Group Decision Making Under Ambiguity - Google Sites

Group Decision Making Under Ambiguity Steffen Keck INSEAD, Boulevard de Constance, 77305 Fontainebleau Cedex, France [email protected]

Enrico Diecidue INSEAD, Boulevard de Constance, 77305 Fontainebleau Cedex, France [email protected]

David Budescu Department of Psychology, Fordham University, Dealy Hall, Bronx, New York 10458, USA [email protected]

Friday, August 12, 2011

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Abstract We report results of an experimental elicitation of certainty equivalents for 15 risky or ambiguous two-outcome gambles. Decision makers (DMs) made decisions in three different settings: (a) individually, (b) individually after discussing decisions with others, and (c) in interacting groups of three. We also manipulated the degree of payoff-communality between subjects. We show that groups are more likely to make ambiguity neutral decisions than individuals, and that individuals also make more ambiguity neutral decisions after discussing the decisions with others. This shift towards higher ambiguity neutrality in groups and after a group discussion is caused by a reduction in both ambiguity aversion and ambiguity seeking. Surprisingly, our results do not show a significant influence of payoff-communality on attitudes towards risk and ambiguity. We attribute the results to the effective and persuasive communication that takes place in groups.

Keywords: Ambiguity, Group Decision Making, Imprecision, Risk, Vagueness JEL classification: C92, D71, D81

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1. Introduction Keynes (1921) and Knight (1921) emphasized that most economic decisions involve vague probabilities (ambiguity1) as opposed to probabilities which are precisely defined (risk). In many cases, these decisions are delegated to groups of DMs -for example committees, management teams and boards of directors. Previous work has studied the differential risk attitudes of individuals and groups, but it is unclear whether groups also differ from individuals with respect to their attitudes towards ambiguity. We address this question in a laboratory experiment in which individuals and groups make decisions under risk or under ambiguity. One rationale for delegating important decisions to groups is that they outperform individuals in a large variety of tasks (Kerr & Tindale, 2004). For example, groups have been shown to learn faster and achieve higher outcomes in strategic settings such as beauty contest (Kocher & Sutter, 2005), signaling- (Cooper & Kagel, 2005) and coordination games (Feri, Irlenbusch & Sutter, 2010). In decisions under risk the evidence about group performance is mixed. Groups show fewer violations of stochastic dominance and Bayesian updating rules (Charness, Karni & Levin, 2007) and make better investment decisions (Sutter, 2007; Rockenbach, Sadrieh & Mathauschek, 2007). Bone, Hey and Suckling (1999) report that decisions under risk made by individuals and groups show similar rates of expected utility violations such as the common-ratio effect. Rockenback et al. (2007) confirm this result and also report no difference between individuals and groups with respect to the rates of preference reversals.

1 Following Ellsberg (1961) vague probabilities are commonly referred to as ambiguous. We follow this convention in our paper. However, see Budescu, Kuhn, Kramer and Johnson (2002) for a discussion pointing out the inadequacy of ambiguity as a descriptive term and advocating the use of imprecision or vagueness instead. We use both terms -ambiguity and vagueness- in this paper.

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Group decisions often involve the aggregation of group members’ attitudes. Previous studies comparing risk attitudes of individuals and groups have found somewhat conflicting results. Zhang and Casari (2009) found groups to be less risk averse than individuals. In contrast, Harrison, Igel-Lau, Rutström and TarazonaGómez (2005), Ambrus, Greiner and Pathak (2009) and Deck, Lee, Reyes and Rosen (2010) did not find differences between the risk attitudes of individuals and groups. Several studies suggest that differences in risk attitudes between individuals and groups depend on the risk level of the decision. Shupp and Williams (2008) showed that groups are less risk averse in low-risk situations and more risk averse when decisions involve high levels of risk. Baker, Laury and Williams (2008) as well as Masclet, Colombier, Denant-Boemont and Lohéac (2009) found a similar pattern. All of these studies have focused on the comparison of risk attitudes between individuals and groups but did not explore potential differences in attitudes towards imprecision. Starting with Ellsberg (1961) numerous studies have shown that in settings which involve ambiguity, individuals’ decisions cannot be reconciled with classical Subjective Expected Utility (SEU) (Savage, 1954). The most common (though, by no means, universal) experimental finding in the literature is ambiguity aversion. Consequently, when evaluating ambiguous gambles or investments, individuals demand an additional “ambiguity premium” on top of the normal risk premium (for an overview of experimental findings see Camerer & Weber, 1992; Etner, Jeleva & Tallon, 2009). Although ambiguity aversion remains the most common finding, diversity in ambiguity attitudes is often found. Ambiguity seeking is commonly observed in the domain of losses (Mangelsdorff & Weber, 1994) and for small probabilities of gains (Einhorn & Hogarth, 1986; Kahn & Sarin, 1988). Budescu, Kuhn, Kramer and

