Elementor #664

Yen-Sheng Chianga,⁎, Yung-Fong Hsub

a Institute of Sociology, Academia Sinica, Taiwan, ROC
b Department of Psychology, National Taiwan University, Taiwan, ROC

T

ARTICLE INFO

Keywords:

Altruistic giving Bystander effect Congestible altruism Dictator game Inequity-aversion model

1. Introduction

ABSTRACT

The extent of altruistic giving is influenced by the numbers of givers and recipients available in a group. Two independent lines of research have addressed the effect. On the one hand, research on the bystander effect shows that a person gives less when givers outnumber recipients than if they are equal in number. On the other, studies of congestible altruism have found that a person gives more when recipients outnumber givers than if they are equal in size. An interesting question is whether giving decreases at a different rate when givers outnumber recipients than it increases the other way around. Answering the question helps illuminate whether the two effects of col- lective giving, which the literature has discussed separately, are governed by the same rule. We conducted a multi-person dictator game experiment to investigate people’s giving behavior in different group sizes of givers and recipients. We found that giving decreases more rapidly when givers outnumber recipients than it increases the other way around. A behavioral economics model is proposed to show how people’s belief about the selfishness of other givers can account for the asymmetry of the two effects.

Examples of altruistic giving, such as donations to charity organization and disaster relief, are ubiquitous in daily life. Although altruism is part of human nature, it varies across individuals and social contexts. In particular, humans’ altruism is influenced by two numeric facts: How many other givers are available? And how many people need help? The first number—the number of givers—is captured by a well-documented phenomenon in social psychology called the “bystander effect” (Darley & Latane, 1968; Fischer et al., 2011), according to which people give less when there are more givers available. The second number—the number of recipients—is addressed in studies of “congestible altruism” (Andreoni, 2007), which indicate that people give more as the number of recipients increases.

The two effects of collective giving can be pieced together by comparing the number of givers (g) with the number of recipients (r). The bystander effect argues that giving is lower when g > r than when g = r. Congestible altruism, on the other hand, suggests giving is higher when g < r than when g = r. Put together, the two effects suggest that giving decreases as the ratio of g/r increases. An interesting question is: How does giving change with respect to g/r? Does it decrease more or less rapidly in the bystander effect (g/r > 1) than it increases in the congestible altruism effect (g/r < 1)? The question touches on a fundamental inquiry of whether

⁎ Corresponding author.
E-mail address: chiangys@gate.sinica.edu.tw (Y.-S. Chiang).

https://doi.org/10.1016/j.joep.2019.06.001

Received 4 July 2018; Received in revised form 2 June 2019; Accepted 4 June 2019

Available online 05 June 2019
0167-4870/ © 2019 Published by Elsevier B.V.

Y.-S. Chiang and Y.-F. Hsu Journal of Economic Psychology 73 (2019) 152–160

the bystander effect and congestible altruism, while discussed separately in the literature, are two sides of the same coin governed by the same behavioral rule.

The (a)symmetry of the bystander effect and congestible altruism is worth studying for both theoretical and practical reasons. Psychologists have shown that a positive and a negative change of a person’s status could impose different effects on his/her be- havior. For example, people react differently to economic losses and gains (Kahneman & Tversky, 1984, 1992); rewards and pun- ishments have different effects on incentivizing people’s behavior (Balliet, Mulder, & Van Lange, 2011); and a promotion and a demotion of social status have different effects on influencing people’s prosocial behavior (Charness & Villeval, 2017; Clark, Masclet, & Villeval, 2010). These examples show that an identical magnitude of an effect could lead to asymmetrical outcomes when the effect is maneuvered to one direction than another. In fact, research on the asymmetry of human behavior has inspired the advancement of the behavioral and decision sciences over the past decades (Kahneman, 2002). Sharing a similar interest, here we investigate whether human altruism has an asymmetric feature when givers outnumber recipients versus the other way around. The investigation helps enhance our understanding of the mentalities that underlie the altruistic behavior of economically advantaged people (givers) when they are a majority versus a minority in a group.

