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Who follows the crowd—Groups or individuals?
Journal of Economic Behavior & Organization 80 (2011) 200–209
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Who follows the crowd—Groups or individuals?夽 René Fahr a,∗ , Bernd Irlenbusch b,1 a b
University of Paderborn, and IZA, Germany University of Cologne, London School of Economics, and IZA, Germany
a r t i c l e
i n f o
Article history: Received 21 July 2008 Received in revised form 20 March 2011 Accepted 22 March 2011 Available online 31 March 2011 JEL classification: C91 C92 D70 D8 Keywords: Information cascades Herding Group behaviour
a b s t r a c t In games of social learning individuals tend to give too much weight to their own private information relative to the information that is conveyed by the choices of others (Weizsäcker, 2010). In this paper we investigate differences between individuals and small groups as decision makers in information cascade situations. In line with results from social psychology as well as results on Bayesian decision making (Charness et al., 2006) we find that groups behave more rationally than individuals. Groups, in particular, are able to abandon their own private signals more often than individuals when it is rational to do so. Our results indicate that the intellective part of the decision task contributes slightly more to the superior performance of groups than the judgmental part. Our findings have potential implications for the design of decision making processes in organisations, finance and other economic settings. © 2011 Elsevier B.V. All rights reserved.
1. Introduction The inclination of humans to follow the crowd is a well documented phenomenon (see for example Surowiecki, 2005). The recent financial crisis, for example, reminded us forcefully that so-called prediction markets, also known as information markets or event futures (Wolfers and Zitzewitz, 2004), where participants trade in contracts whose payoffs depend on unknown future events, might heavily fail when decision makers base their judgement on observed behaviour of other market participants. Herding is likely to impede the efficiency of prediction markets since information aggregation can be significantly reduced (Ray, 2006). Economists have rationalised such behavioural patterns by considering social learning games, in which externalities purely emerge through information deduced from observed actions of others.2 In such games it can indeed be individually optimal to follow the behaviour of previous decision makers, “the herd”, irrespective of private informa-
夽 We are grateful to Jörg Oechssler, Georg Weizsäcker, two anonymous referees and seminar participants in Bonn, Cologne, Innsbruck, Konstanz, and Paderborn for providing valuable comments. Behnud Djawadi and Evgenij Pechimenko programmed the experimental software and together with Anastasia Danilov and Andreas Staffeldt assisted when running the sessions. Support by the Deutsche Forschungsgemeinschaft through grant IR 43/1-1 and through financing the lab at the University of Cologne through the Leibniz-Award to Axel Ockenfels is gratefully acknowledged. ∗ Corresponding author at: Department of Management, University of Paderborn, Warburger Str. 100, D-33098 Paderborn, Germany. Tel.: +49 0 5251 60 2090; fax: +49 0 5251 60 3550. E-mail addresses: [email protected] (R. Fahr), [email protected] (B. Irlenbusch). 1 Department of Management, University of Cologne, Albertus-Magnus-Platz 50923 Köln, Germany. Tel.: +49 0 221 470 1848; fax: +49 0 221 470 1849. 2 Other explanations of herd behaviour are based on payoff externalities, like herding of fund managers in models of reputational herding (for example, Scharfstein and Stein, 1990), or herd behaviour of depositors in bank runs (for example, Diamond and Dybvig, 1983). 0167-2681/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jebo.2011.03.007
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tion (Bikhchandani et al., 1992). Experimental studies on social learning games, however, provide convincing evidence that individuals tend to herd less than would actually be rational since they seem to give excessive weight to their own private information relative to the information that is conveyed by the choices of others (Nöth and Weber, 2003; Goeree et al., 2007; Weizsäcker, 2010). The aim of the present paper is to investigate into the behavioural differences between individuals and small groups as decision makers in social learning games. In particular we are interested in potential differences regarding the degree of rational behaviour and the overemphasis of private information. Such a comparison is important since small groups as decision-making entities are at least as widespread as individuals in business and economic environments. Situations that resemble social learning games occur in many contexts which involve a sequential flow of information revealed through actions by others. Most of the literature contributes to herding behaviour in banking and finance (recent studies include Drehmann et al., 2005; Alevy et al., 2007). Hirshleifer and Teoh (2003) provide a comprehensive review of herd behaviour in capital markets. In the labour market context, hiring decisions and the duration dependence of unemployment can be explained by rational herding (see Kübler and Weizsäcker, 2003; Oberholzer-Gee, 2008). Other examples of rational herding are strategic business decisions like product choice decisions and location choices for bank branches (Bikhchandani et al., 1998). In these situations, decision makers are frequently constituted by small groups rather than by individuals. Investment decisions, for example, are often taken by financial expert groups and not by an individual alone. In the consumer context we observe joint decisions by households each consisting of several members rather than by individuals. While small groups research is a viable research area in social psychology (see Levine and Moreland, 1998; Kerr and Tindale, 2004, for reviews), only recently the economic literature has started to investigate differences in decision making of groups and individuals, examples including Cason and Mui (1997), Bornstein and Yaniv (1998), Cox (2002), Kocher and Sutter (2005), Charness et al. (2006), Rockenbach et al. (2007), and Feri et al. (2010). Charness et al. (2006) investigate a simple decision task under risk. Optimal decision making requires Bayesian updating. They find that a substantial number of individuals who, when making their decisions in isolation, choose first-order stochastically dominated alternatives. This tendency diminishes when the decisions are taken by a group of individuals suggesting that groups are the more rational decision makers. With the exception of this study most of the economic literature on group decisions investigates strategic interaction games and provide mixed evidence on the question whether groups or individuals are the more rational decision makers. Kocher and Sutter (2005) compare decisions by individuals and groups in a beauty contest game. They provide the important result that groups are not better decision makers per se but they seem to learn faster in games in which the mutual level of reasoning is decisive. Cox and Hayne (2006) investigate bidding behaviour of groups in common value auctions. Decisions of groups are found to be less rational compared to individuals when each member of a group has distinct information. The significant difference with respect to rational behaviour disappears when group members have common information. Bone et al. (1999), and Rockenbach et al. (2007) investigate group decisions under risk. Both papers find little support for the hypothesis that group decisions are more consistent with expected utility theory than individual decisions. To our best knowledge the question of differences between decisions taken by a small group compared to an individual in social learning games has not been investigated so far. In particular, it is an open question whether groups or individuals are more inclined to “follow the crowd”. The present paper approaches this issue by comparing decisions of group players with decisions of individual players in a standard experimental social learning game introduced by Anderson and Holt (1997). Individual players are provided with private signals drawn from an unobserved urn. They publicly make predictions in sequence and are paid if they correctly guess which of two urns was used. In such a setting rational cascades can occur, i.e., if initial decisions coincide, then it is rational for subsequent players to follow the established pattern, regardless of their private signal. The new feature in our experiment is an additional group player consisting of three participants. This group player is matched with an individual player and receives the same signal as the individual does. Since the individual player and the group player are in exactly the same decision situation we are able to directly compare their choices. We find that groups are more rational than individuals and are more willing to abandon their own signal in a cascade. As a consequence group players earn higher payoffs than individual players. In a second “full information” treatment, in which players are able to observe the history of private signals, groups behave slightly more rational than individuals. The rationality premium for groups is smaller in this full information treatment than in the private information treatment indicating that the superior performance of groups in the social learning game is driven by the judgmental task element and the intellective task component of the decision task. Our results have important implications for the design of decision making processes in organisations, finance and other economic settings, i.e., whether decision making in certain situations should be entrusted to groups or individuals. In the next section, we describe the theoretical background and the experimental set-up. Section 3 introduces our hypotheses on groups’ behaviour in social learning games by particularly drawing on the findings from social psychology. Our results are presented in section 4 and section 5 concludes. 2. Theory, experimental design and procedure 2.1. A benchmark model of decision making in a social learning game We consider a simple game of social learning as described, for instance, in Anderson and Holt (1997), Alevy et al. (2007) and Dominitz and Hung (2009). There are two possible states of nature ˝ = {A, B}, with the true state denoted by ω ∈ ˝. Both states are equally likely to occur with probabilities Pr(A) = Pr(B) = 1/2. 6 players sequentially take binary decisions, a
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or b, each after receiving a binary private signal s ∈ {sA , sB }. Signals are independently drawn from a distribution depending on ω. If ω = A the distribution is Pr(sA |A) = 2/3 and Pr(sB |A) = 1/3. Analogously, if ω = B the distribution is Pr(sA |B) = 1/3 and Pr(sB |B) = 2/3. Along with her private signal s, each player at the decision node j observes the history of all previous decisions Hj−1 = {h1 , . . ., hj−1 }. The payoff of a decision a or b that matches the true state of nature is given by (a|A) = (b|B) = 1 and otherwise (a|B) = (b|A) = 0. Let us assume that it is common knowledge that all players update their beliefs about the probabilities of ω ∈ according to Bayes’ rule. Supposing that s1 = sA , Bayes’ rule implies Pr(ω = A|s1 = sA ) =
Pr(sA |A)Pr(A) Pr(sA |A)Pr(A) + Pr(sA |B)Pr(B)
=
2 . 3
(1)
Analogously, one obtains Pr(B|sB ) = 2/3 and Pr(A|sB ) = Pr(B|sA ) = 1/3. Given that s1 = sA the expected payoff of the decision a, (a), exceeds that of a decision b, (b), and to maximise expected payoff the first player will decide a. If the second player observes the decision of the first player and also receives a signal s2 = sA , updating according to Bayes’ rule yields 2
Pr(ω = A|H1 = a, s2 = sA ) =
Pr(sA |A) Pr(A) 2 2 Pr(sA |A) Pr(A) + Pr(sA |B) Pr(B)
=
4 . 5
(2)