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Johnson (2002), who analyze certainty equivalents for gambles with vague probabilities and vague outcomes, find no strong modal attitude towards ambiguity in probabilities and predominantly ambiguity seeking (aversion) for vague gains (losses). Du and Budescu (2005) demonstrate that attitudes towards ambiguity in general are malleable and depend on factors such as the locus of the ambiguity (probabilities or outcomes), the choice domain (gains vs. losses) and response modes (pricing or choice). Only a very small number of studies have investigated the effects of social factors on decisions under ambiguity. Curley, Yates & Abrams (1986) found that individuals, who were observed by uninvolved others during their decisions and the resolution of the uncertainty, exhibited significantly more ambiguity aversion than DMs who made their decisions alone. They attributed this finding to the subjects’ fear of being evaluated negatively in case the chosen ambiguous alternative leads to undesirable outcomes. Muthukrishnan, Wathieu and Xu (2009) obtain a similar result. In their study, subjects who anticipated to be informed in the presence of others about the true probability of winning a prize in an ambiguous gamble, were more ambiguity averse, than subjects who anticipated to be informed in private. Trautmann, Vieider and Wakker (2008) report results of an experiment in which the subjects’ preferences where kept unknown to the experimenters, so the possibility of a negative evaluation by others could be completely ruled out. This treatment significantly decreased ambiguity aversion, supporting further the interpretation proposed by Curley et al. (1986). Although all three studies involved individual decisions their results suggest that the interaction with others, either before an individual decision or as part of group decision making procedure, could affect the DMs’ attitudes to ambiguity.

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Keller, Sarin and Sounderpandian (2009) compared the willingness of individuals and dyads to pay for risky and ambiguous gambles. Dyads tended to be more risk averse than their individual members, but there was no difference with respect to ambiguity attitudes. Their interesting study is limited in a number of important ways. First, they only studied dyads. More importantly, their design did not allow them to distinguish between the effects of information sharing and the need to aggregate individual preferences into a group decision. Finally, they did not study systematically how prior individual ambiguity-preferences (like aversion, neutrality or seeking) are aggregated into a group decision and how these attitudes change in this process.

1.1 The Present Study We conducted a laboratory experiment in which DMs made binary choices between sure amounts of money and different risky and ambiguous gambles. We distinguish between individual decisions, individual decisions made after exchanging information with others, and group decisions. This distinction allows us to disentangle two effects often confounded in studies of group decisions. The first is the influence of discussing decisions with others and exchanging information and opinions (see Trautmann and Vieider (2011) for a comprehensive discussion of social influence processes during group interactions). This factor affects both group decisions and individual decisions after a group discussion. The second is the process of aggregation of individual preferences into a group decision and it affects only the group decision. We also examine the payoff sharing arrangement among the group members. In some treatments the outcome of a group decision affected all individuals identically i.e., the group shared a “common fate”. In other situations the outcome of a group

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decision varied across the individual members. Wallach and Kogan (1964) argued that an essential component for the emergence of a “shared responsibility” is that consequences of the group decisions are equally shared by all members and no member can escape the consequences of a bad decision. Following this line of reasoning, we hypothesized that the nature of the payoff sharing arrangement will influence the degree of responsibility individuals feel for the group decision and thus affect risk and ambiguity attitudes. Sutter (2009) found that individuals invested higher amounts of money in a risky investment if they shared their payoffs with other subjects, providing support for this hypothesis for the case of risk. Further evidence is provided by Charness and Jackson (2009), who showed that responsibility for the payoff of another person significantly influenced subjects’ decisions to take strategic risks in a coordination game. Accordingly, we distinguish between four different decision settings each of which has real-life counterparts: a) Group decisions with shared consequences: The decision is made by a group of individuals and all group members experience the same consequences. Consider for example a group of partners deciding whether to expand their business overseas or not. The decision is made by all partners and they all bear its financial consequences whether they are positive or negative. b) Group decisions with individual consequences: The decision is made by a group of individuals but this decision leads to different consequences for each member. For example, a group of franchisees can decide jointly on a common marketing strategy but, due to the particular circumstances of each franchisee, they may end up with different outcomes.