The (a)symmetry of altruistic giving also has practical implications for organizational management and philanthropic cam- paigning. Organizational leaders are constantly facing the challenge of how to allocate resources to group members to maximize work performance and minimize distributional inequity. Understanding how givers—those endowed with resources in the group—perform when they are a majority versus a minority in the group would make it possible to provide useful suggestions to leaders with respect to the allocation of power and resources to colleagues and subordinates. Similarly, in philanthropic organizations, campaign orga- nizers must consider how to raise funds for the needy. As donors’ motivation for giving is influenced by how much their donation would make a difference, which is a function of the number of donors and recipients that the donor perceives, understanding how donors behave in different group sizes of givers and recipients available would help fundraisers design campaigns in a more effi- cacious manner.

To assess the (a)symmetry between the bystander effect and congestible altruism, we manipulate the number of givers and the number of recipients in a multi-person dictator game experiment (Study 1). Our study shows that giving drops more rapidly when givers outnumber recipients (the bystander effect) than it increases the other way around (the congestible altruism effect). To explain the asymmetry of the two effects, we modify Fehr and Schmidt’s (1999) inequity-aversion model, originally a one-giver-versus-one- recipient model, to a multi-person context (Study 2). We show that a giver’s belief about other givers’ selfishness can explain the asymmetry: When a giver believes that more (less) than half of other givers are less generous than him/her, giving drops more (less) rapidly in the bystander effect than it increases in congestible altruism.

2. Literature

There are at least three different lines of research in psychology and economics addressing how the numbers of givers and recipients influence givers’ altruism. One line of research compared what if the giver is alone versus when there are multiple givers around. Another stream of research studied the condition of one recipient compared to the presence of multiple recipients. Finally, there is a third line research arguing that people’s giving behavior may not be sensitive to the quantities of recipients.1 In this paper, we focus on the comparison of the magnitude of the former two effects. We discuss how the setting of our study is different from the final line of research in the concluding section.

2.1. The bystander effect

In social psychology, the bystander effect is one of the most well-noted characteristics of helping behavior (Fischer et al., 2011). It argues that people’s motivation to help is contingent on the availability of other helpers. The bystander effect can be explained from multiple perspectives. First, researchers argue that uncertainty about their own competency and qualifications may undermine people’s willingness to help (Darley & Latane, 1970). As the number of helpers increases, people become more likely to posit that there are more capable others available to help the needy. Second, helping could be construed as collective action, and people may delay their efforts until enough helpers take action (Latané & Dabbs, 1975; MacCoun, 2012). The threshold number of active helpers to motivate a person’s action could be a function of group size. People may raise their thresholds when they see more helpers are available. Third, the presence of other helpers works to release a person’s moral responsibility (Darley & Latane, 1968; Falk & Szech, 2013). Thus, the more helpers available, the more the responsibility is shared and thus the less likely people act to help. Furthermore, scholars argued that the reduction of responsibility is accelerating as the number of helpers increases. For example, Cryder and Loewenstein (2012) contended that “although we would expect the strongest increase when only one person is responsible, we would also expect greater helping when two people are responsible instead of three, for example, or when three are responsible instead of four” (Cryder & Loewenstein, 2012, p. 443).

While the bystander effect can be explained by different theories, it is not easy to tell them apart through observations of real life cases of altruistic giving. In this regard, behavioral game experiments can be a promising method to distinguish the multiple motives that underlie people’s giving behavior. In laboratory environments, researchers can manipulate and control different features of giving behavior, such as givers’ wealth (capability to help), the decision process (simultaneous or sequential), and the provision of

1 We are grateful to a reviewer for reminding us of this line of research. 153

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information about how many givers and recipients are available. Each feature could respond to the core construct of a theory of the bystander effect. Panchanathan, Frankenhuis, and Silk (2013), for example, compared people’s giving behavior when they acted alone versus when there were other givers in the experiment. In their experiment, each giver had the same amount of endowment and made simultaneous decisions of giving with other givers. The result shows that, in line with the bystander effect, people’s giving declines as the number of givers increases.

2.2. Congestible altruism

While the bystander effect addresses the influence of the number of givers, another line of research investigates whether the number of recipients makes a difference in people’s giving behavior, and if so, under what circumstances. Compared to the long history of the bystander effect research, the investigation of the number of recipients is relatively young and the results are somewhat inconclusive. Some studies show that people give more when the number of recipients increases (Andreoni, 2007; Soyer & Hogarth, 2011), while others report the opposite result that people are more attentive to the needs of an individual than a group (Kogut & Ritov, 2005a, 2005b). To reconcile the inconsistency, researchers have located factors, such as identifiability (Kogut & Ritov, 2005b), perceived efficacy (Sharma & Morwitz, 2016), choice overload (Scheibehenne, Greifeneder, & Todd, 2009), and jointness (Hsee, Zhang, Lu, & Xu, 2013) to describe the conditions under which people behave more or less altruistically to a collectivity versus an individual. In this paper, by congestible altruism we mean the research findings that giving increases as the number of recipients increases.