This already shows that two consecutive identical decisions yield a posterior probability of 0.8. Even if the third player receives a private signal sB , the posterior probability for state A would be given by Pr(ω = A|H2 = a, a, s3 = sB ) = 2/3. Thus, the third decision maker should follow the herd and choose a regardless of her own signal. In the example above we call the decisions of the first two players informative for subsequent players. The decision of the third player is not informative since he has to choose a irrespective of his signal. In this situation rational behaviour can be represented by a choice heuristic based on a counting rule (Anderson and Holt, 1997; Goeree et al., 2007). Define the net number of informative a decisions by = (# of informative a decisions) − (# of informative b decisions). An A-cascade, in which the decision a is rational regardless of one’s own signal, occurs if = 2. Analogously a B-cascade occurs if = –2. 2.2. Experimental design and procedure Our experimental design closely followed the seminal experiment by Anderson and Holt (1997).3 In particular, the two states of nature were represented by two urns containing two black and one red marble (urn A) and one black and two red marbles (urn B). In the beginning of each round one urn was randomly selected but remained hidden to the subjects. 6 players chose sequentially. The decision order was determined at random in each round. Before making his choice a player received a (private) signal in the form of a marble, which was randomly drawn from the three marbles in the selected but hidden urn. Two treatments were conducted. In the private information treatment (PIT) a player saw all previous decisions in the sequence before making his own choice. In the full information treatment (FIT) all signals received by players in the sequence before are revealed to the current decision maker.4 In FIT cascades cannot arise since all signals are informative. In addition to the sequential decisions of the 6 individual players in each round we observed one decision by a group player. The one group player consisted of three subjects. After a group discussion, members had to come up with an unanimous decision (which was not included into the decision history visible to subsequent players). The group player was matched to one individual player. This matching remained fixed throughout the whole session, i.e., for all rounds. We will refer to the two decisions by the individual player and by the matched group player as the focal decision pair in this round. The respective individual player is called the focal individual player. Thus, we elicited 15 focal decision pairs in each independent observation. Focal decision pairs are not necessarily equally distributed among decision nodes since their positions in the decision sequences are determined by the random sequence position of the focal individual player in the respective round. The group “shadowed” the focal individual player in the sense that the group player faced exactly the same strategic situation including the same information as the matched individual player. To be precise, in PIT all members of the shadow group observed the same history of preceding choices and received the same (private) signal about the urn as the matched individual player did. In FIT all members of the shadow group observed the same history of signals and received the same own signal as the matched individual player did. To make the two treatments as comparable as possible we used the same sequences of signals and the same positions of focal decision pairs in a sequence, i.e., for each observation in PIT there is one “mirror” observation in FIT with the same sequences of signals and the same positions of the focal decision pair (focal individual player and shadow group) within the decision sequences. The experiment was conducted at the Cologne Laboratory for Economic Research at the University of Cologne in July 2006, October 2006, and January 2009. 216 subjects participated in the 24 sessions (12 for each treatment). One session consisted of 15 rounds. Subjects were recruited by the online recruiting system ORSEE (Greiner, 2004) and were allowed to participate
3 We are aware that using the model of Anderson and Holt (1997) creates some problems for the analysis, e.g., tie-breaking assumptions are necessary. When designing the experiment we felt, however, that it would be good to be comparable to the extensive literature that uses the Anderson and Holt (1997) framework. Additionally, we had the feeling that an ex ante probability of 0.5 substantially simplifies the setting for the participants. See Smith and Sørensen (2000) and C¸elen and Kariv (2004) for extensions of the model. 4 We are grateful to an anonymous referee for suggesting this treatment (FIT).
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in one session only. About half of the students were studying economics and business administration. All 9 subjects in one session received the same introductory talk. In the instructions we referred to the decisions as guesses and to the shadow group as an “additional player.”5 Whether a participant acted as an individual player or a group member was randomly determined after the introduction. The random draw of the marble, the current position in the decision sequence and the history of decisions of preceding players in the current round were shown on the computer screen. Decisions on urn A or urn B were entered into the computer mask. A screenshot is displayed in Fig. A1 in appendix. Participants representing the group player were requested to discuss their choice after they saw the animation of the marble draw on their individual screens.6 When returning to their cubicles they individually had to enter the decision agreed upon. If the entered decisions of the individual group members were not the same they had to discuss their decision again. At the end of a round when all subjects had taken their decisions participants got to know the actually selected urn for that round and they were informed about their payoffs. Subjects earned 1 Thaler for a correct guess in a round which at the end of the experiment was converted to 1.20 Euro. Each member of the shadow group earned 1 Thaler for a correct guess of the group. In addition subjects were paid a show-up fee of 2.50 Euro at the end of the experiment. On average a participant earned in total 17.30 Euro. Neither did participants learn the identity of each other nor could they infer whose turn it was to decide at a certain decision node. Only the members of the group interacted in face-to-face communication. A session lasted for about 90 min.
3. Hypotheses on groups’ behaviour Group performance and group decision making is an extensively studied topic in social psychology. Although there is no general consensus that groups are better decision makers than individuals, several studies point into this direction. As Kerr and Tindale (2004, p. 634) put it: “Although groups tend to outperform individuals in many domains, groups also can fall prey to the same heuristic-based biases found at the individual level.” One main finding from social psychology is that the performance of groups compared to individuals is to a large extent influenced by task characteristics (Hastie, 1986). In intellective tasks, in which the correct solution is demonstrable and can be communicated to other group members, the group performance often approaches or even exceeds the performance of the best group member (Tindale et al., 2003; Levine and Moreland, 1998; Laughlin and Ellis, 1986). Laughlin et al. (2002), for example, show that in a highly intellective task of solving letters-to-numbers problems four-person groups perform better than the best of an equivalent number of independent individuals. Evidence that groups outperform individuals in decisions mimicking monetary policy decisions is also provided in Blinder and Morgan (2005). Experiments on collective induction, i.e., cooperative search for descriptive, predictive, and explanatory generalisations, rules, and principles (cf. Laughlin, 1999), show that groups are fairly effective in correctly retaining information and discarding incorrect hypotheses on general principles or rules (Kerr and Tindale, 2004). In FIT the task is purely intellectual since decision makers do not have to speculate about the rationality of the previous players to infer their private signals from their actions. The decisions in PIT can to a large extent be considered as an intellective task: If one is willing to assume common knowledge of rational players, one can deduce most of the signals corresponding to previous informative decisions by applying Bayes’ rule and iterative reasoning. If one member of the group knows the correct arguments how to do this he or she can demonstrate the reasoning to his or her group members. This argumentation is also in line with the findings of Charness et al. (2006). The application of Bayes’ rule in PIT, however, is based on the beliefs of the decision makers about whether previous players actually behaved rationally. This constitutes a judgmental element in the players’ decisions. In judgmental tasks, defined as evaluative, behavioural, or aesthetic judgements, groups often perform better than the average individual member (Levine and Moreland, 1998; Tindale et al., 2003).7 Building on these findings from social psychology and economics we derive the following hypotheses: Hypothesis (“Rationality” in PIT). Groups tend to behave more rational than individuals. In particular we are interested in the behaviour in cascades, i.e., in a situation, in which it is actually rational to ignore the own signal and follow the crowd:
5
The introductions were in German. A translation is provided in Appendix A. To make sure that the other subjects could not listen to the group discussion and learn about the group’s signal or their decision, we took the following measures: (1) Group members were asked to speak in a low voice. (2) A complete row of cubicles separated the cubicles of the shadow group members from the individual players (see Fig. A.2 in appendix for concrete arrangements). (3) All participants had to wear ear muffs during the whole session—of course, the members of the shadow group were allowed to take them off during group discussions (see Fig. A.2 for a photo of the ear muffs used). (4) During the waiting time subjects were allowed to individually play simple computer games to distract them from their surroundings. 7 The comparison of individual and group decisions is of course highly dependent on the decision procedure applied within the group (unanimity, plurality, majority rule, etc.). For example, if q denotes the probability that an individual has the correct answer, majority voting in the group results in a probability of 3q2 (1 − q) + q3 for obtaining the correct answer in the group. According to the Condorcet Jury Theorem (Condorcet, 1785, p. 279) the group always outperforms the individual if q > 1/2. Hastie and Kameda (2005) in fact argue that the majority rule leads to the best outcomes for truth-seeking group decision. The literature on juries discusses these issues both theoretically and experimentally (see for example, Feddersen and Pesendorfer, 1998; Guarnaschelli et al., 2000). 6