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c) Individual decisions after social interaction with shared consequences: The decision is made by an individual, only after consulting with others. Consider, for example, a senior executive who has the authority to make decisions independently but consults with other members of his organization before deciding. Although the final decision is made by an individual its consequences affect everyone in the company. d) Individual decisions after social interaction with individual consequences: The decision is made by an individual DM who solicits advice from external consultants. Thus, although the decision has benefited from sharing information the ultimate decision made has no effect on the individuals giving advice.

2. Experimental Method 2.1 Experimental Tasks DMs in our experiment (individuals or groups) made choices between sure amounts of money and 15 two-outcome gambles. Each risky (ambiguous) gamble offered the possibility of winning $20 with probability p (range of probabilities p ± ∆), or receiving $0. Gambles differed from each other with respect to the probability of winning p (p = 0.20, 0.35, 0.50, 0.65 and 0.80) and the level of imprecision ∆ (∆ = 0, 0.05, 0.10, 0.20, 0.30, and 0.50) of the probabilities. Not all possible combinations of p and ∆ were implemented: We had 5 different gambles designed around p = 0.50 that offered subjects the possibility of winning $20 with probabilities 0.50 (∆ = 0), 0.45 - 0.55 (∆ = 0.05), 0.40 - 0.60 (∆ = 0.10), 0.20 - 0.80 (∆ = 0.30) and 0 - 1.0 (∆ =0.50), respectively. Probabilities p = 0.20 and 0.80 were only paired with 4 values of ∆ (0, 0.05, 0.10, 0.20), and probabilities p = 0.35 and 0.65 were only paired with ∆ = 0.

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All choices were presented in the form of a “price list”. Each price list consisted of a number of binary choices (15 or 19 depending on the gamble) between the gamble and increasing sure amounts of money (ranging from either $0.50-$7.50; $1.00 - $19.00 or $12.50 - $19.50 and increasing either in $0.50 or $1.00 increments) such that for the first decision a DM should always prefer the gamble and for the last decision always prefer the sure amount of money. The 15 gambles (and their respective price lists) were presented in random order. We presented one of the price lists (p = 0.50, ∆ = 0) twice to test for consistency. Table 1 summarizes the 15 gambles and the price lists used as stimuli. Examples of price list for risky and ambiguous gambles can be found in appendix A. In addition to the 15 price lists, we also included the two classical Ellsberg tasks in the study. We did not find a significant difference between individuals and groups for either of the two tasks. We provide descriptions of the Ellsberg tasks and a brief overview of our findings in appendix B. Insert Table 1 about here We inferred certainty equivalents (CEs) for each gamble from the switching point from preferring the gamble to preferring the sure amounts on each price list. A DM with monotonic preferences for money should have a unique switching point between the two alternatives. We defined the CE for a particular gamble as the midpoint of the switching interval. For example if on a particular price list a DM preferred the gamble over all sure amounts of money ≤ $8 and the sure amount over the gamble for all amounts ≥ $9 we assume that the CE is ($8.00 + $9.00) / 2 = $8.502,3.

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In 16 (out of the 6800 price lists = 0.2%) cases subjects had multiple switches. In these cases we use the first (lower) switching points on the price list to calculate the CEs. 15 of these 16 cases were caused by three individuals who had multiple switches on several price lists. To test for the robustness of our

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To facilitate the decision process subjects were offered the option of using computer-assistance in making their decisions. The computer assistance automatically filled in all choices located on the price list above the choice for which a subject preferred the sure amount of money over the gamble. Analogously, the computer assistance filled in the choices below the choice for which a subject preferred the gamble over the sure amount of money. For example, if a subject indicated a preference for $10 over the gamble the computer-assistance automatically determined that she would also prefer all sure amounts > $10. Similarly if a subject indicated a preference for the gamble over $9 the computer assistance automatically determined that she also prefers the gamble over all sure amounts < $9. Used effectively the computer assistance allowed subjects to complete a particular price list with only two clicks by indicating her switching point. Subjects could deactivate the computer assistance at any time they wished.

