Risk-Averse and Self-Interested Shifts in Groups in Both Median and Random Rules

Abstract

The purpose of this study was to determine whether attitudes toward risk and altruism are affected by being in a group or being alone. In contrast to previous economic research on group decision-making, we excluded the effects of group informal discussions, which are thought to be a “black box” when individuals make decisions in a group. In this regard, the subjects in our experiment were only requested to show their faces to the other members, without further communication. Moreover, we adopted two collective decision rules, i.e., the median rule and the random rule, which provide the truth-telling mechanism. In the experiments of both anonymous investment and donation, we found that the subjects who made decisions in a group offered significantly lower amounts than those who made decisions alone, after controlling for individuals’ risk and altruistic preferences. The findings imply that people are more risk-averse and self-interested when they are in a group, regardless of which collective decision rules are adopted.

1. Introduction

Although a decision-maker is almost always assumed to be an individual in normative economic models, in real-life situations, many important decisions are made by groups such as company boards, management teams, governments, legislators, etc. Meanwhile, since the importance of group decision-making has been growing, economists have been focusing increasing interest on this particular subject.

In the field of social psychology, the study of group decision-making has had a long history. For example, Stoner (1961) [1] conducted the first experiment in which decisions made by groups led to riskier positions, compared to individuals’ decisions, while Moscovici and Zavalloni (1969) [2] noted that decision-making in groups can result in both risky and cautious shifts.1 In related research, Kerr et al. (1996) [6] concluded that group interactions and discussions can yield different results.2

In previous economic studies of group decision-making,3 the preferential differences toward risk and altruism between individuals and groups were examined.4 However, the empirical evidence has been mixed. For instance, Baker et al. (2008), Shupp and Williams (2008), and Masclet et al. (2009) [33,34,35] reported that groups are more risk-averse than individuals, while Mifune et al. (2016) [36] found a similar tendency by comparing individual-on-individual treatment to group-on-individual treatment. Although Rockenbach et al. (2007) and Zhang and Casari (2012) [37,38] found that group decisions can display a risky shift, Harrison et al. (2012) [39] concluded that there are no significant differences between individuals and groups.

Regarding altruistic preferences, Cason and Mui (1997) [40] found that a dictator group was less self-interested than an individual dictator, whereas Luhan et al. (2009) [41] reported the contrary. Specifically, the method of communication within the dictator group in Cason and Mui (1997) [40] was face-to-face, whereas that in Luhan et al. (2009) [41] was online chat. In the latter, determining whether group decision-making was more self-interested than individual decision-making was based on the anonymity within the dictator group.

As the aforementioned economic literature on group decision-making, except for Masclet et al. (2009) [33] and Harrison et al. (2012) [39], featured groups that were allowed to communicate with the other group members via face-to-face discussions or electronic chats, the observed decisions of the groups were due to the mixed effect of the preferences of the individuals being in a group and the group’s formal/informal discussions. Consequently, little is known about the subjects’ actual preferences in terms of how they decide, i.e., alone or in a team.

The present study differs from the previous literature regarding three points. First, we excluded the effects of group informal discussions, which are thought to be a “black box” when individuals make decisions. Second, the prior literature adopted different “collective decision rules” on group decision-making (e.g., majority rule, unanimity, and dictator rule), which may have affected the results of the experiments (Gilet et al., 2009) [42]. To the best of our knowledge, this is the first experiment that compares two collective decision rules, i.e., the median rule and the random rule. Although these two rules can enhance the truth-telling mechanism (see Cason et al., 2006) [43], we determined whether there is a difference between both rules on group decision-making. Finally, we collected data regarding both individuals’ attitudes toward risk and altruism from the same subjects, since the effect of group decision-making may be influenced by these two aspects. We observed that the existence of other group members had a significant influence on both attitudes, regardless of which collective decision rules were adopted.

