternative that is superior on the affective dimension but inferior on the cognitive dimension (e.g., chocolate cake). In contrast, when the availability of processing resources is high, cognitions related to the consequences of choosing the alternatives tend to have a bigger impact on choice compared to when the availability of these resources is low. As a result, the consumer is more likely to choose the alternative that is inferior on the affective dimension but superior on the cognitive dimension (e.g., fruit salad). The moderating roles of the mode of presentation of the alternatives and of a personality variable related to impulsivity are also reported. Copyright 1999 by the University of Chicago.
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Consumers often face emotion-laden choices involving conflicting goals of personal importance (e.g., safety). Research suggests that consumers cope with the negative emotion associated with these choices by avoiding certain behaviors, in particular attribute trade-off making. This research investigates a factor that moderates these coping effects. Four experiments show that simple cognitive load can make consumers less averse to making attribute trade-offs. This research demonstrates, counterintuitively, that a reduction of cognitive resources through increased load can result in more normative decision behavior. Load apparently disinhibits trade-off making by disrupting consumers' abilities to consider relevant self goal information and the negative emotional consequences of trading off something of personal importance, thereby reducing consumers' need to cope.
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Costly life-saving interventions can often be described not only in terms of the number of lives that may be saved but also in terms of the proportion of lives saved out of some total number at risk. In a phenomenon that has been referred to as psychophysical numbing (PN), Fetherstonhaugh, Slovic, Johnson, and Friedrich (1997) found that participants rated an intervention saving a fixed number of lives to be less worth investing in when more total lives were at risk (i.e., when saved lives represented a smaller proportion of the total threat or problem). In two new experiments, life-valuation correlates of PN responding, as well as manipulations of death salience, accountability, and economics focus, were explored in the context of students’ willingness to support mandatory antilock brake requirements for new cars. PN responding was pervasive, but non-PN responders were clearly distinguished by the greater overall value they placed on saving lives. Salience and accountability manipulations did not debias judgments but did tend to rule out low-effort processing as an explanation for these quantity confusions. An emphasis on economic considerations was consistently related to greater PN responding.
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In this paper the Muskat problem which describes a two-phase flow of two fluids, for example, oil and water, in porous media is discussed. The problem involves in seeking two time-dependent harmonic functions u1(x,y,t) and u2(x,y,t) in oil and water regions, respectively, and the interface between oil and water, i.e., the free boundary Γ:y=ρ(x,t), such that on the free boundary u1=u2,Vn=−k1∂u1∂n=−k2∂u2∂n, where n the unit normal vector on the free boundary toward oil region, Vn is the normal velocity of the free boundary Γ, k1 and k2 are positive constants satisfying k1>k2. We prove the existence of classical solution globally in time under some reasonable assumptions. The argument developed in this paper can be used in any multidimensional case.
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The authors analyse an equation governing the motion of an interface between two fluids in a pressure field. In two dimensions, the interface is described by a conformal mapping which is analytic in the exterior of the unit disc. This mapping obeys a non-local nonlinear equation. When there is no pumping at infinity, there is conservation of area and contraction of the length of the interface. They prove global in time existence for small analytic perturbations of the circle as well as nonlinear asymptotic stability of the steady circular solution. The same method yields well-posedness of the Cauchy problem in the presence of pumping.
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We draw out implications of the identifiable victim effect - the greater sympathy shown toward identifiable than statistical victims - for public finance. We first review research showing (1) that people respond more strongly to identifiable than statistical victims even when identification provides absolutely no information about the victims, (2) that the identifiable victim effect is a special case of a more general tendency to react more strongly to identifiable others whether they evoke sympathy or other emotions, and (3) that identifiability influences behavior via the emotional reactions it evokes. Next, we discuss the normative status of the effect, noting that, contrary to the usual assumption that people overreact to identifiable victims, identifiability can shift people's responses in a normatively desirable direction if people are otherwise insufficiently sympathetic toward statistical victims. Finally, we examine implications of the identifiable victim effect for public finance. We show that the identifiable victim effect can influence the popularity of different policies, for example, naturally favoring hidden taxes over those whose incidence is more easily assessed, since a hidden tax has no identifiable victims. Identifiable other effects also influence public discourse, with much of the debate about government spending and taxation being driven by vivid exemplars - iconic victims and perpetrators - rather than any rational calculation of costs and benefits.