2.2 Subjects We recruited a total of 240 undergraduate students from a large east coast university (90 male, 150 female) by an e-mail announcement. Students varied widely with respect to their majors. Average age of the subjects was 20.7 years. All sessions were run at a behavioral laboratory in April 2009. Subjects were paid a $5 show-up

results we also run our analysis excluding those subjects and their groups. This has no influence on the significance of any of our results. 3 In 253 (out of the 6800 price lists = 3.7%) cases decision makers preferred either the gamble over all sure amounts (176 cases = 2.6%) or all sure amounts over the gamble (77 cases = 1.1%) and never switched between the two. To calculate a CE in these cases, we assume that the decision maker would have switched at the next item that could have been listed on the price list. For example if a decision maker preferred a gamble to win $20 with p=0.20 over all amounts between $0 and $7.50 (the upper end on this price list) we assume that the decision maker would have switched for the sure amount of $8.00 and infer the CE to be $7.75 (the midpoint between $7.50 and $8.00). To test for the robustness of our results we also run our analysis excluding those subjects and their groups. This has no influence on the significance of any of our results.

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fee plus what they won (individually or in groups) during the experiment and earned on average $23.2.

2.3 Experimental Design Subject were randomly assigned to one of the 5 experimental treatments summarized in table 2. The experiment consisted of two stages (individual and group decision making) in treatments “GD(shared)”, “GD(shared; counterbalanced)” and “GD(separate)” and of three stages (individual decisions, group discussion and second round of individual decisions) in treatments “IDIN(shared)” and “IDIN(separate)”. Insert Table 2 about here At each stage subjects made decisions for all 16 (15+1 repeated) price lists. In all but one treatment subjects started the experiment with the individual decision making stage. This stage was followed by a group stage and in treatments “IDIN(shared)” and “IDIN(separate)” by another round of individual decision making. To control for possible order-effects, we ran a treatment “GD(shared; counterbalanced)” where we reversed this order and asked subjects to make their decisions first as a group and then individually. To determine final payment for subjects we employed the random incentive system (Starmer & Sugden, 1991; Hey & Lee, 2005). One of the choices made at each stage (except the group discussions in treatments “IDIN shared” and “IDIN separate”) was randomly selected at the end of the experiment and subjects were paid according to their decisions. Depending on their stated preference they either received the sure amount of money, or played the chosen gamble (by a random draw from a real urn filled with red and black chips). For all gambles, drawing a red chip resulted in winning the $20 and drawing a black chip in winning nothing. As explained to

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subjects in the instructions, all urns contained a total of 100 red and black chips in a proportion corresponding to the characteristics of the chosen gamble. For example, a gamble with p = 0.50 and ∆ = 0.10 was represented by a draw from an urn containing 100 chips in total where 40 - 60 were red and the rest black. We chose this procedure in order to make the characteristics of the gambles and the resolution of uncertainty as vivid as possible for subjects4. Whereas the individual decision making stage was identical in all treatments, the group stage varied across treatments in the following way: Treatment “GD(shared)” (Group decisions with shared outcomes): After finishing the first round of individual decisions, subjects were randomly assigned to groups of three and completed the same tasks in the groups. Group members had to make a joint decision about how to fill in the price lists. They were allowed to discuss their choices in a face to face interaction as long as they wished before making one joint decision. Disagreements were resolved by discussing the problem and, if necessary, by a majority vote. Subjects were informed that their payoffs for the group stage (independent of the payoff for their individual decisions) would be determined according to one randomly selected choice the group made. All group members were paid according to the group decision. If the group chose the sure amount each member received this amount. If the group chose the gamble, the gamble would be played once and each member received either the winning prize of $20 or nothing. Treatment “GD(shared; counterbalanced)” (Group decisions with shared outcomes and reversed order): The treatment was identical to “GD(shared)” but the

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The procedure had the potential disadvantage of introducing concerns about a biased urn and thus possibly increase aversion towards ambiguity. To alleviate this concern, subjects were informed that the proportion of red and black chips was -within the parameters of the gambles- determined purely by chance and they had the possibility of inspecting the urns after the payment had taken place (see also Curley et al., 1986 who did not find a significant effect of ruling out such potential concerns).