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Hypothesis (“Following a cascade” in PIT). If in an information cascade the own signal is opposed to the cascade, groups decide against their signal more frequently than individuals. The second hypothesis can only be analysed in PIT since an information cascade cannot occur in FIT. With the help of FIT, however, we will be able to obtain insights into the reasons for a potentially higher group rationality. We define the difference between the rationality percentages of the group and individuals from one independent observation as rationality premium of the group (i.e., the increase in decisions which comply with Bayesian rationality when comparing groups with individuals excluding indifference situations). As explained before, the decision task in PIT has elements of an intellective and a judgmental task while the decision task in FIT is purely intellective. If one assumes that the intellective and the judgmental components contribute additively to a potentially superior group performance in PIT, we can evaluate the relative importance of the intellective and judgmental part by comparing the rationality premiums of groups in the two treatments.8 Hypothesis (“Rationality in intellective and judgmental tasks”). Groups tend to be more rational than individuals in intellective and judgmental tasks. Thus, we expect the rationality premium to be higher in PIT than in FIT, i.e., the superior group performance in FIT might be due to a better performance of groups in intellective tasks whereas the superior performance of groups in PIT might be due to better group performance in intellective and judgmental tasks. 4. Results In the analysis we assume that in general all players believe that their predecessors decided in accordance with iterated application of Bayes’ rule.9 If the informative decisions or signals from the history together with the current (private) signal make both states of nature equally likely we call this an indifference situation. For simplicity we assume that it is common knowledge that all players follow their own signal in an indifference situation.10 If in a given history a player has unambiguously violated Bayes’ rule in PIT, for example, when he should have chosen the same decision as his predecessors irrespective of his signal but he did not, we make the assumption that it is common knowledge among all following players that the deviating player followed his private signal (for evidence supporting this assumption see Anderson and Holt, 1997; Drehmann et al., 2007; Dominitz and Hung, 2009).11 Given these assumptions, we call a decision Bayesian, if it is in line with Bayesian rationality. A situation, in which following the crowd is consistent with Bayesian rationality irrespective of the own signal, is referred to as an information cascade situation. Recall that such a situation can only occur in PIT. We call an information cascade situation a cascade dilemma if the own signal is opposed to the action suggested by the cascade. If a subject rationally decides against his or her own signal in a cascade dilemma we call this behaviour following the cascade. If a subject follows his or her signal in a cascade dilemma we denote this behaviour as a break of a cascade. Note that a break of a cascade is considered to always be informative for subsequent players because of the assumption that the respective player followed her own signal. In our statistical analysis we treat each session as one independent observation, which each comprises 15 focal decision pairs (instances). We start our analysis by concentrating on all 180 focal decision pairs of individuals and their shadow group players in PIT. A comparison of the focal decision pairs guarantees a clean ceteris paribus analysis. Recall that the experimental design ensures that the respective two players – individual and shadow group – are exactly in the same decision situation, i.e., they see the same history and the same private signal. To check for the robustness of our results in
8 Note, however, that one could argue that the difference between the decision tasks in PIT and FIT is not purely judgmental. Since information cascades cannot occur in FIT, iterative reasoning – which arguably is a more difficult intellective task, see, for example, Kübler and Weizsäcker (2004) – is only necessary in PIT but not in FIT to infer the right private signals from previous players’ actions. 9 We are grateful to a referee for pointing out that given this assumption, a finding that groups are “more rational” than individuals might (partly) be driven by systematically different beliefs of groups and individuals, i.e., groups might more strongly believe in predecessors’ ability to apply Bayes’ rule than individuals. One possible reason could be that groups are more able to interpret the actions of predecessors in a way that is in line with Bayes’ rule (whenever this is feasible). Therefore, it might be more difficult for groups to imagine that predecessors did not follow Bayes’ rule. To unambiguously control for this possibility one would need to design further experiments that also elicit the beliefs of the two player types. In an attempt to relax this definition of rationality and to allow for potential errors we followed the suggestions of Anderson and Holt (1997), Goeree et al. (2007), and others and econometrically estimated error rates in PIT by assuming a logistic distribution of independent shocks to expected payoffs. It turned out that with very few exceptions the error model predicted the decisions exactly as the model we describe here. We ran two estimates to determine two parameters, i.e. I based on the decisions of the focal individual players and G based on the decisions of the shadow group decisions. The two parameter are I and G are estimated under the restriction that the sensitivity to payoff differences across different levels of reasoning about others’ behavior is the same. It turns out that the two sensitivity parameters are indeed different, i.e., 5.95 (s.e. 0.85) and 7.74 (s.e. 0.67) indicating that the error rate of focal individuals is higher than the error rate of focal groups (the values are weakly significantly different in a one-sided likelihood ratio test: 2 -value: 3.47, p = 0.063). Details on these estimations and on additional estimations where we allow for different i for each level i of reasoning are available upon request from the authors. 10 In fact our data provide evidence in favour of this assumption. In particular we find that in all 12 sessions in indifference situations in PIT individual players follow their own signal in the majority of instances with a majority of 93:27 (Binomial test with an event probability of 1/2, p = 0.000, two-sided). 11 Note the consequences of this assumption for the application of the counting rule. Consider a history H5 = a, a, a, a, b. The decision maker at the fifth decision node obviously violates Bayesian behaviour since he finds himself in a cascade situation and should choose a irrespective of his private signal. In such a case we assume that all following players take for granted that this decision maker followed his private signal, i.e., that his signal was sB . The decisions at the third and fourth decision node are considered to be non-informative since these players have been in a cascade situation. The fifth decision again becomes informative for subsequent players. The counting heuristic after the fifth player’s action would return = 1.
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Table 1 Descriptive statistics for focal decision pairs in PIT. Decision
Total
Cascade dilemma
Indifference
Node 1 Node 2 Node 3 Node 4 Node 5 Node 6 Total Percentage
24 37 27 34[4] 38[11] 20[1] 180[16] 100.00
– – 5 6 10[1] 8 29[1] 16.11
– 10 – 7[2] 3[3] 0 20[5] 11.11
Focal individuals
Groups
Bayesian
Bayesian excl. indifferences
Bayesian
Bayesian excl. indifferences
23 37 24 31[4] 31[9] 18[1] 164[14] 91.11
23 27 24 24[2] 28[6] 18[1] 144[9] 90.00
23 37 25 34[4] 36[10] 20[1] 175[15] 97.22
23 27 25 27[2] 33[7] 20[1] 155[10] 96.88
“Total” gives the total number of focal decision pairs. “Cascade dilemma” denotes the number of cascade dilemmas faced by the focal individual players and the group players. “Indifference” denotes the number of situations in which the focal individual players and the group players are indifferent according to Bayes. “Bayesian” denotes the number of cases in which the focal individual players/group players decided according to Bayes or decided anything when they were indifferent. “Bayesian excl. indifference” denotes the number of cases in which the focal individual players/group players decided according to Bayes excluding indifference situations. Percentages are given relative to the total number of 180 focal decision pairs (or relative to the total number of 160 focal decision pairs excluding indifferences). Values in [] give the number of focal decision pairs that are preceded in their round by an unambiguous violation of Bayesian behaviour.
the subsequent analysis we also compare average behaviour of all individuals with average behaviour of the group players in PIT. To disentangle the influence of group decision making on intellective and judgmental components in the current decision task we compare the findings of PIT with those of FIT in the second subsection of this result section. If not stated otherwise statistical significances of comparisons within PIT are obtained by applying the exact Wilcoxon sign-rank test for two related samples. Comparisons within FIT and between treatments are performed by using the Mann–Whitney-U test.12 4.1. Comparison of individual and group decisions in PIT Table 1 provides a descriptive overview of cascades, indifference situations, and Bayesian behaviour for the focal decision pairs for each position in the decision sequence in PIT. By definition, in our setting cascade situations can only be observed beginning with decision node 3. The first and third players in a decision sequence cannot be indifferent. The fifth player in a decision sequence can only be indifferent if a break of a cascade occurred before. Bayesian decisions are reported including or excluding indifferences. Observation “Rationality” in PIT In PIT the average percentage of Bayesian decisions for the 12 independent observations of focal individual players is 91.11 and it is 97.22 for the group players. In fact the number of Bayesian decisions of group players is significantly higher (on average by 7.51 percent) than the one of focal individual players (z = 1.841, p = 0.039, exact, one-sided). We therefore reject the null hypothesis that the level of rationality for groups is equal or lower than the level of rationality for individuals in favour of hypothesis “Rationality” which suggests a more rational behaviour of groups.13 Observation “Following a cascade” in PIT When comparing the fractions of players following the cascade in a cascade dilemma for focal decision pairs (12 matched pairs) we find a significantly higher average fraction for groups than for individuals which supports our hypothesis on the more rational behaviour of groups in cascade dilemmas (z = 2.220, p = 0.016, exact, one-sided). The observed higher group rationality should result in higher payoffs for groups. Indeed, the average earning of group players is 11.58 Euro compared to 10.33 Euros for individual players. A Wilcoxon-test shows that groups perform significantly better and guess the right urn more often than individuals (z = 2.434, p = 0.010, exact, one-sided). To provide additional evidence for the robustness of our findings we compare for all individual players including the focal players with the group behaviour, i.e., we compare average decisions of similar but not necessarily identical situations of groups and all individuals. About one third of all individuals in cascade dilemmas trust their private signal more than the information implied by the cascade. This provides supportive evidence in favour of our second hypothesis, i.e., groups in cascade dilemmas rationally follow the cascade more often than all individuals. While 85% of the decisions of focal individuals in indifference situations are decisions complying with the private information, the percentage is 77.5% for all
12 For comparisons within PIT the Wilcoxon sign-rank test for two related samples has to be applied because the decisions of the shadow group player are not independent from the decisions of the matched focal individual (with the exception of the decision in the first round). The reason is that decisions of the focal individual in previous rounds are observed by the other individual players who in turn determine the histories that are observed by the focal decision pairs in subsequent periods. This is not the case in FIT because here only signals are observed but not decisions. When applying the Mann–Whitney-U test for the comparisons in PIT we obtain the same significances as with the Wilcoxon sign-rank test. 13 To learn more about the ability of groups to abandon their private signal – which of course is sometimes rational and sometimes not – we inspect the behaviour of focal decision pairs in more detail by differentiating between situations where players follow their own signal or deviate. Focal individuals follow their own signal significantly more often than groups (z = 1.951, p = 0.031, exact, one-sided). This tendency can be observed in indifference situations (17 out of 20 vs. 11 out of 20, z = 0.813, p = 0.25, exact, one-sided) as well as in cascades (12 out of 29 vs. 3 out of 29, z = 2.214, p = 0.016, exact, one-sided).
