Social discounting and delay discounting

Social discounting was measured as the amount of money a participant was willing to forgo to give a fixed amount (usually $75) to another person. In the first experiment, amount forgone was a hyperbolic function of the social distance between the giver and receiver. In the second experiment, degree of social discounting was an increasing function of reward magnitude whereas degree of delay discounting was a decreasing function of reward magnitude. In the third experiment, the shape of the function relating delayed rewards to equally valued immediate rewards for another person was predicted from individual delay and social discount functions. All in all, the studies show that the social discount function, like delay and probability discount functions, is hyperbolic in form. Copyright © 2007 John Wiley & Sons, Ltd.     

Delay, Probability, and Social Discounting in A Public Goods Game

A human social discount function measures the value to a person of a reward to another person at a given social distance. Just as delay discounting is a hyperbolic function of delay, and probability discounting is a hyperbolic function of odds-against, social discounting is a hyperbolic function of social distance. Experiment 1 obtained individual social, delay, and probability discount functions for a hypothetical $75 reward; participants also indicated how much of an initial $100 endowment they would contribute to a common investment in a public good. Steepness of discounting correlated, across participants, among all three discount dimensions. However, only social and probability discounting were correlated with the public-good contribution; high public-good contributors were more altruistic and also less risk averse than low contributors. Experiment 2 obtained social discount functions with hypothetical $75 rewards and delay discount functions with hypothetical $1,000 rewards, as well as public-good contributions. The results replicated those of Experiment 1; steepness of the two forms of discounting correlated with each other across participants but only social discounting correlated with the public-good contribution. Most participants in Experiment 2 predicted that the average contribution would be lower than their own contribution.     

Axiomatizing geometric constructions

In this survey paper, we present several results linking quantifier-free axiomatizations of various Euclidean and hyperbolic geometries in languages without relation symbols to geometric constructibility theorems. Several fragments of Euclidean and hyperbolic geometries turn out to be naturally occurring only when we ask for the universal theory of the standard plane (Euclidean or hyperbolic), that can be expressed in a certain language containing only operation symbols standing for certain geometric constructions.     

Hyperbolic value addition and general models of animal choice

Three mathematical models of choice--the contextual-choice model (R. Grace, 1994), delay-reduction theory (N. Squires & E. Fantino, 1971), and a new model called the hyperbolic value-added model--were compared in their ability to predict the results from a wide variety of experiments with animal subjects. When supplied with 2 or 3 free parameters, all 3 models made fairly accurate predictions for a large set of experiments that used concurrent-chain procedures. One advantage of the hyperbolic value-added model is that it is derived from a simpler model that makes accurate predictions for many experiments using discrete-trial adjusting-delay procedures. Some results favor the hyperbolic value-added model and delay-reduction theory over the contextual-choice model, but more data are needed from choice situations for which the models make distinctly different predictions.     

Charity Begins at Home: Cultural Differences in Social Discounting and Generosity

People often consider how their actions influence others when making decisions. However, we are not equally generous to everyone alike. Our willingness to share resources declines as a function of social distance between the decision maker and the recipient. This function is likely to be influenced by culture, but research on behavioral decision making is still lacking empirical evidence. In Western societies, individuals generally perceive themselves as autonomous and independent from others, whereas the distinction between self and close others is less sharply defined by Eastern individuals where relationships and group membership are more centralized. Therefore, the social discount function should reflect this difference in the distinction of self and others by a reduced decline in generosity over close social distances. A social decision‐making task was adapted to the intercultural context, and data were collected in Germany and China. For seven different social distances, we estimated how much money German and Chinese subjects were willing to forego to give a certain reward to another person. A hyperbolic model was fitted to the data. We found that other‐regarding generosity declines as a function of social distance independent of cultural identity. However, German subjects showed a marked drop in generosity across close social distances, which was significantly less pronounced in Chinese participants. Copyright © 2013 John Wiley & Sons, Ltd.     

The Simplest Axiom System for Hyperbolic Geometry Revisited,Again

Dependencies are identified in two recently proposed first-order axiom systems for plane hyperbolic geometry. Since the dependencies do not specifically concern hyperbolic geometry, our results yield two simpler axiom systems for absolute geometry.     