To compare the risk and altruistic attitudes of groups and individuals, our experiment was composed of two parts. First, all of the subjects were asked to conduct an individual task. For risk attitude, we implemented the lottery choice task introduced by Holt and Laury (2002) [44]. For altruism attitude, we used a standard public goods game (PGG). These variables were utilized as controls for individuals’ preferences toward risk and altruism in our regression model. Second, we separated the subjects into individual-choice and group-choice tasks and then conducted an anonymous investment game and donation game in each task. For the group-choice task, the subjects were requested to only show their faces to the other members, without further communication. Meanwhile, each Player made the same decision by the median rule condition and the random rule condition, after which he/she received the same payoff.

The remainder of this study is as follows. Section 2 introduces our experimental design and procedure, while Section 3 presents the results of the experiment. Finally, Section 4 includes a discussion of the findings and the conclusions.

2. Materials and Methods

Figure 1 presents our experimental design, which consists of two parts. In Part 1, all of the subjects were asked to perform an individual task, as mentioned later in this section (i.e., Tasks 1 and 2). After the decisions in Part 1 were made, the instructions in Part 2 were presented. In Part 2, the subjects performed Tasks 3 and 4 after being randomly separated into the individual-choice task and the group-choice task.5 For the group-choice task, the subjects were divided into a group of three and the collective decision rule was either the median or the random rule, both of which provided the truth-telling mechanism at the time of decision-making. Since the collective decision rule applied in the group-choice task in Part 2 was predetermined, this became the name of the experiment. However, since the explanation of the collective decision rule was provided after the decisions in Part 1, the difference in the collective decision rules did not affect the decisions in this part.

2.1. Part 1 (Tasks 1 and 2)

In this section, we describe our task in more detail. In Task 1, the lottery choice experiment introduced by Holt and Laury (2002) [44] was conducted, in which the subjects were asked to choose between a “safe” (Option A) and a “risky” (Option B) option. All 10 decisions simultaneously appeared (as shown in

Table 1. Lottery choice experiment (Holt and Laury 2002 [44]).

Decision	Option A				Option B				Proportion of Subjects
	Probability	Payoff	Probability	Payoff	Probability	Payoff	Probability	Payoff
1	10%	¥200	90%	¥160	10%	¥380	90%	¥10	0.6
2	20%	¥200	80%	¥160	20%	¥380	80%	¥10	0.3
3	30%	¥200	70%	¥160	30%	¥380	70%	¥10	0.6
4	40%	¥200	60%	¥160	40%	¥380	60%	¥10	5.2
5	50%	¥200	50%	¥160	50%	¥380	50%	¥10	13.9
6	60%	¥200	40%	¥160	60%	¥380	40%	¥10	12.5
7	70%	¥200	30%	¥160	70%	¥380	30%	¥10	28.4
8	80%	¥200	20%	¥160	80%	¥380	20%	¥10	27.0
9	90%	¥200	10%	¥160	90%	¥380	10%	¥10	8.7
10	100%	¥200	0%	¥160	100%	¥380	0%	¥10	2.9

Note: The last column provides the proportion of the subjects who chose the risky option (Option B) for the first time out of the 10 decisions. To calculate the proportions, we used the data from the subjects who did not switch back to this task. These two columns were not displayed to the subjects.

). At the time of the experiment, 110 yen equaled approximately one US dollar. One decision was randomly chosen by the computer for payment at the end of the experiment. Additionally, we calculated the coefficient of relative risk aversion based on the constant relative risk aversion (CRRA) utility function:

$$u_i\left(Y_i\right)=\frac{Y_i{}^{1-{\gamma }_i}}{1-{\gamma }_i}$$

where ${\gamma }_i$ is the coefficient of relative risk aversion and $Y_i$ represents the lottery outcomes for subject i. In this case, the coefficient was less than 0 for the subjects who were risk-seeking, equal to 0 for the subjects who were risk-neutral, and greater than 0 for the subjects who were risk-averse.

In Task 2, a standard PGG was used to measure individual altruistic preferences. Specifically, the subjects determined how much of the 200-yen endowment to keep or invest in public goods. The payoffs were determined by the contributions of each member being doubled and evenly divided between the members. While Masclet et al. (2009) [35] controlled the socio-demographic variables, such as salaried and self-employed workers, we used these variables as controls in the regression model (e.g., Task 1: risk preference; Task 2: altruistic preference).