2.3. An integrated view of the two effects

Studies of the bystander effect and those of congestible altruism are both concerned with how group size influences people’s giving behavior. Although one investigates the impact of the size of givers while the other addresses the recipients, in theory they are not as separate as how they are treated in the literature. We can use the ratio of the number of givers over that of recipients to link together the two effects. The bystander effect argues that giving is less when g/r > 1 than g/r = 1, whereas congestible altruism argues giving is greater when g/r < 1 than g/r = 1. Put together, the two effects suggest that giving decreases as g/r increases. The question is how it declines over g/r. Would giving change at a different rate in the condition of g/r ≥ 1 than g/r ≤ 1?

Technically, g/r is not on the same scale between g/r > 1 and g/r < 1. Thus, to examine whether giving drops at different rates in g/r > 1 and g/r < 1, in what follows we use ln(g/r) to evaluate its relationship with giving. In so doing, g/r = 1 will be on the central point that divides the axis of ln(g/r) into two symmetric halves, allowing us to examine changes of giving on the same scale for g/r > 1 and g/r < 1.

There are three possible ways in which giving decreases along ln(g/r): (1) giving decreases at the same rate in g/r ≥ 1 as in g/ r ≤ 1, suggesting a linear relationship between giving and ln(g/r); (2) giving decreases more rapidly in g/r ≥ 1 than in g/r ≤ 1—a concave relationship; and (3) giving decreases less rapidly in g/r≥1 than g/r≤1—a convex relationship. To assess which re- lationship stands, we conduct a game experiment to seek some empirical evidence.

3. Study 1: The dictator game experiment

3.1. Design

We modify the conventional two-person Dictator game to a multi-person context. Different group sizes of givers g = {1, 8, 15} and recipients r = {1, 8, 15} are manipulated in the game. We test seven combinations of group sizes: (g, r) = (1, 1), (8, 8), (15, 15), (1, 8), (1, 15), (15, 1), (8, 1). The first three scenarios capture the condition of g/r = 1, while the latter four address g/r < 1 and g/ r > 1, respectively. The order of the seven scenarios is randomized to each participant in the experiment.

In each scenario, each participant, playing the role as the dictator, decides whether to share with recipient(s) the money ($200 in local currency and roughly twice the minim um hourly wage in the country). When there is more than one recipient, the dictator’s giving would be equally shared by each recipient. Most importantly, the dictator is informed of how many other dictators (including zero) are joining him/her in making the giving decision. Detailed instructions for the game experiment can be found in the Appendix.

We use the strategy method, popularly used in experimental economics research, to collect people’s giving decisions (Selten, 1967). Participants make a giving decision in each of the seven scenarios. For each participant, a randomly selected scenario is used to calculate his/her final payoff.

3.2. Subjects

A total of 108 participants (53 females; average ages = 21.75 years) were recruited to our experiment from a large public uni- versity in the country. They were assigned to eight sessions held over the course of one week in a computer lab on campus.

3.3. Procedure

The experiment was conducted as a survey operated on the online platform, Qualtrics. Each participant received thorough in- structions on the game rules before starting the experiment. A session was concluded when all participants completed the survey.

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Fig. 1. Distribution of giving over different group sizes of givers and recipients. The horizontal axis denotes the log value of the number of givers over that of recipients. Denser colors of the data points represent higher frequencies. The red curve shows the Lowess fitting. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Each of them was paid a show-up fee ($150 in local currency). We held a lottery for each of them to choose a scenario from which we calculate their additional payoffs. We contacted each participant one week later to pay them the earnings.

We emphasized to the participants that the rules of the game were real and that participants’ decisions would determine how much they and others would receive in the experiment. Although the interaction in our experiment was not on a real time basis, we assured participants that their decisions would be paired up with others’ to calculate payoffs after we collected their experiment data. The experiment was approved by the institutional review board of the institution that funded the research.