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Table 2 Summary of comparison of group and individual decisions in PIT. Focal individuals
Bayesian decisions [Bayesian decisions] Bayesian excl. indifferences [Bayesian excl. indifferences] Follow own signal [Follow own signal] Follow own signal in cascade dilemma [Follow own signal in cascade dilemma]
All individuals
Relation
p
Z
Relation
p
Z
> [>] > [>] < [<] < [<]
0.039 [0.043] 0.035 [0.035] 0.031 [0.047] 0.016 [0.016]
1.841 [1.825] 1.895 [1.823] 1.951 [1.719] 2.220 [2.220]
> [>] > [>] < [<] < [<]
0.004 [0.003] 0.004 [0.003] 0.195 [0.212] 0.006 [0.002]
2.517 [2.589] 2.511 [2.589] 0.904 [0.863] 2.433 [2.746]
The relation “>” (“<”) indicates that the value for groups is larger (smaller) than the value of individuals. Values in [] consider only those instances that are not preceded by an unambiguous violation of Bayesian behaviour in their round. All p-values refer to exact, one-sided Wilcoxon sign-rank tests for two related samples.
individuals which is also well above the number of 55% for groups (a detailed analysis is available from the authors upon request). In Table 2 we summarise statistical tests of differences in the percentages of Bayesian decision within a session between the group and the focal player when (i) excluding instances preceded by an unambiguous violation of Bayesian behaviour within their round (which might have confused subsequent players) and (ii) excluding instances with indifference situations. The hypothesis of higher group rationality is supported by the results presented in Table 2. The first block reports the comparisons within focal decision pairs discussed above. The second block summarises the corresponding comparisons between groups and all individuals. On average the percentage of group decisions complying with Bayesian rationality is significantly higher (by 6.6 percent) when compared to all individuals. 4.2. Disentangling the group decision effect regarding intellective and judgmental elements The fact that decisions in FIT are taken with full information about the signals reduces the decision task in FIT to a purely intellective one. When comparing the average behaviour of all individuals with the average behaviour of group players in FIT we find a significantly higher number of Bayesian decisions of groups than individuals (z = 2.986, p = 0.001, exact one-sided, Mann–Whitney-U-test). This finding that groups decide to a larger extent in line with Bayesian rationality in FIT provides additional support for our Hypothesis “Rationality”. Observation “Rationality in intellective and judgmental tasks” Comparing the decisions of all individuals and groups the rationality premium is significantly higher in PIT than in FIT (z = 1.681, p = 0.048, exact, one-sided, Mann–Whitney-U-test). To get a rough quantification of the group performance in purely intellective tasks (as in FIT) compared to judgmental and intellective tasks (as in PIT) we compare the average rationality premium in PIT with that of FIT. The average rationality premium in PIT is 5.93 percentage points compared to an average rationality premium of 3.43 percentage points in FIT. These numbers suggest that the better performance of groups in intellective tasks explains about 60% leaving about 40% to the judgmental part. 5. Conclusion The present study compares the behaviour of groups and individuals as decision makers in a social learning game. Groups turn out to comply consistently better with Bayesian rationality than individuals which is in line with previous findings by Charness et al. (2006). In particular groups rationally follow a cascade significantly more often than individuals when facing a cascade dilemma. To better understand why groups might outperform individual decision makers in social learning games we compare our finding with a situation where players can directly observe all signals in the preceding sequence. Such a decision task is a purely intellective one. Our comparison reveals that groups seem to be superior to individuals in intellective as well as judgmental tasks with a slightly higher weight on the former. For example, expert groups in financial markets might be able to infer the right information from the actions of other market participants better than individual traders. Our results potentially provide important implications for environments with scope for social learning. In particular, ceteris paribus, they might be less likely to put too much weight on their own private information. An analogous effect might also be present in consumer choice situations when comparing decisions of households consisting of one or more members. Additionally, our findings promise to be valuable for the design of organisations. When shaping an organisation and its decision making processes one can often arrange for an individual decision maker or alternatively employ a small group of people, like boards, committees, or teams, to take certain decisions. A recruiting decision, for example, might well be taken by a single personnel manager or by a hiring committee. Given our results, a hiring committee might be more inclined to reject an applicant on the basis of a longer unemployment history because the committee might correctly asses the meaning of a sequence of negative evaluations by other firms. A single recruiting specialist, on the other hand, might tend to follow
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his own impression in the job interview and thereby underemphasise the information revealed by an (unexplained) long unemployment period. Similar lines of reasoning can be applied to other strategic business decisions in which a variant of social learning is involved. In the light of our findings, it can be argued that in such situations small groups might be the better decision makers. Groups as decision entity, of course, come with the cost of involving more personnel in the decision task. Thus, the designers of organisations are likely to have to deal with this particular trade-off. Although our findings indicate that groups seem to be more rational actors in social learning environments, further research is still needed to identify the exact mechanisms that drive the results. Do groups perform in such situations like the most capable group member or do group discussions generate additional value in the group decision process? Video experiments, for example, might provide some illuminating insights regarding these questions. In our study groups are randomly formed. The question arises whether it is possible to strengthen our results by identifying specific group compositions in which group members possess certain desirable personality characteristics. It would certainly also be very interesting to investigate adequate field settings in order to confirm our results in real world environments, for example, by a comparison of group-managed or individual-managed funds. By raising these questions we hope that our study not only reports interesting findings but also initiates promising further research directions regarding the investigation of social learning by groups. Appendix A. Instructions (Original instructions were in German. They are available from the authors upon request. Differences in treatments are indicated by {PIT:. . .} and {FIT:. . .}, respectively) Figs. A1 and A2.
Fig. A1. Screenshot. The sample screenshot shows the situation in round 1, at the 3rd decision node right after a random draw of a marble from the selected urn. The original screens were in German.
Fig. A2. Cubicle arrangement and ear muffs. Cubicle arrangement in a session; individual decision makers I1 , . . ., I6 were seated in cubicles of one row and the three participants G1 , G2 G3 representing the shadow group player were seated in adjacent cubicles in a remote row. Cubicles denoted by x remained empty. All participants were wearing ear muffs.
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Basic Information • • • • • •
There are two urns, each containing 3 marbles. Urn A contains 2 black marbles and 1 red marble. Urn B contains 1 black marble and 2 red marbles. The distribution of the coloured marbles in the urns will be the same during the entire experiment. There are 6 players. The experiment consists of 15 periods. Course of a period
• At the beginning of each period one urn (urn A or urn B) is chosen with equal probability by a random generator of the computer. Players are not informed about which urn has actually been drawn. The selected urn will not change during one period. • In a randomly determined order the six players are asked one by one to guess which urn has been drawn. The order in which the six players have to state their guesses is randomly determined in each period. • Before a player states his guess, one out of three marbles is drawn with equal probability from the selected urn and it is shown to the currently deciding player. {PIT: The other players do not see the drawn marble.} • After having seen the randomly drawn marble, the currently deciding player is asked to guess whether the selected urn in this period is urn A or urn B. • The {PIT: guesses} {FIT: signals} of all previous players in one period are shown to the currently deciding player before he states his guess. • When all players have submitted their guesses about the selected urn, the period ends and the actual randomly chosen urn in this period is announced. Additional Player • In addition to the six players there is one additional player who is constituted by a group of 3 participants. • The additional player is permanently matched with one specific individual player and decides simultaneously with this player. The decision of the additional player has to be unanimous within the group. • Before the additional player decides, every member of the group is shown the same marble draw as the matched individual player as well as all the {PIT: guesses} {FIT: signals} of the other players in the current period. • {PIT: The guess of the additional player is not announced to subsequent players.} Pay offs • • • •
In case of a correct guess by a player, he is paid 1 Thaler. In case of a correct guess by the additional player, each group member is paid 1 Thaler. The exchange rate is: 1 Thaler = EUR 1.20. Every subjects is paid EUR 2.50 as a fix show up fee.
Please note: During the entire experiment it is not allowed to communicate. Please keep wearing your ear muffs during the experiment. If you have any questions, please give a hand signal. All decisions are made anonymously, i.e., none of the other participants has information about the identity of a certain decision maker. Also, the payoffs are anonymous, i.e., no participant learns the payoff of another participant. We wish you success! References Alevy, J.E., Haigh, M.S., List, J.A., 2007. Information cascades: evidence from a field experiment with financial markets profession. Journal of Finance 62 (1), 151–180. Anderson, L.R., Holt, C.A., 1997. Information cascades in the laboratory. American Economic Review 87 (5), 847–862. Bikhchandani, S., Hirshleifer, D., Welch, I., 1992. A theory of fads, fashion, custom, and cultural change as informational cascades. Journal of Political Economy 100 (5), 992–1026. Bikhchandani, S., Hirshleifer, D., Welch, I., 1998. Learning from the behaviour of others: conformity, fads, and informational cascades. Journal of Economic Perspectives 12 (3), 151–170. Blinder, A.S., Morgan, J., 2005. Are two heads better than one? Monetary policy by committee. Journal of Money, Credit and Banking 37 (5), 789–811. Bone, J., Hey, J., Suckling, J., 1999. Are groups more (or less) consistent than individuals? Journal of Risk and Uncertainty 18 (1), 63–81. Bornstein, G., Yaniv, I., 1998. Individual and group behaviour in the ultimatum game: are groups more ‘rational’ players? Experimental Economics 1, 101–108. Cason, T.N., Mui, V.-L., 1997. A laboratory study of group polarisation in the team dictator game. Economic Journal 107, 1465–1483. C¸elen, B., Kariv, S., 2004. Distinguishing informational cascades from herd behavior in the laboratory. American Economic Review 94 (3), 484–498.