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The Muskat, or Muskat-Leibenzon, problem describes the evolution of the interface between two immiscible fluids in a porous medium or Hele-Shaw cell under applied pressure gradients or fluid injection/extraction. In contrast to the Hele-Shaw problem (the one-phase version of the Muskat problem), there are few nontrivial exact solutions or analytic results for the Muskat problem. For the stable, forward Muskat problem, in which the higher-viscosity fluid expands into the lower-viscosity fluid, we show global-in-time existence for initial data that is a small perturbation of a flat interface. The initial data in this result may contain weak (e.g., curvature) singularities. For the unstable, backward problem, in which the higher-viscosity fluid contracts, we construct singular solutions that start off with smooth initial data but develop a point of infinite curvature at finite time. © 2004 Wiley Periodicals, Inc.
Article
Prior research has confirmed Thomas Schelling's observation that people are more sympathetic and hence generous toward specific identified victims than toward “statistical” victims who are yet to be identified. In the study presented in this article we demonstrate an equivalent effect for punitiveness. We find that people are more punitive toward identified wrongdoers than toward equivalent, but unidentified, wrongdoers, even when identifying the wrongdoer conveys no meaningful information about him or her. To account for the effect of identifiability on both generosity and punitiveness, we propose that affective reactions of any type are stronger toward an identified than toward an unidentified target. Consistent with such an account, the effect of identifiability on punishing behavior was mediated by self-reported anger. Copyright © 2005 John Wiley & Sons, Ltd.
Article
People's greater willingness to help identified victims, relative to non-identified ones, was examined by varying the singularity of the victim (single vs. a group of eight individuals), and the availability of individually identifying information (the main difference being the inclusion of a picture in the “identified” versions). Results support the proposal that the “identified victim” effect is largely restricted to situations with a single victim: the identified single victim elicited considerably more contributions than the non-identified single victim, while the identification of the individual group members had essentially no effect on willingness to contribute. Participants also report experiencing distress when the victim is single and identified more than in any other condition. Hence, the emotional reaction to the victims appears to be a major source of the effect. Copyright © 2005 John Wiley & Sons, Ltd.
Article
The problem of the encroachment of water into an oil sand is formulated as a new type of potential problem, namely, that of finding potential distributions in two regions of different ``constants'' (``conductivities'') which are separated by a surface, each point of which has a velocity proportional to the vector gradient of the potential at the point, and such that the area swept out by the moving interface assumes the ``constant'' appropriate to that of the encroaching side of the interface. The cases of strictly linear, radial and spherical systems, in which the shapes of the interfaces are evident from symmetry requirements, are solved in detail and discussed graphically. The zeroth approximation to the general problem which gives the history of a line of fluid particles in a homogeneous system is also treated in detail. Analytical and graphical solutions are presented for (1) systems with elliptical boundaries, (2) an infinite linear source driving fluid into an isolated sink, and (3) the history of a ring of fluid particles travelling from a source to a sink. The relation of the analytical results to the practical problems of the encroachment of water into oil bearing sands is discussed both for the solutions of the general problem and those of the zeroth approximation.
Article
People’s greater willingness to help identified victims, relative to non-identified ones, was examined by eliciting real contributions to targets varying in singularity (a single individual vs. a group of several individuals), and the availability of individually identifying information (the main difference being the inclusion of a picture in the “identified” versions). Results of the first and second experiments support the proposal that for identified victims, contributions for a single victim exceed contributions for a group when these are judged separately, but preference reverses when one has to choose between contributing to the single individual and contributing to the group. In a third experiment, ratings of emotional response were elicited in addition to willingness to contribute judgments. Results suggest that the greater contribution to a single victim relative to the group stems from intensified emotions evoked by a single identified victim rather than from emotions evoked by identified victims in general.
Article
This paper introduces a theoretical framework that describes the importance of affect in guiding judgments and decisions. As used here, “affect” means the specific quality of “goodness” or “badness” (i) experienced as a feeling state (with or without consciousness) and (ii) demarcating a positive or negative quality of a stimulus. Affective responses occur rapidly and automatically—note how quickly you sense the feelings associated with the stimulus word “treasure” or the word “hate”. We argue that reliance on such feelings can be characterized as “the affect heuristic”. In this paper we trace the development of the affect heuristic across a variety of research paths followed by ourselves and many others. We also discuss some of the important practical implications resulting from ways that this heuristic impacts our daily lives.
Article
It was shown recently by Cordoba, Faraco and Gancedo that the 2D porous media equation admits weak solutions with compact support in time. The proof, based on the convex integration framework, uses ideas from the theory of laminates, in particular T4 configurations. In this note we calculate the explicit relaxation of IPM, thus avoiding T4 configurations. We then use this to construct weak solutions to the unstable interface problem (the Muskat problem), as a byproduct shedding new light on the gradient flow approach introduced by Otto.