3.4. Result

Participants’ giving decisions (out of the endowment of $200) vary across different conditions of the number of givers and recipients. For the seven combinations of (g, r) tested in the experiment: (1, 1), (8, 8), (15, 15), (1, 8), (1, 15), (15, 1), (8, 1), the mean of giving in each of the conditions are: 58.44, 51.80, 50.91, 73.61, 76.32, 22.14, and 27.18. The respective standard deviations are: 44.68, 43.07, 45.88, 63.16, 69.52, 39.20, and 40.29. Fig. 1 shows more clearly participants’ giving against different combinations of group sizes of givers and recipients. As noted, taking a log transformation of g/r divides the axis into two symmetric halves, making it easier to compare the relationship with giving for g/r ≥ 1 and g/r ≤ 1. Our goal is to check whether the slopes are different in the two segments.

The smooth-fit curve (Lowess regression) in Fig. 1 shows that the slope is slightly flatter for g/r ≤ 1 than g/r ≥ 1. To assess more accurately the difference in slopes, we run a Tobit regression on giving separated by g/r ≥ 1 and g/r < 1, specified in the following equation:

Y=a+b1ln rg I rg 1 +b2ln rg I gr<1 (1)

where Y represents the amount of giving; g and r are the numbers of givers and recipients in a scenario, respectively; and I is an indicator variable equal to 1 if the condition specified within the parenthesis is satisfied, and 0 otherwise.2 Tobit regression is adopted here as the dependent variable giving is bound between 0 and 200 (endowment). As each participant made multiple giving decisions

2Note that the regression result remains the same if we move the cases of g/r = 1 to the second regressor; that is, Y=a+b1ln(rg)I(rg >1)+b2ln(gr)I(rg 1).

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Journal of Economic Psychology 73 (2019) 152–160

Table 1

Tobit regression results for Eq. (1) (Number of cases = 756). Estimates

Variables

Intercept

ln(g)I(g 1) rg

ln(g)I(g < 1) rr

N

Model 1

45.63*** (5.34) *** −15.19 (1.61) *** −8.11 (2.07)

Model 2

49.52*** (5.54) *** −15.44 (1.61) *** −7.86 (2.02) −0.25 (0.15)

Standard errors are within the parentheses. **p < 0.01.
*p < 0.05.

*** p < 0.001.

in the experiment, to address the repeated-measure issue we follow a conventional method to cluster standard errors of the regression coefficients by participants (Arai, 2009; Wooldridge, 2003).

Table 1 reports the estimation result for Eq. (1). In model 1, as expected giving decreases with ln(g/r). Furthermore, the result shows that the two regression coefficients are different (b1 < b2). To know whether the difference of b1 − b2 is statistically sig- nificant, we3follow the approach proposed by Clogg, Petkova, and Haritou (1995) to conduct the Z test for the difference of the coefficients. The result shows that the difference is significant (Z = −3.28; p-value = 0.0005).

We also consider whether group size (the number of givers and recipients N=g+r) influences the estimation result, as is specified in Eq. (2).

Y=a+b1ln rg I rg 1 +b2ln rg I gr <1 +b3N (2)

The result of model 2 in Table 1 shows that the main effects (b1 and b2) remain significant, while the effect of group size is not. In fact, if we repeat the previous approach (Clogg et al., 1995) to examine the difference between b1 and b2 in model 2, the evidence for the difference is even stronger (Z = −3.53; p-value = 0.0002).

We also use an alternative way—the interaction effect—to check for a difference in the slopes of the relationships. The idea is that we can treat g/r ≥ 1 and g/r ≤ 1 as two “groups.” While they are originally set on the opposite sides of the axis of ln(g/r), we can horizontally move one group to the other side so that the two groups will share the same values of ln(g/r).4 More importantly, if giving drops at different rates in the two groups, it would be shown by an interaction effect when we regress giving on ln(g/r) with respect to the two groups. Following this method, indeed we found a significant interaction effect between the two groups (p- value = 0.008).

Our multi-person dictator game experiment reveals that the slope of the bystander effect is steeper than that of the congestible- altruism effect, suggesting that giving has a concave, negative relationship with ln(g/r). It means that when there are more givers than recipients, adding one more giver to the game would induce a greater reduction in giving than the increment of giving triggered by the addition of one more recipient when there are more recipients than givers. What accounts for the asymmetry? Below we present a modified behavioral economics model to address this question.