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Charness, G., Karni, E., Levin, D., 2006. Individual and Group Decision Making Under Risk: An Experimental Study of Bayesian Updating and Violations of First-order Stochastic Dominance. Discussion Paper University of Santa Barbara. Condorcet, Marie Jean Antoine Nicolas de Caritat, Marquis de, 1785. Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix. Paris: l’Imprimerie Royale [fascimile edition New York: Chelsea, 1972]. Comprised of: Discours préliminaire, pp i-cxci; Essai, pp. 1–304. Cox, J.C., 2002. Trust, reciprocity, and other-regarding preferences: groups vs. individuals and males vs. females. In: Zwick, R., Rapoport, A. (Eds.), Advances in Experimental Business Research. Kluwer Academic Publishers, Dordrecht, pp. 331–350. Cox, J.C., Hayne, S.C., 2006. Barking up the right tree: are small groups rational agents? Experimental Economics 9, 209–222. Diamond Dougla, S.W., Dybvig, P.H., 1983. Bank runs, deposit insurance and liquidity. Journal of Political Economy 91 (3), 401–419. Dominitz, J., Hung, A.A., 2009. Empirical models of discrete choice and belief updating in observational learning experiments. Journal of Behavioral Economics and Organization 69, 94–109. Drehmann, M., Oechssler, J., Roider, A., 2005. Herding and contrarian behavior in financial markets: an internet experiment. American Economic Review 95 (5), 1403–1426. Drehmann, M., Oechssler, J., Roider, A., 2007. Herding with and without payoff externalities—an internet experiment. International Journal of Industrial Organization 25, 391–415. Feddersen, T., Pesendorfer, W., 1998. Convicting the innocent: the inferiority of unanimous jury verdicts. American Political Science Review 92 (1), 23–35. Feri, F., Irlenbusch, B., Sutter, M., 2010. Efficiency gains from team-based coordination-large-scale experimental evidence. American Economic Review 100 (4), 1892–1912. Greiner, B., 2004. An online recruiting system for economic experiments. 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Journal of Economic Behavior & Organization journal homepage: www.elsevier.com/locate/jebo
Who follows the crowd—Groups or individuals?夽 René Fahr a,∗ , Bernd Irlenbusch b,1 a b
University of Paderborn, and IZA, Germany University of Cologne, London School of Economics, and IZA, Germany
a r t i c l e
i n f o
Article history: Received 21 July 2008 Received in revised form 20 March 2011 Accepted 22 March 2011 Available online 31 March 2011 JEL classification: C91 C92 D70 D8 Keywords: Information cascades Herding Group behaviour
a b s t r a c t In games of social learning individuals tend to give too much weight to their own private information relative to the information that is conveyed by the choices of others (Weizsäcker, 2010). In this paper we investigate differences between individuals and small groups as decision makers in information cascade situations. In line with results from social psychology as well as results on Bayesian decision making (Charness et al., 2006) we find that groups behave more rationally than individuals. Groups, in particular, are able to abandon their own private signals more often than individuals when it is rational to do so. Our results indicate that the intellective part of the decision task contributes slightly more to the superior performance of groups than the judgmental part. Our findings have potential implications for the design of decision making processes in organisations, finance and other economic settings. © 2011 Elsevier B.V. All rights reserved.
1. Introduction The inclination of humans to follow the crowd is a well documented phenomenon (see for example Surowiecki, 2005). The recent financial crisis, for example, reminded us forcefully that so-called prediction markets, also known as information markets or event futures (Wolfers and Zitzewitz, 2004), where participants trade in contracts whose payoffs depend on unknown future events, might heavily fail when decision makers base their judgement on observed behaviour of other market participants. Herding is likely to impede the efficiency of prediction markets since information aggregation can be significantly reduced (Ray, 2006). Economists have rationalised such behavioural patterns by considering social learning games, in which externalities purely emerge through information deduced from observed actions of others.2 In such games it can indeed be individually optimal to follow the behaviour of previous decision makers, “the herd”, irrespective of private informa-
夽 We are grateful to Jörg Oechssler, Georg Weizsäcker, two anonymous referees and seminar participants in Bonn, Cologne, Innsbruck, Konstanz, and Paderborn for providing valuable comments. Behnud Djawadi and Evgenij Pechimenko programmed the experimental software and together with Anastasia Danilov and Andreas Staffeldt assisted when running the sessions. Support by the Deutsche Forschungsgemeinschaft through grant IR 43/1-1 and through financing the lab at the University of Cologne through the Leibniz-Award to Axel Ockenfels is gratefully acknowledged. ∗ Corresponding author at: Department of Management, University of Paderborn, Warburger Str. 100, D-33098 Paderborn, Germany. Tel.: +49 0 5251 60 2090; fax: +49 0 5251 60 3550. E-mail addresses: [email protected] (R. Fahr), [email protected] (B. Irlenbusch). 1 Department of Management, University of Cologne, Albertus-Magnus-Platz 50923 Köln, Germany. Tel.: +49 0 221 470 1848; fax: +49 0 221 470 1849. 2 Other explanations of herd behaviour are based on payoff externalities, like herding of fund managers in models of reputational herding (for example, Scharfstein and Stein, 1990), or herd behaviour of depositors in bank runs (for example, Diamond and Dybvig, 1983). 0167-2681/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jebo.2011.03.007
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tion (Bikhchandani et al., 1992). Experimental studies on social learning games, however, provide convincing evidence that individuals tend to herd less than would actually be rational since they seem to give excessive weight to their own private information relative to the information that is conveyed by the choices of others (Nöth and Weber, 2003; Goeree et al., 2007; Weizsäcker, 2010). The aim of the present paper is to investigate into the behavioural differences between individuals and small groups as decision makers in social learning games. In particular we are interested in potential differences regarding the degree of rational behaviour and the overemphasis of private information. Such a comparison is important since small groups as decision-making entities are at least as widespread as individuals in business and economic environments. Situations that resemble social learning games occur in many contexts which involve a sequential flow of information revealed through actions by others. Most of the literature contributes to herding behaviour in banking and finance (recent studies include Drehmann et al., 2005; Alevy et al., 2007). Hirshleifer and Teoh (2003) provide a comprehensive review of herd behaviour in capital markets. In the labour market context, hiring decisions and the duration dependence of unemployment can be explained by rational herding (see Kübler and Weizsäcker, 2003; Oberholzer-Gee, 2008). Other examples of rational herding are strategic business decisions like product choice decisions and location choices for bank branches (Bikhchandani et al., 1998). In these situations, decision makers are frequently constituted by small groups rather than by individuals. Investment decisions, for example, are often taken by financial expert groups and not by an individual alone. In the consumer context we observe joint decisions by households each consisting of several members rather than by individuals. While small groups research is a viable research area in social psychology (see Levine and Moreland, 1998; Kerr and Tindale, 2004, for reviews), only recently the economic literature has started to investigate differences in decision making of groups and individuals, examples including Cason and Mui (1997), Bornstein and Yaniv (1998), Cox (2002), Kocher and Sutter (2005), Charness et al. (2006), Rockenbach et al. (2007), and Feri et al. (2010). Charness et al. (2006) investigate a simple decision task under risk. Optimal decision making requires Bayesian updating. They find that a substantial number of individuals who, when making their decisions in isolation, choose first-order stochastically dominated alternatives. This tendency diminishes when the decisions are taken by a group of individuals suggesting that groups are the more rational decision makers. With the exception of this study most of the economic literature on group decisions investigates strategic interaction games and provide mixed evidence on the question whether groups or individuals are the more rational decision makers. Kocher and Sutter (2005) compare decisions by individuals and groups in a beauty contest game. They provide the important result that groups are not better decision makers per se but they seem to learn faster in games in which the mutual level of reasoning is decisive. Cox and Hayne (2006) investigate bidding behaviour of groups in common value auctions. Decisions of groups are found to be less rational compared to individuals when each member of a group has distinct information. The significant difference with respect to rational behaviour disappears when group members have common information. Bone et al. (1999), and Rockenbach et al. (2007) investigate group decisions under risk. Both papers find little support for the hypothesis that group decisions are more consistent with expected utility theory than individual decisions. To our best knowledge the question of differences between decisions taken by a small group compared to an individual in social learning games has not been investigated so far. In particular, it is an open question whether groups or individuals are more inclined to “follow the crowd”. The present paper approaches this issue by comparing decisions of group players with decisions of individual players in a standard experimental social learning game introduced by Anderson and Holt (1997). Individual players are provided with private signals drawn from an unobserved urn. They publicly make predictions in sequence and are paid if they correctly guess which of two urns was used. In such a setting rational cascades can occur, i.e., if initial decisions coincide, then it is rational for subsequent players to follow the established pattern, regardless of their private signal. The new feature in our experiment is an additional group player consisting of three participants. This group player is matched with an individual player and receives the same signal as the individual does. Since the individual player and the group player are in exactly the same decision situation we are able to directly compare their choices. We find that groups are more rational than individuals and are more willing to abandon their own signal in a cascade. As a consequence group players earn higher payoffs than individual players. In a second “full information” treatment, in which players are able to observe the history of private signals, groups behave slightly more rational than individuals. The rationality premium for groups is smaller in this full information treatment than in the private information treatment indicating that the superior performance of groups in the social learning game is driven by the judgmental task element and the intellective task component of the decision task. Our results have important implications for the design of decision making processes in organisations, finance and other economic settings, i.e., whether decision making in certain situations should be entrusted to groups or individuals. In the next section, we describe the theoretical background and the experimental set-up. Section 3 introduces our hypotheses on groups’ behaviour in social learning games by particularly drawing on the findings from social psychology. Our results are presented in section 4 and section 5 concludes. 2. Theory, experimental design and procedure 2.1. A benchmark model of decision making in a social learning game We consider a simple game of social learning as described, for instance, in Anderson and Holt (1997), Alevy et al. (2007) and Dominitz and Hung (2009). There are two possible states of nature ˝ = {A, B}, with the true state denoted by ω ∈ ˝. Both states are equally likely to occur with probabilities Pr(A) = Pr(B) = 1/2. 6 players sequentially take binary decisions, a