2.2. Part 2 (Tasks 3 and 4)

In Tasks 3 and 4, we used the anonymous investment and donation game. In this case, the subjects received a 200-yen endowment and decided how much money to invest or donate, ranging from 0 yen to 200 yen (in intervals of 10 yen). In Task 3, their investment options were as follows: 50% possibility of winning 2.5 times their invested amount or 50% possibility of losing their entire investment. In Task 4, they donated money to the Japanese Red Cross Society.

As explained earlier, the subjects were randomly allotted individual-choice and group-choice tasks. While their choice became their decision in the individual-choice task, the group decision was based on the collective decision rule (i.e., the median rule or the random rule) applied to the choices of the team members in the group-choice task, after which each team member received the same payoff. For the median rule, the instruction sheets explained that the median value was the middle value in the sorted order of values, after which the group decision was determined according to the median values. For the random rule, the subjects were instructed that the group decision was based on the choices of the group members, which were randomly selected with a one-third possibility. This setting enabled us to observe the individual choices for the group-choice task while considering both the median and random rules. Hence, the group choice is referred to as the “individual choice in a group” for the remainder of this study.

Furthermore, the subjects were told that the members of the groups are identical in Tasks 3 and 4. Meanwhile, they were not allowed to communicate with one another, since we attempted to exclude the effects of the group discussions from the decision-making processes. However, we considered that if there were no interactions between the group members before making any decisions, then the members would not realize that they were indeed assigned to groups. Therefore, to increase the credibility of our experiment, we used the same mutual identification6 employed in Bohnet and Frey (1999) [45], in which each member of the group would stand up and show their face to the other members (in silence).

Following these tasks, we ran other decision-related tasks, in which the subjects were asked to individually answer the post-experimental questionnaire, including the questions related to social value orientation (SVO). Further details are discussed in the Section 3.

2.3. Procedure

Overall, we managed our experiment according to the standards of economic experiments. The instruction sheets were individually distributed and the information was read aloud to the subjects at the beginning of each part. All of the tasks required one-shot anonymous decisions,7 and there was no feedback until the end of the experiment. All of the subjects were undergraduate students from various disciplines at the Kochi University of Technology, Kyoto Sangyo University, and Kansai University, recruited via the university website and e-mail solicitation.8 We conducted 18 sessions between July 2015 and December 2017. No subject participated in more than one session. The experiment was programmed and conducted by using z-Tree software (Fischbacher, 2007) [47]. The subjects were individually seated in front of a computer screen. On average, each session lasted for approximately 1 h and 15 min, including the post-experiment questionnaire and final payment of the subjects. Each participant in this study earned 2140 yen (on average).

3. Results

3.1. Descriptive Statistics

Of the 360 subjects in our experiment, we excluded eight subjects who switched back more than twice and four subjects who chose the safe option (Option A) among the 10 decisions in the risk attitude task (Task 1).9 As for the rest of the subjects, 320 did not switch back at all, while 28 subjects switched back once. For the subjects who switched back once, we followed the procedure in Lusk and Coble (2005), Harrison et al. (2007), and Anderson and Mellor (2008) [48,49,50] to calculate the range of relative risk attitude. Thus, the final sample size consisted of 348 subjects (59.77% males and 40.23% females).10

Table 2. Variable definitions.

Variables	Definition
Investment	The amount of investment (Task 3), from 0 to 200
Donation	The amount of donation (Task 4), from 0 to 200
Risk preference	The level of “Risk preference” (Task 1)
Contributions	The amount of contribution in the PGG (Task 2)
Group dummy	Dummy variable for the subjects assigned to the group-choice tasks
Prosocial	Dummy variable for the subjects defined as “Prosocial” in the SVO method
Male	The gender dummy variable (1 if male, 0 otherwise)
University	The university dummy variable (the baseline variable is Kansai University)

provides the definitions of the variables used in this study.

Table 3. Descriptive statistics for the group-choice sub-sample: Median rule (MR) vs. Random rule (RR).