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order in which individual and group decisions were made was reversed. Subjects were assigned to groups of three and completed tasks as a group first, followed by the same tasks individually. Treatment “GD(separate)” (Group decisions with separate outcomes): This treatment differs from treatment “GD(shared)” only in the way final payoffs for the group stage was determined. At the end of the experiment one choice made during the group stage was selected randomly and the group members paid according to their group decision. Either they all received the sure amount corresponding to this choice, or the gamble was played separately for each group member. Thus, the final payoffs of the members could be different, as some won the gamble while others did not. Treatment “IDIN(separate)” (Individual decisions after group interaction with separate outcomes): After finishing their first round of individual decisions, subjects were assigned to groups of three. Group members worked through the same tasks as at the individual stage, but the group decisions did not affect their final payoffs. Subjects were told that the group stage only served to expose them to the other group members’ opinions which they could take into account when making individual decisions later on. Subjects were allowed to discuss their decisions freely, and as long as they wished. After the group stage, each group member completed, again, all the tasks individually with the understanding that this second round of individual decisions count towards their final payoff (on top of earnings bases on the first round). The final payoffs for this stage were determined by choosing one decision for each group member separately and either playing out the gamble or paying the sure amount of money depending on the subject’s decision. Treatment “IDIN(shared)” (Individual decisions after group interaction with shared outcomes): This treatment differs from treatment “IDIN(separate)” only in the

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way final payoffs for the third stage was determined. One choice of a randomly determined group member was randomly selected for the whole group. Depending on the decisions the group member made in the round of individual decisions for this choice problem, the corresponding gamble was played out and each group member received either $20 or nothing, or the sure amount was credited to all group members. Thus, payoffs were identical for all members of the group.

2.4 Procedure Subjects were welcomed to the lab, instructed about the general procedure of the experiment and assigned to an individual computer. All instructions were presented to subjects on their computer screens, and a hard copy of the instructions was available for reference5. The software included an introduction of the tasks subjects were asked to complete, and an explanation of how to use the software to make decisions. To ensure that all subjects fully understood the instructions, they were required to pass four quiz questions before being allowed to start the experiment. Subjects were also encouraged to ask questions at any time they wished. After all subjects completed the price lists individually, the computer instructed them to move to their “group” computers which were located in the same room (to avoid inter-group communication the group computers were positioned at different corners of the room). All three group members were seated in front of one monitor and one of them was assigned to enter the group decisions. In treatments “GD(shared), GD(shared; counterbalanced) and GD(separate)” the experiment ended after the second stage and all group members were paid and debriefed. In treatment “GD(shared; counterbalanced)” all 3 subjects started the experiment at their group

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A copy of the instructions can be found can be found in the supplementary material.

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computers, and then moved to the individual computers. In treatments “IDID(shared)” and “IDID(separate)” subjects returned to their individual computers after the group stage, and repeated the same tasks individually. Upon completion of the task, subjects were debriefed and paid.

3. Results 3.1 Reliability To measure the reliability and consistency of the subjects’ decisions we calculated the Mean Absolute Difference (MAD) between the two CEs obtained from the replicated gamble and its price list (p = 0.50, ∆ = 0). Groups made more reliable decisions than individuals (MAD = 0.34 for groups compared with MAD = 0.91 for individuals; aggregated over all three group treatments). We also found that individual decisions made after group discussions are more reliable (MAD = 0.70) than those made before (MAD = 1.00). In the subsequent analysis we averaged the two CEs obtained from the repeated gamble leaving us 15 observations for each individual/group at each stage of the experiment. 3.2 Monotonicity in probabilities Violations of monotonicity are very common (Birnbaum, 1992; Birnbaum, Coffey, Mellers & Weiss, 1992; Birnbaum & Sutton, 1992; Charness et al., 2007). Birnbaum (1992) used a procedure similar to ours to elicit CEs and found that “70% of the subjects showed at least one violation of monotonicity and 50% of the subjects violated monotonicity more often than they satisfied it” (p.312). We find that for 173 of the 240 individual subjects (72%) in all five treatments (excluding stage III decisions) and 39 of the 45 groups (87%) in the three group treatments, monotonicity