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or b, each after receiving a binary private signal s ∈ {sA , sB }. Signals are independently drawn from a distribution depending on ω. If ω = A the distribution is Pr(sA |A) = 2/3 and Pr(sB |A) = 1/3. Analogously, if ω = B the distribution is Pr(sA |B) = 1/3 and Pr(sB |B) = 2/3. Along with her private signal s, each player at the decision node j observes the history of all previous decisions Hj−1 = {h1 , . . ., hj−1 }. The payoff of a decision a or b that matches the true state of nature is given by (a|A) = (b|B) = 1 and otherwise (a|B) = (b|A) = 0. Let us assume that it is common knowledge that all players update their beliefs about the probabilities of ω ∈ according to Bayes’ rule. Supposing that s1 = sA , Bayes’ rule implies Pr(ω = A|s1 = sA ) =
Pr(sA |A)Pr(A) Pr(sA |A)Pr(A) + Pr(sA |B)Pr(B)
=
2 . 3
(1)
Analogously, one obtains Pr(B|sB ) = 2/3 and Pr(A|sB ) = Pr(B|sA ) = 1/3. Given that s1 = sA the expected payoff of the decision a, (a), exceeds that of a decision b, (b), and to maximise expected payoff the first player will decide a. If the second player observes the decision of the first player and also receives a signal s2 = sA , updating according to Bayes’ rule yields 2
Pr(ω = A|H1 = a, s2 = sA ) =
Pr(sA |A) Pr(A) 2 2 Pr(sA |A) Pr(A) + Pr(sA |B) Pr(B)
=
4 . 5
(2)
This already shows that two consecutive identical decisions yield a posterior probability of 0.8. Even if the third player receives a private signal sB , the posterior probability for state A would be given by Pr(ω = A|H2 = a, a, s3 = sB ) = 2/3. Thus, the third decision maker should follow the herd and choose a regardless of her own signal. In the example above we call the decisions of the first two players informative for subsequent players. The decision of the third player is not informative since he has to choose a irrespective of his signal. In this situation rational behaviour can be represented by a choice heuristic based on a counting rule (Anderson and Holt, 1997; Goeree et al., 2007). Define the net number of informative a decisions by = (# of informative a decisions) − (# of informative b decisions). An A-cascade, in which the decision a is rational regardless of one’s own signal, occurs if = 2. Analogously a B-cascade occurs if = –2. 2.2. Experimental design and procedure Our experimental design closely followed the seminal experiment by Anderson and Holt (1997).3 In particular, the two states of nature were represented by two urns containing two black and one red marble (urn A) and one black and two red marbles (urn B). In the beginning of each round one urn was randomly selected but remained hidden to the subjects. 6 players chose sequentially. The decision order was determined at random in each round. Before making his choice a player received a (private) signal in the form of a marble, which was randomly drawn from the three marbles in the selected but hidden urn. Two treatments were conducted. In the private information treatment (PIT) a player saw all previous decisions in the sequence before making his own choice. In the full information treatment (FIT) all signals received by players in the sequence before are revealed to the current decision maker.4 In FIT cascades cannot arise since all signals are informative. In addition to the sequential decisions of the 6 individual players in each round we observed one decision by a group player. The one group player consisted of three subjects. After a group discussion, members had to come up with an unanimous decision (which was not included into the decision history visible to subsequent players). The group player was matched to one individual player. This matching remained fixed throughout the whole session, i.e., for all rounds. We will refer to the two decisions by the individual player and by the matched group player as the focal decision pair in this round. The respective individual player is called the focal individual player. Thus, we elicited 15 focal decision pairs in each independent observation. Focal decision pairs are not necessarily equally distributed among decision nodes since their positions in the decision sequences are determined by the random sequence position of the focal individual player in the respective round. The group “shadowed” the focal individual player in the sense that the group player faced exactly the same strategic situation including the same information as the matched individual player. To be precise, in PIT all members of the shadow group observed the same history of preceding choices and received the same (private) signal about the urn as the matched individual player did. In FIT all members of the shadow group observed the same history of signals and received the same own signal as the matched individual player did. To make the two treatments as comparable as possible we used the same sequences of signals and the same positions of focal decision pairs in a sequence, i.e., for each observation in PIT there is one “mirror” observation in FIT with the same sequences of signals and the same positions of the focal decision pair (focal individual player and shadow group) within the decision sequences. The experiment was conducted at the Cologne Laboratory for Economic Research at the University of Cologne in July 2006, October 2006, and January 2009. 216 subjects participated in the 24 sessions (12 for each treatment). One session consisted of 15 rounds. Subjects were recruited by the online recruiting system ORSEE (Greiner, 2004) and were allowed to participate
3 We are aware that using the model of Anderson and Holt (1997) creates some problems for the analysis, e.g., tie-breaking assumptions are necessary. When designing the experiment we felt, however, that it would be good to be comparable to the extensive literature that uses the Anderson and Holt (1997) framework. Additionally, we had the feeling that an ex ante probability of 0.5 substantially simplifies the setting for the participants. See Smith and Sørensen (2000) and C¸elen and Kariv (2004) for extensions of the model. 4 We are grateful to an anonymous referee for suggesting this treatment (FIT).
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in one session only. About half of the students were studying economics and business administration. All 9 subjects in one session received the same introductory talk. In the instructions we referred to the decisions as guesses and to the shadow group as an “additional player.”5 Whether a participant acted as an individual player or a group member was randomly determined after the introduction. The random draw of the marble, the current position in the decision sequence and the history of decisions of preceding players in the current round were shown on the computer screen. Decisions on urn A or urn B were entered into the computer mask. A screenshot is displayed in Fig. A1 in appendix. Participants representing the group player were requested to discuss their choice after they saw the animation of the marble draw on their individual screens.6 When returning to their cubicles they individually had to enter the decision agreed upon. If the entered decisions of the individual group members were not the same they had to discuss their decision again. At the end of a round when all subjects had taken their decisions participants got to know the actually selected urn for that round and they were informed about their payoffs. Subjects earned 1 Thaler for a correct guess in a round which at the end of the experiment was converted to 1.20 Euro. Each member of the shadow group earned 1 Thaler for a correct guess of the group. In addition subjects were paid a show-up fee of 2.50 Euro at the end of the experiment. On average a participant earned in total 17.30 Euro. Neither did participants learn the identity of each other nor could they infer whose turn it was to decide at a certain decision node. Only the members of the group interacted in face-to-face communication. A session lasted for about 90 min.
3. Hypotheses on groups’ behaviour Group performance and group decision making is an extensively studied topic in social psychology. Although there is no general consensus that groups are better decision makers than individuals, several studies point into this direction. As Kerr and Tindale (2004, p. 634) put it: “Although groups tend to outperform individuals in many domains, groups also can fall prey to the same heuristic-based biases found at the individual level.” One main finding from social psychology is that the performance of groups compared to individuals is to a large extent influenced by task characteristics (Hastie, 1986). In intellective tasks, in which the correct solution is demonstrable and can be communicated to other group members, the group performance often approaches or even exceeds the performance of the best group member (Tindale et al., 2003; Levine and Moreland, 1998; Laughlin and Ellis, 1986). Laughlin et al. (2002), for example, show that in a highly intellective task of solving letters-to-numbers problems four-person groups perform better than the best of an equivalent number of independent individuals. Evidence that groups outperform individuals in decisions mimicking monetary policy decisions is also provided in Blinder and Morgan (2005). Experiments on collective induction, i.e., cooperative search for descriptive, predictive, and explanatory generalisations, rules, and principles (cf. Laughlin, 1999), show that groups are fairly effective in correctly retaining information and discarding incorrect hypotheses on general principles or rules (Kerr and Tindale, 2004). In FIT the task is purely intellectual since decision makers do not have to speculate about the rationality of the previous players to infer their private signals from their actions. The decisions in PIT can to a large extent be considered as an intellective task: If one is willing to assume common knowledge of rational players, one can deduce most of the signals corresponding to previous informative decisions by applying Bayes’ rule and iterative reasoning. If one member of the group knows the correct arguments how to do this he or she can demonstrate the reasoning to his or her group members. This argumentation is also in line with the findings of Charness et al. (2006). The application of Bayes’ rule in PIT, however, is based on the beliefs of the decision makers about whether previous players actually behaved rationally. This constitutes a judgmental element in the players’ decisions. In judgmental tasks, defined as evaluative, behavioural, or aesthetic judgements, groups often perform better than the average individual member (Levine and Moreland, 1998; Tindale et al., 2003).7 Building on these findings from social psychology and economics we derive the following hypotheses: Hypothesis (“Rationality” in PIT). Groups tend to behave more rational than individuals. In particular we are interested in the behaviour in cascades, i.e., in a situation, in which it is actually rational to ignore the own signal and follow the crowd:
5
The introductions were in German. A translation is provided in Appendix A. To make sure that the other subjects could not listen to the group discussion and learn about the group’s signal or their decision, we took the following measures: (1) Group members were asked to speak in a low voice. (2) A complete row of cubicles separated the cubicles of the shadow group members from the individual players (see Fig. A.2 in appendix for concrete arrangements). (3) All participants had to wear ear muffs during the whole session—of course, the members of the shadow group were allowed to take them off during group discussions (see Fig. A.2 for a photo of the ear muffs used). (4) During the waiting time subjects were allowed to individually play simple computer games to distract them from their surroundings. 7 The comparison of individual and group decisions is of course highly dependent on the decision procedure applied within the group (unanimity, plurality, majority rule, etc.). For example, if q denotes the probability that an individual has the correct answer, majority voting in the group results in a probability of 3q2 (1 − q) + q3 for obtaining the correct answer in the group. According to the Condorcet Jury Theorem (Condorcet, 1785, p. 279) the group always outperforms the individual if q > 1/2. Hastie and Kameda (2005) in fact argue that the majority rule leads to the best outcomes for truth-seeking group decision. The literature on juries discusses these issues both theoretically and experimentally (see for example, Feddersen and Pesendorfer, 1998; Guarnaschelli et al., 2000). 6