Group-Choice Sub-Sample	Median Rule		Random Rule		MR—RR
	Mean	Std. Dev.	Mean	Std. Dev.	p-Value
Investment	101.74	67.41	84.65	56.50	0.12
Donation	31.20	54.39	31.86	50.61	0.19
Risk preference	0.44	0.41	0.51	0.60	0.30
Contributions	63.91	74.83	47.56	59.98	0.36
Prosocial	0.42	0.50	0.43	0.50	0.93
Male	0.78	0.41	0.48	0.50	0.000 ***

Note: Median rule (N = 92), Random rule (N = 86). Except for the proportion of “Male,” there was no significant difference between the median rule and random rule sub-samples regarding the amount of donation and investment, the level of “Risk preference” (Task 1) and “Contributions” (Task 2) (by the non-parametric Mann-Whitney U-test), and the proportion of the subjects who were defined as “Prosocial” in the SVO method (by the chi-square test of independence). Only the proportion of “Male” was significantly different between the median rule and random rule sub-samples (78.26% vs. 47.67%; *** p < 0.01; using the chi-square test of independence).

and

Table 4. Descriptive statistics for the individual-choice sub-sample: Median rule (MR) vs. Random rule (RR).

Individual-Choice Sub-Sample	Median Rule		Random Rule		MR—RR
	Mean	Std. Dev.	Mean	Std. Dev.	p-Value
Investment	116.24	62.45	111.53	68.11	0.64
Donation	52.59	66.92	43.65	61.81	0.42
Risk preference	0.52	0.53	0.53	0.50	0.89
Contributions	67.29	69.03	58.59	64.87	0.50
Prosocial	0.45	0.50	0.51	0.50	0.44
Male	0.64	0.48	0.48	0.50	0.045 **

Note: Median rule (N = 85), Random rule (N = 85). Only the proportion of “Male” was significantly different between the median rule and random rule sub-samples (63.53% vs. 48.24%; ** p < 0.05; using the chi-square test of independence).

present the descriptive statistics for the group-choice and individual-choice sub-samples, respectively (For each sub-sample, we compared the median rule condition and the random rule condition to determine if there was a population effect between the two conditions since the sessions of the median rule condition occurred at the Kochi University of Technology (87 subjects; 64.37% males) and Kyoto Sangyo University (90 subjects; 77.78% males). However, the random rule condition took place at Kansai University (171 subjects; 47.95% males). Based on our comparison, there was no significant difference between the conditions, except for the proportion of “Male” (the group-choice sub-sample: 78.26% males vs. 47.67% males, p < 0.01; and the individual-choice sub-sample: 63.53% males vs. 48.24% males, p < 0.01, using the chi-square test of independence).

3.2. Group Effect

3.2.1. Risk Attitude

To extract the effect of being assigned to groups, we conducted a regression model, controlling for several other factors. Since our dependent variable was left- and right-censored variables (values from 0 to 200), we ran a Tobit model, which is widely used in economic models. We estimated the coefficients in the investment regression, in which the independent variables include: the individual attitudes measured in Task 1; the “group-choice” dummy variables (whether assigned to the group-choice tasks); an interaction term between “group-choice” and “random rule”; the university dummy variables; and the gender dummy variables. Model 2 includes the independent variable of the contributions in the PGG (Task 2), for robustness checks in the regression. We also presented the marginal effects on the expected value of the censored outcome estimated after the Tobit model.

Table 5. Estimation results: Investment (Tobit model).

Investment	Model 1	Marginal	Model 2	Marginal
		Effects		Effects
Risk preference	−47.36 ***	−34.29 ***	−46.51 ***	−33.66 ***
	(10.92)	(7.60)	(10.76)	(7.49)
Group dummy	−28.38 **	−20.32 **	−27.74 **	−19.87 **
	(13.15)	(9.14)	(13.10)	(9.12)
Interaction term	−12.84	−9.33	−11.74	−8.52
(group × random rule)	(18.74)	(13.61)	(18.57)	(13.48)
Contributions	-	-	0.16 **	0.11 **
	-	-	(0.08)	(0.06)
Male	28.36 ***	20.82 ***	27.70 ***	20.32 ***
	(9.25)	(6.78)	(9.16)	(6.71)
Kochi University of Technology	−5.33	−3.86	−7.09	−5.13
	(14.80)	(10.68)	(14.61)	(10.53)
Kyoto Sangyo University	7.82	5.68	7.09	5.15
	(16.65)	(12.14)	(16.51)	(12.03)
Constant	133.9 ***	-	124.4 ***	-
	(12.29)	-	(12.98)	-
Observations	348		348
Log pseudolikelihood	−1493.9		−1491.4

