How Does Group Identity Affect Individual Decision

How Does Group Identity Affect Individual
Decision-Making?
Elliott Ash and Jessica Van Parysú
April 3, 2015
Abstract
This paper provides a theoretical and empirical analysis of sequential decisionmaking that allows agents to update their beliefs differentially based on the group
membership of other players. We study a model in which agents update their beliefs
about a hidden state of the world based the actions of predecessors, with the behavioral
innovation that there may be differential updating based on the group identities of their
predecessors. Unlike previous games studied in the context of group identity, payoffs
are not contingent on the actions of other players and there is zero scope for strategic
interaction. Still, in an experimental implementation of our model we find that induced
group identity has an effect. Lab participants are more likely to form information
cascades when they receive information from in-group members, and they are more
likely to break cascades when they receive information from out-group members. Since
information cascades transmit less information to subsequent players in a round, rounds
with more in-group members have lower social welfare.
Department of Economics, Columbia University.
Contact:
[email protected],
[email protected]. Columbia Experimental Lab for the Social Sciences (CELSS) has provided
financial support for this research.
ú
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1
Introduction
Behavioral biases in favor of one’s group and against outsiders play a substantial role
in human social relations, yet the determinants of those biases are still poorly understood.
While group identity bias can affect outcomes in public goods games (e.g., Eckel and Grossman, 2005), there is less evidence about how it affects individual decision-making when
payoffs are not a function of collective actions. This paper determines whether group bias
can affect individual decision-making even when payoffs are only a function of individual
actions. Our evidence supports the idea that group identity bias can affect individual
decision-making. When group membership is salient, lab participants under-weight messages from out-group members and over-weight messages from in-group members, relative
to the Bayesian optimum.
Our conceptual approach is based on Bikhchandani et al.’s (1992) model of information
cascades, where individuals act sequentially and often ignore their own signals to conform
with the actions of predecessors. This model provides an attractive microfoundation for herding behavior observed in culture, politics, financial markets, and other domains (Bikhchandani et al, 1998; Bikhchandani and Sharma, 2000).1 Our innovation is to allow agents to
update their beliefs differently depending on whether their predecessors are in-group or outgroup members. Specifically, we hypothesize that agents will under-weight the actions of
their out-group predecessors and over-weight the actions of their in-group predecessors relative to a situation in which there is no group identity. Small differences in the weighting of
actions across groups can have large impacts on social welfare by changing the probability
that an information cascade forms.
We take the model’s predictions to data with a controlled laboratory experiment based
on Anderson and Holt (1997). In this task, participants make a guess on a random state
of the world after observing an informative signal. Because participants act sequentially,
they can observe the actions of their predecessors, so information cascades are likely to
form. The central predictions from Bikhchandani et al. (1992) have been confirmed in the
lab, although human players form fewer information cascades than agents in the standard
models (Anderson and Holt, 1997; Hung and Plott, 2001; Goeree et al. 2007). Our innovation
to the information cascade experiment is that we instill feelings of group identity using
treatments from previous works in the literature (Chen and Li, 2009; Masella et. al, 2014).
We then assess whether information learned from the actions of out-group predecessors is
used differently from information learned from the actions of in-group predecessors.
We find that group identity has an effect on participants’ decision-making. Relative to
1
For recent theory work in this literature see Eyster and Rabin (2010) and Guarino and Jehiel (2013).
2
the case where group identities are obscured, participants are more likely to conform to the
actions of their in-group predecessors and they are less likely to conform to the actions of
their out-group predecessors. In rounds where group identity is salient, social welfare is
7-15% lower with higher shares of in-group members because participants are more likely to
follow the actions of their predecessors and to form information cascades. Since information
cascades transmit less information to subsequent players in a round, the average payoffs to
players in those rounds are lower.
These results contribute to previous work on induced group identity in experimental
economics. This literature includes Eckel and Grossman (2005), who find that in-group
bias can reduce free-riding in public goods games, while out-group bias can increase freeriding. Charness et al. (2007) find that participants play more aggressively against out-group
members in Battle of the Sexes and Prisoners’ Dilemma games, and that the effect is strongest
when group membership is rendered salient. Using a broader selection of games, Chen and Li
(2009) produce evidence consistent with higher altruism toward in-group members relative
to out-group members, while Masella et al. (2014) find that performance incentives can
crowd out in-group altruism.
All of these papers elucidate the effects of group identity in strategic settings where players
have the opportunity to help or hurt others. The equilibrium outcome, in-group favoritism
in social dilemmas, can be rationalized in an evolutionary game-theoretic framework (e.g.,
Fu et al., 2012). In our setting, however, there is no social dilemma, no scope for cooperation
or conflict. But still we find that group identity has an effect on decision-making.