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Hypothesis (“Following a cascade” in PIT). If in an information cascade the own signal is opposed to the cascade, groups decide against their signal more frequently than individuals. The second hypothesis can only be analysed in PIT since an information cascade cannot occur in FIT. With the help of FIT, however, we will be able to obtain insights into the reasons for a potentially higher group rationality. We define the difference between the rationality percentages of the group and individuals from one independent observation as rationality premium of the group (i.e., the increase in decisions which comply with Bayesian rationality when comparing groups with individuals excluding indifference situations). As explained before, the decision task in PIT has elements of an intellective and a judgmental task while the decision task in FIT is purely intellective. If one assumes that the intellective and the judgmental components contribute additively to a potentially superior group performance in PIT, we can evaluate the relative importance of the intellective and judgmental part by comparing the rationality premiums of groups in the two treatments.8 Hypothesis (“Rationality in intellective and judgmental tasks”). Groups tend to be more rational than individuals in intellective and judgmental tasks. Thus, we expect the rationality premium to be higher in PIT than in FIT, i.e., the superior group performance in FIT might be due to a better performance of groups in intellective tasks whereas the superior performance of groups in PIT might be due to better group performance in intellective and judgmental tasks. 4. Results In the analysis we assume that in general all players believe that their predecessors decided in accordance with iterated application of Bayes’ rule.9 If the informative decisions or signals from the history together with the current (private) signal make both states of nature equally likely we call this an indifference situation. For simplicity we assume that it is common knowledge that all players follow their own signal in an indifference situation.10 If in a given history a player has unambiguously violated Bayes’ rule in PIT, for example, when he should have chosen the same decision as his predecessors irrespective of his signal but he did not, we make the assumption that it is common knowledge among all following players that the deviating player followed his private signal (for evidence supporting this assumption see Anderson and Holt, 1997; Drehmann et al., 2007; Dominitz and Hung, 2009).11 Given these assumptions, we call a decision Bayesian, if it is in line with Bayesian rationality. A situation, in which following the crowd is consistent with Bayesian rationality irrespective of the own signal, is referred to as an information cascade situation. Recall that such a situation can only occur in PIT. We call an information cascade situation a cascade dilemma if the own signal is opposed to the action suggested by the cascade. If a subject rationally decides against his or her own signal in a cascade dilemma we call this behaviour following the cascade. If a subject follows his or her signal in a cascade dilemma we denote this behaviour as a break of a cascade. Note that a break of a cascade is considered to always be informative for subsequent players because of the assumption that the respective player followed her own signal. In our statistical analysis we treat each session as one independent observation, which each comprises 15 focal decision pairs (instances). We start our analysis by concentrating on all 180 focal decision pairs of individuals and their shadow group players in PIT. A comparison of the focal decision pairs guarantees a clean ceteris paribus analysis. Recall that the experimental design ensures that the respective two players – individual and shadow group – are exactly in the same decision situation, i.e., they see the same history and the same private signal. To check for the robustness of our results in
8 Note, however, that one could argue that the difference between the decision tasks in PIT and FIT is not purely judgmental. Since information cascades cannot occur in FIT, iterative reasoning – which arguably is a more difficult intellective task, see, for example, Kübler and Weizsäcker (2004) – is only necessary in PIT but not in FIT to infer the right private signals from previous players’ actions. 9 We are grateful to a referee for pointing out that given this assumption, a finding that groups are “more rational” than individuals might (partly) be driven by systematically different beliefs of groups and individuals, i.e., groups might more strongly believe in predecessors’ ability to apply Bayes’ rule than individuals. One possible reason could be that groups are more able to interpret the actions of predecessors in a way that is in line with Bayes’ rule (whenever this is feasible). Therefore, it might be more difficult for groups to imagine that predecessors did not follow Bayes’ rule. To unambiguously control for this possibility one would need to design further experiments that also elicit the beliefs of the two player types. In an attempt to relax this definition of rationality and to allow for potential errors we followed the suggestions of Anderson and Holt (1997), Goeree et al. (2007), and others and econometrically estimated error rates in PIT by assuming a logistic distribution of independent shocks to expected payoffs. It turned out that with very few exceptions the error model predicted the decisions exactly as the model we describe here. We ran two estimates to determine two parameters, i.e. I based on the decisions of the focal individual players and G based on the decisions of the shadow group decisions. The two parameter are I and G are estimated under the restriction that the sensitivity to payoff differences across different levels of reasoning about others’ behavior is the same. It turns out that the two sensitivity parameters are indeed different, i.e., 5.95 (s.e. 0.85) and 7.74 (s.e. 0.67) indicating that the error rate of focal individuals is higher than the error rate of focal groups (the values are weakly significantly different in a one-sided likelihood ratio test: 2 -value: 3.47, p = 0.063). Details on these estimations and on additional estimations where we allow for different i for each level i of reasoning are available upon request from the authors. 10 In fact our data provide evidence in favour of this assumption. In particular we find that in all 12 sessions in indifference situations in PIT individual players follow their own signal in the majority of instances with a majority of 93:27 (Binomial test with an event probability of 1/2, p = 0.000, two-sided). 11 Note the consequences of this assumption for the application of the counting rule. Consider a history H5 = a, a, a, a, b. The decision maker at the fifth decision node obviously violates Bayesian behaviour since he finds himself in a cascade situation and should choose a irrespective of his private signal. In such a case we assume that all following players take for granted that this decision maker followed his private signal, i.e., that his signal was sB . The decisions at the third and fourth decision node are considered to be non-informative since these players have been in a cascade situation. The fifth decision again becomes informative for subsequent players. The counting heuristic after the fifth player’s action would return = 1.
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Table 1 Descriptive statistics for focal decision pairs in PIT. Decision
Total
Cascade dilemma
Indifference
Node 1 Node 2 Node 3 Node 4 Node 5 Node 6 Total Percentage
24 37 27 34[4] 38[11] 20[1] 180[16] 100.00
– – 5 6 10[1] 8 29[1] 16.11
– 10 – 7[2] 3[3] 0 20[5] 11.11
Focal individuals
Groups
Bayesian
Bayesian excl. indifferences
Bayesian
Bayesian excl. indifferences
23 37 24 31[4] 31[9] 18[1] 164[14] 91.11
23 27 24 24[2] 28[6] 18[1] 144[9] 90.00
23 37 25 34[4] 36[10] 20[1] 175[15] 97.22
23 27 25 27[2] 33[7] 20[1] 155[10] 96.88
“Total” gives the total number of focal decision pairs. “Cascade dilemma” denotes the number of cascade dilemmas faced by the focal individual players and the group players. “Indifference” denotes the number of situations in which the focal individual players and the group players are indifferent according to Bayes. “Bayesian” denotes the number of cases in which the focal individual players/group players decided according to Bayes or decided anything when they were indifferent. “Bayesian excl. indifference” denotes the number of cases in which the focal individual players/group players decided according to Bayes excluding indifference situations. Percentages are given relative to the total number of 180 focal decision pairs (or relative to the total number of 160 focal decision pairs excluding indifferences). Values in [] give the number of focal decision pairs that are preceded in their round by an unambiguous violation of Bayesian behaviour.
the subsequent analysis we also compare average behaviour of all individuals with average behaviour of the group players in PIT. To disentangle the influence of group decision making on intellective and judgmental components in the current decision task we compare the findings of PIT with those of FIT in the second subsection of this result section. If not stated otherwise statistical significances of comparisons within PIT are obtained by applying the exact Wilcoxon sign-rank test for two related samples. Comparisons within FIT and between treatments are performed by using the Mann–Whitney-U test.12 4.1. Comparison of individual and group decisions in PIT Table 1 provides a descriptive overview of cascades, indifference situations, and Bayesian behaviour for the focal decision pairs for each position in the decision sequence in PIT. By definition, in our setting cascade situations can only be observed beginning with decision node 3. The first and third players in a decision sequence cannot be indifferent. The fifth player in a decision sequence can only be indifferent if a break of a cascade occurred before. Bayesian decisions are reported including or excluding indifferences. Observation “Rationality” in PIT In PIT the average percentage of Bayesian decisions for the 12 independent observations of focal individual players is 91.11 and it is 97.22 for the group players. In fact the number of Bayesian decisions of group players is significantly higher (on average by 7.51 percent) than the one of focal individual players (z = 1.841, p = 0.039, exact, one-sided). We therefore reject the null hypothesis that the level of rationality for groups is equal or lower than the level of rationality for individuals in favour of hypothesis “Rationality” which suggests a more rational behaviour of groups.13 Observation “Following a cascade” in PIT When comparing the fractions of players following the cascade in a cascade dilemma for focal decision pairs (12 matched pairs) we find a significantly higher average fraction for groups than for individuals which supports our hypothesis on the more rational behaviour of groups in cascade dilemmas (z = 2.220, p = 0.016, exact, one-sided). The observed higher group rationality should result in higher payoffs for groups. Indeed, the average earning of group players is 11.58 Euro compared to 10.33 Euros for individual players. A Wilcoxon-test shows that groups perform significantly better and guess the right urn more often than individuals (z = 2.434, p = 0.010, exact, one-sided). To provide additional evidence for the robustness of our findings we compare for all individual players including the focal players with the group behaviour, i.e., we compare average decisions of similar but not necessarily identical situations of groups and all individuals. About one third of all individuals in cascade dilemmas trust their private signal more than the information implied by the cascade. This provides supportive evidence in favour of our second hypothesis, i.e., groups in cascade dilemmas rationally follow the cascade more often than all individuals. While 85% of the decisions of focal individuals in indifference situations are decisions complying with the private information, the percentage is 77.5% for all
12 For comparisons within PIT the Wilcoxon sign-rank test for two related samples has to be applied because the decisions of the shadow group player are not independent from the decisions of the matched focal individual (with the exception of the decision in the first round). The reason is that decisions of the focal individual in previous rounds are observed by the other individual players who in turn determine the histories that are observed by the focal decision pairs in subsequent periods. This is not the case in FIT because here only signals are observed but not decisions. When applying the Mann–Whitney-U test for the comparisons in PIT we obtain the same significances as with the Wilcoxon sign-rank test. 13 To learn more about the ability of groups to abandon their private signal – which of course is sometimes rational and sometimes not – we inspect the behaviour of focal decision pairs in more detail by differentiating between situations where players follow their own signal or deviate. Focal individuals follow their own signal significantly more often than groups (z = 1.951, p = 0.031, exact, one-sided). This tendency can be observed in indifference situations (17 out of 20 vs. 11 out of 20, z = 0.813, p = 0.25, exact, one-sided) as well as in cascades (12 out of 29 vs. 3 out of 29, z = 2.214, p = 0.016, exact, one-sided).