4. Study 2: An adapted inequity-aversion model

We adapt Fehr and Schmidt’s (1999) inequity-aversion model to illustrate the conditions under which an individual exhibits a stronger or weaker bystander effect than congestible altruism. Inspired by earlier work by Panchanathan et al. (2013), we generalize the model to encompass multiple factors for how a giver shares with others in the game.

The model is presented in the following equation:

3 The formula for the test is: Z = b1 b2 , where SE stands for standard errors of the regression coefficients. SE2 +SE2

b1 b2
4 We deliberately add a constant value of −1 × ln(1/15) to each data point for g/r ≤ 1. In so doing, the data of g/r ≤ 1, originally negative or zero

on ln(g/r), now become zero or positive and share the same values with the data of g/r ≥ 1 on the axis ln(g/r). 156

Y.-S. Chiang and Y.-F. Hsu Journal of Economic Psychology 73 (2019) 152–160

Table 2

Parameter values tested for the numeric experiment (gray areas replicate the laboratory experiment setting and they are fixed rather than the explanatory parameters).

U = x g p ( x ̄ x )

g ( 1 p ) ( x x ) r I ( ( g p ( E x ̄ ) + g ( 1 p ) ( E x ) + ( E x ) ) r

l e t D = ( g p ( E x ̄ ) + g ( 1 p ) ( E x ) + ( E x ) ) r

if D > x then I = if D < x

0 otherwise

x )

Eq. (3) shows the utility (U) of a giver consists of four parts. The first part is the remaining payoff x that the focal giver enjoys after giving out E-x, where E is the endowment. The second part represents envy—a reduction in utility, weighted by α, when a giver compares with the wealthier givers (with a proportion of p). The third part refers to guilt—also a reduction in utility, weighted by β, derived from comparing with the poorer givers (with a proportion of 1-p). According to the original model (Fehr & Schmidt, 1999), they assume that 0 ≤ β ≤ α < 1. The final part is a loss of utility in the comparison with the recipients, regardless whether they are wealthier or poorer than the focal giver. Details of each part are elaborated as follows.

The second and third parts of Eq. (3) represent a loss of utility when a giver compares with the wealthier and the poorer givers. Suppose that the focal giver believes a proportion (p) of other givers would donate less than s/he does. Given that each giver has an endowment, giving less means that these givers would end up being wealthier than the focal giver. Accordingly, the remaining proportion 1-p of the givers are the poorer ones, who are believed to donate more than the focal giver does. We further assume that wealthy givers, on average, leave x ̄ payoff for themselves and the poor givers keep x for themselves. Specifically, we assume that x ̄ = x + (E x)u and x = vx, where u and v are two parameters to represent the gap in wealth between the focal giver and the wealthy and the poor givers, respectively. The two parameters are bound between 0 and 1; that is, 0 < u < 1 and 0 < v < 1, to make sure that the wealthier (poorer) givers give less (more) than the focal giver.

The fourth element of Eq. (3) addresses the comparison with the recipients. Since in the game the donations from givers are equally distributed to each recipient, represented by the term D in the equation, the question at stake is whether all of the r recipients are wealthier or poorer than the focal giver. If D > x, it suggests that a giver would have a reduction in utility (envy) weighed by α when comparing with the recipients, who are wealthier than him/her; in contrast, if D < x, a giver would have a loss of utility (guilt) weighed by β when comparing with all of the recipients, who are poorer than the focal giver.

In what follows, we aim to fit the inequity-aversion model described by Eq. (3) to the laboratory experiment data to see what combination of parameter values of the model best account for the pattern of the asymmetry of the bystander effect and congestible altruism we observed in the laboratory experiment. The parameter values being tested are listed in Table 2. We tested the same numbers of givers and recipients as in the laboratory experiment. The endowment is also set to E = 200 as in the experiment.5

To be more specific, for each pair of the numbers of givers (g) and recipients (r), we ran through each combination of parameter

5 In fact, the numeric simulation shows that endowment size (E) does NOT make a difference in influencing the giving behavior of the model. 157

(3)

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values in Table 2 to search for the optimal giving (E-x) that would maximize the utility of a giver, as specified by Eq. (3). For theoretical reason, we relax the original assumption made by Fehr and Schmidt (1999) to consider a more general range for the two parameters: 0 ≤ β ≤ 1 and 0 ≤ α ≤ 1. As optimization of Eq. (3) is mathematically intractable by derivative because of the condi- tional variable I in the last term, we turned to numeric simulation to search for the utility-maximizing giving (E-x).