Note: Significance levels: *** p < 0.01, ** p < 0.05, * p < 0.1. Robust standard errors are in parentheses.

presents the estimation results of the regression on investment, in which robust standard errors were utilized. Of primary interest is the estimated marginal effects of the “group-choice” variable. Based on the findings, we can confirm that it is negative and significant at the 0.05 level, which indicates that the subjects in the group were generally more risk-averse than individuals. According to the estimated marginal effects, the subjects were more likely to decrease their investment by approximately 20.3 yen (on average) in Model 1, and 19.9 yen in Model 2 (in which the subjects were asked to invest in their options, ranging from 0 yen to 200 yen in Task 3). Note that the estimated coefficients of the interaction term between “group-choice” and “random rule” were not significant in both models. These results indicate that the effects of being assigned to groups have the same impact, regardless of whether collective decision rules are adopted in investments.

As for the other independent variables, the marginal effects of risk attitude assessed by the CRRA were negative and significant at the 0.01 level, which indicates that the more risk-averse subjects tended to decrease their amount of investment. With regard to the gender effect, the males generally invested more than the females by approximately 20 yen (on average) in both models, at a significance level of 0.01.

3.2.2. Altruistic Preferences

In the previous section, we confirmed that the subjects who made decisions in a group tended to decrease their investment in both collective decision rules. As for the regression results of donation in

Table 6. Estimation results: Donation (Tobit model).

Donation	Model 1	Marginal	Model 2	Marginal
		Effects		Effects
Contributions	0.32 ***	0.15 ***	0.32 ***	0.15 ***
	(0.10)	(0.05)	(0.10)	(0.05)
Group dummy	−43.28 **	−23.78 **	−42.46 **	−23.27 **
	(17.68)	(10.59)	(17.66)	(10.55)
Interaction term	34.70	15.82	34.20	15.60
(group × random rule)	(23.64)	(10.07)	(23.50)	(10.02)
Prosocial	45.92 ***	19.32 ***	45.70 ***	19.22 ***
	(12.33)	(4.30)	(12.38)	(4.33)
Risk preference	-	-	8.55	4.14
	-	-	(12.24)	(5.92)
Male	−23.83 *	−12.54 *	−22.98 *	−12.04 *
	(12.16)	(6.82)	(12.31)	(6.87)
Kochi University of Technology	23.06	10.77	22.96	10.72
	(19.22)	(8.68)	(19.24)	(8.68)
Kyoto Sangyo University	13.49	6.38	13.37	6.32
	(18.69)	(8.62)	(18.67)	(8.61)
Constant	−15.98	-	−21.20	-
	(14.65)	-	(17.13)	-
Observations	348		348
Log pseudolikelihood	−1139.5		−1139.2

Note: Significance levels: *** p < 0.01, ** p < 0.05, * p < 0.1. Robust standard errors are in parentheses.

,11 the subjects in the group-choice tasks significantly decreased their donation, compared to those in the individual-choice tasks, at a significance level of 0.05. For the regression results, the subjects in the group were more self-interested than individuals. On average, they decreased their donation by approximately 23.8 yen in Model 1 and 23.3 yen in Model 2 (the range of the donation choice was 0 yen to 200 yen in Task 4). We also found that the coefficients of the interaction term between “group-choice” and “random rule” were not statistically significant in the donation regression. These results indicate that the group effects were robust in both collective decision rules. Moreover, after comparing the estimated marginal effects of the “group-choice” variable and the mean of the two dependent variables, i.e., investment (mean = 113.89 yen) and donation (mean = 48.12 yen),12 the effects of being assigned to the groups on altruism were greater than those on risk attitudes (marginal effects; 20.3 yen on risk attitudes vs. 23.8 yen on altruism in Model 1).