Article
We show that a general class of active scalar equations, including porous media and certain magnetostrophic turbulence models, admit non-unique weak solutions in the class of bounded functions. The proof is based upon the method of convex integration recently implemented for equations of fluid dynamics in [2,3]. Comment: 19 pages
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Incluye bibliografía e índice
Article
We define mental contamination as the process whereby a person has an unwanted response because of mental processing that is unconscious or uncontrollable. This type of bias is distinguishable from the failure to know or apply normative rules of inference and can be further divided into the unwanted consequences of automatic processing and source confusion, which is the confusion of 2 or more causes of a response. Mental contamination is difficult to avoid because it results from both fundamental properties of human cognition (e.g., a lack of awareness of mental processes) and faulty lay beliefs about the mind (e.g., incorrect theories about mental biases). People's lay beliefs determine the steps they take (or fail to take) to correct their judgments and thus are an important but neglected source of biased responses. Strategies for avoiding contamination, such as controlling one's exposure to biasing information, are discussed.
Article
Cognitive-experiential self-theory integrates the cognitive and the psychodynamic unconscious by assuming the existence of two parallel, interacting modes of information processing: a rational system and an emotionally driven experiential system. Support for the theory is provided by the convergence of a wide variety of theoretical positions on two similar processing modes; by real-life phenomena--such as conflicts between the heart and the head; the appeal of concrete, imagistic, and narrative representations; superstitious thinking; and the ubiquity of religion throughout recorded history--and by laboratory research, including the prediction of new phenomena in heuristic reasoning.
Article
Although it has been claimed that people care more about identifiable than statistical victims, demonstrating this "identifiable victim effect" has proven difficult because identification usually provides information about a victim, and people may respond to the information rather than to identification per se. We show that a very weak form of identifiability--determining the victim without providing any personalizing information--increases caring. In the first, laboratory study, subjects were more willing to compensate others who lost money when the losers had already been determined than when they were about to be. In the second, field study, people contributed more to a charity when their contributions would benefit a family that had already been selected from a list than when told that the family would be selected from the same list. Copyright 2003 by Kluwer Academic Publishers
Article
Subjects were less willing to pay for government medical insurance for diseases when the number of people who could not be cured was higher, holding constant the number who could be cured. In a second experiment, willingness to pay (from a hypothetical government windfall) for risk reduction was unaffected by whether the risk was described in terms of percentage or number of lives saved, even though subjects knew that the risks in question differed in prevalence. These results are consistent with the findings of Fetherstonhaugh et al., Jenni and Loewenstein, and others. I suggest that these results can be explained in terms of a general tendency to confuse proportions and differences, a confusion that is analogous to other confusions of quantitative dimensions in children, adults, the news media, and perhaps even the epidemiological literature. Copyright 1997 by Kluwer Academic Publishers
Article
It is widely believed that people are willing to expend greater resources to save the lives of identified victims than to save equal numbers of unidentified or statistical victims. There are many possible causes of this disparity which have not been enumerated previously or tested empirically. We discuss four possible causes of the "identifiable victim effect" and present the results of two studies which indicate that the most important cause of the disparity in treatment of identifiable and statistical lives is that, for identifiable victims, a high proportion of those at risk can be saved. Copyright 1997 by Kluwer Academic Publishers
Every dog has its day—but at what price? The Register Guard, Reflective and impulsive determi-nants of social behavior
  • J Song
  • a
  • F Strack
  • R Deutsch
Song, J. (2002, April 26). Every dog has its day—but at what price? The Register Guard, 15A. Strack, F., & Deutsch, R. (2004). Reflective and impulsive determi-nants of social behavior. Personality and Social Psychology Review, 8(3), 220–247.
Every dog has its day-but at what price? The Register Guard
  • J Song
Song, J. (2002, April 26). Every dog has its day—but at what price? The Register Guard, 15A.
The affect heuristic Heuristics and biases: The psychology of intuitive judgment
  • P Slovic
  • M Finucane
  • E R Peters
  • D G Macgregor
Slovic, P., Finucane, M., Peters, E. R., & MacGregor, D. G. (2002). The affect heuristic. In T. Gilovich, D. Griffin, & D. Kahneman (Eds.), Heuristics and biases: The psychology of intuitive judgment (pp. 397–420). New York: Cambridge University Press.