There are a total of 88,209 (9 × 11 × 11 × 9 × 9) combinations of parameter values in Table 2 (in non-gray cells). For each combination, we searched for the optimal amount of giving (E-x) that would maximize the utility function specified by the parameter values imported to Eq. (3). We then compared the relationship of the optimal giving and ln(g/r) for g/r ≥ 1 (bystander effect) and g/ r ≤ 1 (congestible altruism). To be more specific, we collected the regression coefficients (Tobit regression, same as being used to analyze the experiment data in Study 1) of the optimal giving on ln(g/r)) for g/r ≥ 1 (bystander effect) and g/r ≤ 1 (congestible altruism) respectively. Among the 88,209 combinations of parameter values, we located those whose result of the regression coef- ficients is closest to the results of the laboratory experiment in Table 1. We found four parameter combinations that minimize the absolute difference in the regression coefficients from our experiment finding: They are (p = 0.8, α = 0, β = 0.5, 0.6, 0.7 or 0.8, u = 0.9, v = 0.2). These parameters generated regression coefficients of −17.24 for the bystander effect and −15.20 for the con- gestible altruism effect. Note that although the best fit parameters here show that α < β, there is some empirical research, such as Blake et al. (2015), that found β < α, as was originally assumed by Fehr and Schmidt (1999).

Alternatively, we can consider a different approach to estimate the optimal parameter values that would reflect participants’ decisions of giving in the various combinations of the number of givers and recipients in Study 1. For instance, we can use the “quadratic scoring rule” proposed by Selten (1998) for parameter optimization.6 In this case, the most optimal parameter value would be the one from which the derived optimal giving would be most similar in prevalence to the choices of giving made by participants in the experiment for a certain condition of the number of givers and recipients. The results of parameter optimization using this method are reported in Appendix C. Note that this method estimates the optimal parameter values based on the fitness of the model with participants’ giving decisions, while the approach described earlier estimates the optimal parameters based on the fitness with the aggregate outcome (regression coefficients). The foci of the fitness are at different levels though between the two methods.

Searching for the optimal parameter values of the Fehr-Schmidt model (Eq. (3)) that replicates our experiment finding is only one purpose of the numeric simulation. After all, these parameter values simply inform us why the participants behaved in the way we observed in the experiment. A broader and more interesting question that our one-time experiment cannot answer is under what circumstances would the bystander effect be greater or lesser than the congestible altruism effect. To this end, we found the varieties of the results over the 88,209 parameter values valuable to address the question. Here, we attempt to check how the difference in the regression coefficients between the bystander effect and congestible altruism is influenced by the five parameters, p, α, β, u, and v in the model.

We first deleted simulation cases that generate a positive relationship between giving and ln(g/r), which was never found in literature.7 We then focused on the remaining cases (n = 64,838) and ran an ordinary regression on the difference of the two regression coefficients: Δb = b2 − b1, where b1 < 0 as in Eq. (1) is the Tobit regression coefficient of the bystander effect, whereas b2 < 0 is the regression coefficient of the congestible altruism effect.

The regression results are reported in Table 3. The results suggest that the asymmetry of the two effects become even more widened when people are more envious of the richer (represented by the effect of α); less guilty for the poorer (represented by β), and, in the meantime, a higher proportion (p) of givers are believed to give very little (represented by u) to recipients, and the remaining more generous givers donate much less than the focal giver (represented by v).

The finding above is built on the foundation of the inequity-aversion model by Fehr and Schmidt (1999). To what extents the model truly reflects people’s mentality in the experiment needs to be verified in the future—a point we would briefly comment in the concluding section.

Finally, there may be a concern that the intervals of our parameter estimation in Table 2 is too sparse. To mitigate the concern, we slightly shorten the interval to 0.05 and re-run the numeric simulation. The results are qualitatively the same. We report the com- parison of the results in the appendix for readers’ reference.