Obedience and Believing a Person

I argue that there is a mutually illuminating parallel between the concept of obedience and the concept of believing a person. Just as both believing what a person says and believing what a person says for the reason that the person says it are insufficient for believing the person, so acting as a person demands and acting as a person demands for the reason that the person demands it are insufficient for obeying the person. Unlike the concept of believing a person, however, the concept of obedience has two distinct senses, one applying to coerced action and one applying to non‐coerced action based on authoritative directives. While the former sense of obedience has no theoretical analogue, the latter sense of obedience can be understood as the practical analogue of the theoretical case of believing a person, making room for a deep parallel between believing and acting on authority.     

Concave utility,transaction costs,and risk in measuring discounting of delayed rewards

Research has consistently found that the decline in the present values of delayed rewards as delay increases is better fit by hyperbolic than by exponential delay-discounting functions. However, concave utility, transaction costs, and risk each could produce hyperbolic-looking data, even when the underlying discounting function is exponential. In Experiments 1 (N = 45) and 2 (N = 103), participants placed bids indicating their present values of real future monetary rewards in computer-based 2nd-price auctions. Both experiments suggest that utility is not sufficiently concave to account for the superior fit of hyperbolic functions. Experiment 2 provided no evidence that the effects of transaction costs and risk are large enough to account for the superior fit of hyperbolic functions.     

Did Jesus Discover Forgiveness?

This essay explores Hannah Arendt's claim that Jesus was the “discoverer” of forgiveness. It assesses Charles Griswold's view that person‐to‐person forgiveness is in evidence in Greek culture and practice before Jesus. The essay refines Griswold's view and suggests that person‐to‐person forgiveness is a cultural universal. The essay makes observations about the significance of the different words that denote person‐to‐person forgiveness; it also explores the implications of reading the New Testament writings on person‐to‐person forgiveness in the chronological order in which they were written. From a close reading of the early New Testament documents, the essay makes two suggestions about the Western tradition of forgiveness. First, it suggests that Paul the apostle is the first to identify person‐to‐person forgiveness as a moral virtue. Second, it suggests that in the Synoptic tradition, Jesus is the first to identify person‐to‐person forgiveness as a discrete category of behavior distinct, for example, from pardoning, excusing, waiving, or ignoring the wrongs of others.     

Social reactions to adult crying: the help-soliciting function of tears

The authors investigated how people believe they respond to crying individuals. Participants (N = 530) read 6 vignettes describing situations in which they encountered a person who either cried or did not cry. Participants reported they would give more emotional support to and express less negative affect toward a crying person than a noncrying person. However, regression analyses revealed that participants judged a crying person less positively than a noncrying person and felt more negative feelings in the presence of a crying person than a noncrying person. The valence of the situation strongly moderated these reactions. Overall, results support the theory that crying is an attachment behavior designed to elicit help from others.     

Dream rebound: the return of suppressed thoughts in dreams

Abstract— People spent 5 min before sleep at home writing their stream of thought as they suppressed thoughts of a target person, thought of the person, or wrote freely after mentioning the person. These presleep references generally prompted people to report increased dreaming about the person. However, suppression instructions were particularly likely to have this influence, increasing dreaming about the person as measured both by participants' self-ratings of their dreams and by raters' coding of mentions of the person in written dream reports. This effect was observed regardless of emotional attraction to the person.     

Knowing Other People: A Second‐Person Framework

What does it mean to know another person, and how is such knowledge different from other kinds of knowledge? These questions constitute an important part of what I call ‘second‐person epistemology’ – the study of how we know other people. I claim that knowledge of other people is not only central to our everyday lives, but it is a kind of knowledge that is unlike other kinds of knowledge. In general, I will argue that second‐person knowledge arises from repeated interactions with another person, and that it also requires employment of certain cognitive abilities and a unique kind of second‐order knowledge. This paper provides the framework for a second‐person epistemology by examining some of our ordinary claims about what it means to know another person. I describe four conditions that typically characterize knowing another person. Then I describe the psychological grounds of knowing a person. Finally, I conclude with some thoughts about the unique symmetries of second person knowledge and the role of such knowledge in our broader epistemological endeavours.     