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in

p

was

fully

satisfied

and

we

observed:

CE p = 0.2 ≤ CE p = 0.35 ≤ CE p = 0.5 ≤ CE p = 0.65 ≤ CE p = 0.8 .6 Consistent with the results of Charness, Karni and Levin (2007) groups showed less violations of monotonicity than individuals. 3.3 Group vs. Individual Decisions Table 3 shows the mean individual and group CEs for the 15 gambles (risky and ambiguous) in treatments “GD(shared), GD(shared; counterbalanced) and GD(separate)”. Insert Table 3 about here 3.3.1 Risk attitudes For all probability levels p>0.20, the means of individual- and group CEs of risky gambles were lower than the gambles’ expected values which indicates risk aversion. For p = 0.20, there was no systematic difference between the mean of group and individual CEs and the gamble’s expected value. Group CEs were consistently higher than individual CEs indicating less risk aversion in groups. A 5 (probability level) X 2 (individuals vs. groups7) X 3 (treatment) mixed ANOVA (N=45) revealed that the difference in CEs for risky gambles between individuals and groups was significant, (F[1,42]=11.78, p=0.001). It also showed a significant effect of probability levels on CEs, (F[4,168]=1397.34, p0.10 for all interactions).

6 Most violations of monotonicity are caused by comparisons between CEs obtained from gambles with similar probabilities. If we exclude gambles with p = 0.35 and p= 0.65 from the analysis, almost all CEs (239 individuals and 45 groups) are monotonic in p. 7 Individuals are represented by the mean CE of the three group members’ individual decisions.

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3.3.2 Ambiguity attitudes We computed ambiguity premiums (APs) for each of the 10 ambiguous gambles by subtracting the CE of the ambiguous gamble from the CE of the risky gamble with the same probability level8. Ambiguity premiums greater than (equal to, smaller than) zero indicate ambiguity aversion (neutrality, seeking). We computed the proportion of individual and group decisions which exhibited a particular ambiguity attitude (seeking, neutral, averse) based on this measure, and we classified each DM according to the ambiguity attitude he/she exhibited for the majority of the 10 ambiguous gambles. A DM was classified as ambiguity seeking (neutral, averse) when 6 or more of the DM’s decisions were ambiguity seeking (neutral, averse). About one third (31% of the groups and 35% of the individual DMs) were classified as ambiguity averse; 20% of the groups were ambiguity neutral compared to 11% of the individuals and 8% of the individuals, but none of the groups, were ambiguity seeking; 49% of the groups and 46% of the individuals did not exhibit a dominant ambiguity attitude. Table 4 presents mean ambiguity premiums and the distribution of ambiguity attitudes for each of the 10 ambiguous gambles for individuals and groups across all three conditions. Insert Table 4 about here With only three exceptions, mean individual and group ambiguity premiums were strictly positive indicating ambiguity aversion. A 10 (gambles) X 2 (individuals9 vs. groups) X 3 (treatments) mixed ANOVA (N=45) with ambiguity premiums as the 8

For all 10 ambiguous gambles, ambiguity premiums were positively correlated with risk premiums (mean r=0.50 for groups and mean r=0.42 for individuals). Previous studies have found mixed result concerning the correlation of risk and ambiguity attitudes. Cohen, Jaffray, & Said, 1985, Curley et al., 1986 and Kuhn, & Budescu 1996 report no correlation whereas Lauriola and Levin (2001), Lauriola, Levin and Hart (2007) and Kocher and Trautmann (2010) find risk and ambiguity attitudes to be positively correlated. 9 Individuals are represented by the mean AP of the three group members’ individual decisions.

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dependent variable did not show a significant difference between individuals and groups (F[1,42]=0.23, p=0.64). Ambiguity premiums were also not significantly different across the three treatments (F[2,42]=0.70, p=0.50). Naturally the ambiguity premium varied significantly across gambles (F[9,378]=14.2, p0.09 for all interactions). The classification of decisions as either ambiguity seeking, ambiguity neutral or ambiguity averse allows for a more detailed analysis. It is remarkable that for all levels of p and of ∆ the proportion of ambiguity neutral decisions was higher for groups than for individuals (table 4). This difference between individuals and groups was significant according to a Wilcoxon Signed-ranks Test (WST), N=45, z=4.41, p