For the other independent variables, the amount of contribution in the PGG was positively associated with the amount of donation, at a significance level of 0.01. To check the robustness of the donation regression, we controlled the subjects’ prosocial orientation in both models, measured by the SVO developed by Van Lange et al. (1997, 2007) [52,53]. In this case, the dummy variable of “Prosocial” equals 1 if the subjects were defined as “prosocial” in the SVO method, or 0 otherwise.13 The coefficients for both the “Contributions” and “Prosocial” variables were positive and statistically significant at the 0.01 level. Hence, we can capture and control the other aspects of altruism by introducing the “Prosocial” dummy variable, as defined in the SVO method.

3.3. Effect of the Collective Decision Rule

3.3.1. Risk Attitude

Based on the aforementioned result that the coefficients for the interaction term between “group-choice” and “random rule” were not significant in both investment and donation, it indicates that the group effects are robust and have the same impact on both collective decision rules. However, to determine more precisely whether there is no difference between the median and random rule on group decision-making, we extracted the “group-choice” sub-sample (N = 178) and ran a regression model by adding “random rule” dummy variables and “random rule” interaction terms to our model.14 In

Table 7. Estimation results for the group-choice sub-sample (Tobit Model).

Group-Choice Sub-Sample	Model 1	Marginal	Model 2	Marginal	Model 3	Marginal
	Investment	Effects	Donation	Effects	Donation	Effects
Risk preference	−88.19 ***	−66.76 ***	-	-	−19.73	−8.96
	(21.85)	(15.57)	-	-	(27.24)	(12.35)
Interaction term	57.88 **	40.50 **	-	-	35.22	14.86
(random rule × risk preference)	(25.10)	(15.63)	-	-	(32.24)	(12.58)
Random rule	−40.68 **	−30.66 **	30.19	12.01	−2.67	−1.23
	(16.77)	(11.94)	(22.22)	(7.55)	(21.49)	(9.97)
Contributions	-	-	0.28	0.12	0.15	0.07
	-	-	(0.19)	(0.08)	(0.13)	(0.06)
Interaction term	-	-	−0.29	−0.13	-	-
(random rule × contributions)	-	-	(0.25)	(0.12)	-	-
Prosocial	-	-	43.14 ***	16.56 ***	42.33 ***	16.35 ***
	-	-	(15.89)	(5.05)	(15.76)	(5.04)
Male	25.04 **	18.83 **	−16.13	−7.90	−15.90	−7.81
	(11.21)	(8.32)	(15.89)	(8.35)	(15.99)	(8.42)
Constant	126.6 ***	-	−39.13 *	-	−21.59	-
	(14.65)	-	(23.41)	-	(23.33)	-
Observations	178		178		178
Log pseudolikelihood	−780.1		−549.2		−549.4

Note: Significance levels: *** p < 0.01, ** p < 0.05, * p < 0.1. Robust standard errors are in parentheses.

, Model 1 reports the regression results of investment, while Models 2 and 3 of donation regression for the “group-choice” sub-sample (Model 3 controls for individuals’ risk preferences).

According to the results of investment (Model 1), the marginal effect of the “random rule” dummy variable was negative and significant at the 0.05 level. This indicates that the subjects were more likely to decrease their investment by approximately 30.7 yen (on average) when the random rule was adopted. In addition, the coefficients for the interaction term between “Random rule” and “Risk preference” were positive and significant at the 0.05 level. Regarding Figure 2,15 to aid the discussion, the risk-seeking subjects tended to decrease their investment more than the risk-averse subjects. In seeking a possible explanation for these results, we assumed that whereas the probability (one-third) that his/her choices were selected is obvious in the random rule, the probability of the selection is ambiguous in the median rule (MR). Hence, the group effects (the risk-averse shift in the groups) had a greater impact on the random rule than those on the MR, since the subjects realized that their choices may be selected for the group decisions. Furthermore, the risk-seeking subjects were more affected by the group effects than the risk-averse subjects, since the former probably understood that their preferences were relatively higher than those of the other subjects. Consequently, they decreased their investment to a large extent, i.e., they refrained from risk-taking behavior by considering the group decisions.