The Role of Temporal and Spatial Information Cues in Locating Missing Persons

Prospective person memory refers to the search for a missing or wanted person. Performance on prospective person memory tasks has been found to be poor in field‐based experiments. Prior research suggests that the size of the search space may influence success on prospective person memory tasks. In the present research, we gave participants randomly assigned temporal and spatial cues about a mock missing person's whereabouts. Participants were offered a monetary reward for accurately reporting seeing the missing person. Participants who were told the missing person would appear in the building, where they were, had higher expectations of encountering the missing person and made more sightings than participants told the missing person would appear on the university campus. Expectations of encounter predicted participants' intent to look for the missing person, which predicted actual looking behavior, which ultimately predicted accurate sightings.Copyright © 2016 John Wiley & Sons, Ltd.     

Sun and water: on a modulus-based measurement of happiness

Most happiness researchers use semantic differential or Likert scales to assess happiness. Such conventionally used scales are susceptible to scale renorming (interpretation of scales differently in different contexts) and can produce a specious relativism effect (e.g., rating a low-income person happier than a high-income person in situations where the low-income person is not happier). Building on related psychophysical measurements, the authors propose a simple, survey-friendly, modulus-based scale of happiness and show that it is less susceptible to specious relativism than conventional rating scales but can still catch genuine relativism (e.g., rating a low-income person to be happier than a high-income person in situations where the low-income person is indeed happier).     

The Simplest Axiom System for Plane Hyperbolic Geometry

We provide a quantifier-free axiom system for plane hyperbolic geometry in a language containing only absolute geometrically meaningful ternary operations (in the sense that they have the same interpretation in Euclidean geometry as well). Each axiom contains at most 4 variables. It is known that there is no axiom system for plane hyperbolic consisting of only prenex 3-variable axioms. Changing one of the axioms, one obtains an axiom system for plane Euclidean geometry, expressed in the same language, all of whose axioms are also at most 4-variable universal sentences. We also provide an axiom system for plane hyperbolic geometry in Tarski's language L _B which might be the simplest possible one in that language.     

Using logistic regression to estimate delay-discounting functions.

The monetary choice questionnaire (MCQ) and similar computer tasks ask preference questions in order to ascertain indifference, the perceived equivalence of immediate versus larger delayed rewards. Indifference data are then fitted with a hyperbolic function, summarizing the decline in perceived value with delay time. We present a fitting method that estimates the hyperbolic parameter k directly from survey responses. Binary preferences are modeled as a function of time (X2) and a transformed reward ratio (X1), yielding logistic regression coefficients beta 2 and beta 1. The hyperbolic parameter emerges as k = beta 2/beta 1, where the logistic predicted p = .5 (the definition of indifference). The MCQ was administered to 1,073 adolescents and was scored using both standard and logistic methods. The means for In(k) were similar (standard, -4.53; logistic, -4.51), and the results were highly correlated (rho = .973). Simulated MCQ data showed that k was unbiased, except where beta 1 > or = -1, indicating a vague survey response. Jackknife standard errors provided excellent coverage.     

Identifying between‐person and within‐person factors to enhance understanding of observed score profiles

This study aims to reparameterize ordinary factors into between‐ and within‐person factor effects and utilize an array of the within‐person factor loadings as a latent profile which encapsulates all score responses of individuals in a population. To illustrate, the Woodcock–Johnson III (WJ‐III) tests of cognitive abilities were analysed and one between‐ and two within‐person factors were identified. The scoring patterns of individuals in the WJ‐III sample were interpreted according to the within‐person factor patterns. Regression analyses were performed to examine how much the within‐person factors accounted for the person scoring patterns and criterion variables. Finally, the importance and applications of the between‐ and within‐person factors are discussed.     

Learning about what others were doing: verb aspect and attributions of mundane and criminal intent for past actions

Scientists have long been interested in understanding how language shapes the way people relate to others, yet it remains unclear how formal aspects of language influence person perception. We tested whether the attribution of intentionality to a person is influenced by whether the person's behaviors are described as what the person was doing or as what the person did (imperfective vs. perfective aspect). In three experiments, participants who read what a person was doing showed enhanced accessibility of intention-related concepts and attributed more intentionality to the person, compared with participants who read what the person did. This effect of the imperfective aspect was mediated by a more detailed set of imagined actions from which to infer the person's intentions and was found for both mundane and criminal behaviors. Understanding the possible intentions of others is fundamental to social interaction, and our findings show that verb aspect can profoundly influence this process.