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Table 2 Summary of comparison of group and individual decisions in PIT. Focal individuals
Bayesian decisions [Bayesian decisions] Bayesian excl. indifferences [Bayesian excl. indifferences] Follow own signal [Follow own signal] Follow own signal in cascade dilemma [Follow own signal in cascade dilemma]
All individuals
Relation
p
Z
Relation
p
Z
> [>] > [>] < [<] < [<]
0.039 [0.043] 0.035 [0.035] 0.031 [0.047] 0.016 [0.016]
1.841 [1.825] 1.895 [1.823] 1.951 [1.719] 2.220 [2.220]
> [>] > [>] < [<] < [<]
0.004 [0.003] 0.004 [0.003] 0.195 [0.212] 0.006 [0.002]
2.517 [2.589] 2.511 [2.589] 0.904 [0.863] 2.433 [2.746]
The relation “>” (“<”) indicates that the value for groups is larger (smaller) than the value of individuals. Values in [] consider only those instances that are not preceded by an unambiguous violation of Bayesian behaviour in their round. All p-values refer to exact, one-sided Wilcoxon sign-rank tests for two related samples.
individuals which is also well above the number of 55% for groups (a detailed analysis is available from the authors upon request). In Table 2 we summarise statistical tests of differences in the percentages of Bayesian decision within a session between the group and the focal player when (i) excluding instances preceded by an unambiguous violation of Bayesian behaviour within their round (which might have confused subsequent players) and (ii) excluding instances with indifference situations. The hypothesis of higher group rationality is supported by the results presented in Table 2. The first block reports the comparisons within focal decision pairs discussed above. The second block summarises the corresponding comparisons between groups and all individuals. On average the percentage of group decisions complying with Bayesian rationality is significantly higher (by 6.6 percent) when compared to all individuals. 4.2. Disentangling the group decision effect regarding intellective and judgmental elements The fact that decisions in FIT are taken with full information about the signals reduces the decision task in FIT to a purely intellective one. When comparing the average behaviour of all individuals with the average behaviour of group players in FIT we find a significantly higher number of Bayesian decisions of groups than individuals (z = 2.986, p = 0.001, exact one-sided, Mann–Whitney-U-test). This finding that groups decide to a larger extent in line with Bayesian rationality in FIT provides additional support for our Hypothesis “Rationality”. Observation “Rationality in intellective and judgmental tasks” Comparing the decisions of all individuals and groups the rationality premium is significantly higher in PIT than in FIT (z = 1.681, p = 0.048, exact, one-sided, Mann–Whitney-U-test). To get a rough quantification of the group performance in purely intellective tasks (as in FIT) compared to judgmental and intellective tasks (as in PIT) we compare the average rationality premium in PIT with that of FIT. The average rationality premium in PIT is 5.93 percentage points compared to an average rationality premium of 3.43 percentage points in FIT. These numbers suggest that the better performance of groups in intellective tasks explains about 60% leaving about 40% to the judgmental part. 5. Conclusion The present study compares the behaviour of groups and individuals as decision makers in a social learning game. Groups turn out to comply consistently better with Bayesian rationality than individuals which is in line with previous findings by Charness et al. (2006). In particular groups rationally follow a cascade significantly more often than individuals when facing a cascade dilemma. To better understand why groups might outperform individual decision makers in social learning games we compare our finding with a situation where players can directly observe all signals in the preceding sequence. Such a decision task is a purely intellective one. Our comparison reveals that groups seem to be superior to individuals in intellective as well as judgmental tasks with a slightly higher weight on the former. For example, expert groups in financial markets might be able to infer the right information from the actions of other market participants better than individual traders. Our results potentially provide important implications for environments with scope for social learning. In particular, ceteris paribus, they might be less likely to put too much weight on their own private information. An analogous effect might also be present in consumer choice situations when comparing decisions of households consisting of one or more members. Additionally, our findings promise to be valuable for the design of organisations. When shaping an organisation and its decision making processes one can often arrange for an individual decision maker or alternatively employ a small group of people, like boards, committees, or teams, to take certain decisions. A recruiting decision, for example, might well be taken by a single personnel manager or by a hiring committee. Given our results, a hiring committee might be more inclined to reject an applicant on the basis of a longer unemployment history because the committee might correctly asses the meaning of a sequence of negative evaluations by other firms. A single recruiting specialist, on the other hand, might tend to follow
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his own impression in the job interview and thereby underemphasise the information revealed by an (unexplained) long unemployment period. Similar lines of reasoning can be applied to other strategic business decisions in which a variant of social learning is involved. In the light of our findings, it can be argued that in such situations small groups might be the better decision makers. Groups as decision entity, of course, come with the cost of involving more personnel in the decision task. Thus, the designers of organisations are likely to have to deal with this particular trade-off. Although our findings indicate that groups seem to be more rational actors in social learning environments, further research is still needed to identify the exact mechanisms that drive the results. Do groups perform in such situations like the most capable group member or do group discussions generate additional value in the group decision process? Video experiments, for example, might provide some illuminating insights regarding these questions. In our study groups are randomly formed. The question arises whether it is possible to strengthen our results by identifying specific group compositions in which group members possess certain desirable personality characteristics. It would certainly also be very interesting to investigate adequate field settings in order to confirm our results in real world environments, for example, by a comparison of group-managed or individual-managed funds. By raising these questions we hope that our study not only reports interesting findings but also initiates promising further research directions regarding the investigation of social learning by groups. Appendix A. Instructions (Original instructions were in German. They are available from the authors upon request. Differences in treatments are indicated by {PIT:. . .} and {FIT:. . .}, respectively) Figs. A1 and A2.
Fig. A1. Screenshot. The sample screenshot shows the situation in round 1, at the 3rd decision node right after a random draw of a marble from the selected urn. The original screens were in German.
Fig. A2. Cubicle arrangement and ear muffs. Cubicle arrangement in a session; individual decision makers I1 , . . ., I6 were seated in cubicles of one row and the three participants G1 , G2 G3 representing the shadow group player were seated in adjacent cubicles in a remote row. Cubicles denoted by x remained empty. All participants were wearing ear muffs.
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Basic Information • • • • • •
There are two urns, each containing 3 marbles. Urn A contains 2 black marbles and 1 red marble. Urn B contains 1 black marble and 2 red marbles. The distribution of the coloured marbles in the urns will be the same during the entire experiment. There are 6 players. The experiment consists of 15 periods. Course of a period
• At the beginning of each period one urn (urn A or urn B) is chosen with equal probability by a random generator of the computer. Players are not informed about which urn has actually been drawn. The selected urn will not change during one period. • In a randomly determined order the six players are asked one by one to guess which urn has been drawn. The order in which the six players have to state their guesses is randomly determined in each period. • Before a player states his guess, one out of three marbles is drawn with equal probability from the selected urn and it is shown to the currently deciding player. {PIT: The other players do not see the drawn marble.} • After having seen the randomly drawn marble, the currently deciding player is asked to guess whether the selected urn in this period is urn A or urn B. • The {PIT: guesses} {FIT: signals} of all previous players in one period are shown to the currently deciding player before he states his guess. • When all players have submitted their guesses about the selected urn, the period ends and the actual randomly chosen urn in this period is announced. Additional Player • In addition to the six players there is one additional player who is constituted by a group of 3 participants. • The additional player is permanently matched with one specific individual player and decides simultaneously with this player. The decision of the additional player has to be unanimous within the group. • Before the additional player decides, every member of the group is shown the same marble draw as the matched individual player as well as all the {PIT: guesses} {FIT: signals} of the other players in the current period. • {PIT: The guess of the additional player is not announced to subsequent players.} Pay offs • • • •
In case of a correct guess by a player, he is paid 1 Thaler. In case of a correct guess by the additional player, each group member is paid 1 Thaler. The exchange rate is: 1 Thaler = EUR 1.20. Every subjects is paid EUR 2.50 as a fix show up fee.
Please note: During the entire experiment it is not allowed to communicate. Please keep wearing your ear muffs during the experiment. If you have any questions, please give a hand signal. All decisions are made anonymously, i.e., none of the other participants has information about the identity of a certain decision maker. Also, the payoffs are anonymous, i.e., no participant learns the payoff of another participant. We wish you success! References Alevy, J.E., Haigh, M.S., List, J.A., 2007. Information cascades: evidence from a field experiment with financial markets profession. Journal of Finance 62 (1), 151–180. Anderson, L.R., Holt, C.A., 1997. Information cascades in the laboratory. American Economic Review 87 (5), 847–862. Bikhchandani, S., Hirshleifer, D., Welch, I., 1992. A theory of fads, fashion, custom, and cultural change as informational cascades. Journal of Political Economy 100 (5), 992–1026. Bikhchandani, S., Hirshleifer, D., Welch, I., 1998. Learning from the behaviour of others: conformity, fads, and informational cascades. Journal of Economic Perspectives 12 (3), 151–170. Blinder, A.S., Morgan, J., 2005. Are two heads better than one? Monetary policy by committee. Journal of Money, Credit and Banking 37 (5), 789–811. Bone, J., Hey, J., Suckling, J., 1999. Are groups more (or less) consistent than individuals? Journal of Risk and Uncertainty 18 (1), 63–81. Bornstein, G., Yaniv, I., 1998. Individual and group behaviour in the ultimatum game: are groups more ‘rational’ players? Experimental Economics 1, 101–108. Cason, T.N., Mui, V.-L., 1997. A laboratory study of group polarisation in the team dictator game. Economic Journal 107, 1465–1483. C¸elen, B., Kariv, S., 2004. Distinguishing informational cascades from herd behavior in the laboratory. American Economic Review 94 (3), 484–498.
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