5. Discussion

We investigated whether altruistic giving changes at different rates when givers outnumber recipients than the other way around. The mentalities that underlie people’s giving behavior could be different in the two conditions. When givers dominate the group, most people in the group are equally resourceful and there are only a few in need of financial help. People give less in this condition not only because they expect many other givers are available to help the few recipients—the free-riding mentality, but also because they fear that too much giving, according to the inequality-version model, could put them in inferior economic positions to those of many other givers. In contrast, when a group is filled with recipients, the very few givers are likely to feel responsible for helping the great number of the economic disadvantaged recipients—the mentality of heroic altruism. Furthermore, their giving will not have much influence on their economic positions in the group, as there are only a few others as equally resourceful as they are. The free- riding mentality makes a person more selfish, while the heroic altruism mentality makes a person more altruistic. While whether humans are selfish or altruistic in nature remains a topic of debate (Miller, 1999; Zaki & Mitchell, 2013), scholars generally agree that

6 We are grateful to a reviewer for the suggestion.
7 For the theoretical reason, we provide a full analysis (n = 88,209) in Appendix D for readers’ reference.

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Table 3

Ordinary least-squared regression on the difference in the regression coefficients of the bystander effect and congestible altruism: Δb = b2 − b1 (Number of cases = 64,838).

Variables

Intercept
p (proportion of givers believed to be less generous than the focal giver) α (weight of loss of utility due to envy)
β (weight of loss of utility due to guilt)
u (gap from the wealthy givers; a larger value means a larger gap)
v (gap from the poor givers; a larger value means a smaller gap)

Standard errors are reported in the parentheses. **p < 0.01.
*p < 0.05.

*** p < 0.001.

Estimates

81.57*** (5.17) 36.88*** (4.59) 59.99*** (3.80) *** −36.47 (4.21) *** 187.60 (4.38) *** −138.92 (4.53)

people are likely to be drawn to either selfishness or altruism depending on the mechanisms at work. The question is whether the attractions are of equal strength: Would it be easier to become selfish when the selfishness-eliciting mechanism is triggered than to become altruistic when the altruism-promotion mechanism is activated? We argue that a comparison of the velocity of behavioral changes, as we exemplified in the paper, could provide a new direction to the debate about the human nature of selfishness and altruism.

It is noteworthy that people’s giving decision may not always be sensitive to the number of recipients, as earlier research sug- gested (Baron, 1997; Frederick & Fischhoff, 1998; Kahneman & Ritov, 1994). In a comprehensive review article, Baron (1997) listed and critiqued a number of reasons to why people’s decisions are insensitive to the quantities of valuable goods they want to give. For example, there is a “budget constraint” bias, which leads people to believe that if they donate money to a national park, for instance, another national park of a similar kind would not be equally financed (Baron, 1997, p. 75). As another example, there is a “avail- ability” bias that argued that the goods people think of when making the giving decision are not of the same type of another good when they make a similar giving decision, for example, donation for medical insurance for transplants of different organs (Baron, 1997, p. 76). We argued that our study design—the multi-person dictator game—is immune to the kinds of biases for at least two reasons. First, the object of donation in our study is money and the value is objective to every participant. The ambiguity of the effect of the good being evaluated, such as the uncertainty of how much a person’s donation would help reduce the casualty of traffic accidents (Baron & Greene, 1996), is not expected to occur in our study. Second, the number of givers and recipients is relatively small and was made very clear in our experiment. As pointed out by Baron (1997, p. 84), people usually have difficulty in assessing how much their donation would help reduce the death rates in a big city such as Philadelphia (1.5 million at that time). In contrast, the number of givers and recipients are relatively small and cognitively manageable in our experiment. We believe the reasons and others not fully discussed here may explain why in our study people’s giving decisions are sensitive to the quantities of actors in the experiment.

There are issues left open for future study. First, more experimental work is needed to confirm that our experimental finding is not attributable to the limitation of small sample size and particular cultural and social influences affecting our participants (Henrich, Heine, & Norenzayan, 2010). Conducting the experiment across a wider spectrum of cultural and social contexts would help increase the replicability of behavioral science research (Open Science Collaboration, 2015). Moreover, it would also introduce a richer set of explanatory variables at the societal level to analyze the asymmetry of the two effects of giving behavior. Second, although we propose a modified inequity-aversion model to explain why the bystander effect is stronger than congestible altruism, the model’s validity remains unverified. It is also an open question whether there are other competing theories to account for our experimental finding. We suggest future study can use more state-of-the-art methods to assess people’s physical reaction and brain activities to verify the theory and test the explanatory power of different models for the asymmetry of the bystander effect and congestible altruism that we found in our study. Thirdly, drawing on our research finding researchers can use computer simulation to simulate altruistic giving in events at larger scales such as charity donation and online crowdfunding in the real world.

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