3.3.2. Altruistic Preferences

For the altruistic task, although Figure 3 suggests that the other-regarding subjects tended to decrease their level of donation more than the self-interested subjects in the random rule, the coefficients of the “random rule” dummy variables and the “random rule” interaction terms were not significant in all of the models in Table 7. Thus, we concluded that the significant difference between both rules that were previously captured was not observed in the donation task. We also conducted the same regression model for the individual-choice sub-sample (N = 170) in

Table 8. Estimation results for the individual-choice sub-sample (Tobit model).

Individual-Choice Sub-Sample	Model 1	Marginal	Model 2	Marginal	Model 3	Marginal
	Investment	Effects	Donation	Effects	Donation	Effects
Risk preference	−64.18 ***	−44.37 ***	-	-	−1.42	−0.72
	(24.16)	(16.07)	-	-	(28.52)	(14.55)
Interaction term	41.05	28.18	-	-	21.39	10.59
(random rule × risk preference)	(36.61)	(24.58)	-	-	(39.29)	(18.75)
Random rule	−22.22	−14.90	−29.55	−16.10	−30.83	−16.83
	(24.56)	(15.79)	(24.23)	(13.88)	(29.92)	(17.21)
Contributions	-	-	0.42 **	0.21 **	0.49 ***	0.25 ***
	-	-	(0.20)	(0.10)	(0.16)	(0.08)
Interaction term	-	-	0.16	0.08	-	-
(random rule × contributions)	-	-	(0.30)	(0.15)	-	-
Prosocial	-	-	47.73 **	21.70 ***	49.74 **	22.42 ***
	-	-	(19.73)	(7.56)	(19.85)	(7.45)
Male	34.57 **	24.82 **	−35.53 *	−19.74 *	−34.20 *	−18.92 *
	(14.61)	(10.64)	(18.16)	(10.63)	(18.44)	(10.73)
Constant	141.2 ***	-	0.21	-	−6.04	-
	(18.77)	-	(20.58)	-	(23.95)	-
Observations	170		170		170
Log pseudolikelihood	−709.9		−587.4		−587.3

Note: Significance levels: *** p < 0.01, ** p < 0.05, * p < 0.1. Robust standard errors are in parentheses.

. We found that announcing the collective decision rule, i.e., the MR or the random rule, did not create a significant difference in the individual-choice tasks.

4. Conclusions

This study determined whether attitudes toward risk and altruism are affected by being in a group or being alone. Our experiment was designed to exclude the effects of informal discussions in a group by forbidding communication between the members of the group and adopting two collective decision rules, i.e., the median rule and the random rule, both of which enhanced the truth-telling mechanism at the time of group decision-making. Our results showed that the subjects who made decisions in a group tended to decrease their amount of investment and donation (on average) in both rules. These results are in line with previous economic literature (see Shupp & Williams, 2008; Luhan et al., 2009; Masclet et al., 2009 [34,35,41], as cited in the Introduction). However, the prior literature only discussed the communication effects and different “collective decision rules” to reach an agreement in group decision-making (e.g., majority rule, unanimity, dictator rule, etc.). In the present study, we found that the subjects’ were more risk-averse and self-interested when they were assigned to a group in which the members had a common interest in both the median and the random rule. In addition, upon comparing both rules, we found that the group effects (the risk-averse shift in investment) had a greater impact on the random rule than those on the MR and that the risk-seeking subjects were more affected by the group effects than the risk-averse subjects, i.e., they decreased their level of investment at a higher rate.

Overall, our results shed light on the “black box” of group decision-making, as mentioned in the Introduction. Ambrus et al. (2015) [56] found that median group members had a significant influence on group decisions via free discussions in the trust game and risk-tasking game of Holt and Laury (2002) [44], while Luhan et al. (2009) [41] reported that most self-interested group members had the greatest impact on group decisions via electronic chat in the dictator game. While the median group members in the prior works might have caused preference shifts when assigned to a group, these works only focused on how individual preferences were aggregated to the group attitude (i.e., preference aggregation). However, preference shifts might have also occurred by the existence of other group members. Therefore, we suggest that these two effects (i.e., preference shifts and aggregation) were most likely mixed up in prior research.