More broadly, this research is relevant to the large social-science literature on discrimination, conformism, and their attendant social problems (Becker, 1957; Hogg, 2013). In a
political-economy context, group bias can frustrate bi-partisan negotiations or reduce electoral accountability for shirking (Landa and Duell, 2014). In a labor market context, group
bias can reduce human capital investments (Loury, 1977), and it may interfere with the
student-teacher relationship (Dee, 2004). We hope our results will motivate field work that
tries to distinguish group effects on individual decision-making from strategic decisions that
are associated with collective action problems.
The rest of the paper is organized into the following sections: Section 2 provides a
conceptual model. Section 3 describes the experiment design, while Section 4 formalizes our
hypotheses. Section 5 reports our results and Section 6 concludes with a discussion and ideas
for future research.
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2
Conceptual Framework
This section presents a conceptual framework for understanding how agents might update
their beliefs differently depending on whether they receive information from in-group vs.
out-group members. We begin by supposing that in the absence of group identity, agents
update their beliefs according to Bayes rule. When we introduce group identity, however, we
hypothesize that agents will attach weights to information learned from in-group and outgroup members. In particular, we hypothesize that agents will over-weight the information
learned from their group members and under-weight the information learned from their outgroup members relative to a situation in which agents do not have information about other
agents’ group identities. The implications of our conceptual framework are such that agents
will be more likely to conform to the actions of their predecessors when their predecessors are
in-group members and they will be less likely to conform to the actions of their predecessors
when their predecessors are out-group members.
2.1
The Baseline Information Cascade Model
We begin by describing a standard information cascade model, which we will then modify
to include agents’ group identities. First, we consider a world with a finite set of identical
agents, indexed by their sequence of play (their “turn”), i œ {1, ..., N }. There is a binary, true
state of the world, ◊ = {0, 1}, where agents share the accurate prior Pr (◊ = 1) = ” = 1/2.
Each agent takes a binary action xi = {0, 1}, where the agent cares only whether the
action matches the state of the world. In particular, we assume that the agent’s utility
equals 1 if xi = ◊ and zero otherwise. Before choosing xi , each agent observes a binary,
independent, and noisy signal about the state of the world, si = {h, l}. We assume that
Pr (si = h|◊ = 1) = Pr (si = l|◊ = 0) = p > 12 , which means that the signal is informative
about the state of the world.
Agents move sequentially to choose the state of the world, xi . When an agent moves,
she has observed her own signal, si , as well as the actions of her predecessors, which we
represent by x≥i . The agent can use this information to update her prior on ◊. Formally,
let µi (si , x≥i ) = P (◊ = 1 | si , x≥i ) be agent i’s posterior belief that ◊ = 1. We restrict our
analysis to Perfect Bayesian Equilibria.
To understand how agents ought to choose their actions to maximize their payoffs, consider the optimal strategy of the first agent (i = 1). By Bayes’ Rule, if she receives a high
signal, the agent’s posterior is
4
Pr (s1 = h | ◊ = 1) P (◊ = 1)
Pr (s1 = h | ◊ = 1) Pr (◊ = 1) + Pr (s1 = h | ◊ = 0) Pr (◊ = 0)
p( 12 )
=
p( 12 ) + (1 ≠ p)( 12 )
= p > 1/2
µ1 (h, ÿ) =
and similarly if she receives a low signal,
µ1 (l, ÿ) = 1 ≠ p < 1/2.
Intuitively, the first agent chooses x1 = 1 if she receives a high signal and x1 = 0 if she
receives a low signal. If subsequent agents believe Agent 1 is rational, then subsequent
agents can intuit Agent 1’s signal from her action, and thus, Agent 1’s signal becomes
common knowledge.
Now follow the same exercise (see Bikhchandani et al. 1992 for details), Agent 2 has a
strict preference for x2 = 1 if s1 = s2 = h and a strict preference for x2 = 0 if s1 = s2 = l.
If s1 ”= s2 and ” = 12 , then Agent 2 is indifferent between the choices, so we assume that she
randomizes.
As more agents move and make decisions under this setup, an information cascade is
increasingly likely to occur. An information cascade occurs when ÷ n such that, ’m > n,
all agents take the same action (i.e., xn+1 = xn+2 = . . . = xN ). For example, given our
assumptions thus far, the case of x1 = x2 triggers a rational cascade for all subsequent agents.
The reason is that regardless of which signal Agent 3 observes, her signal is not enough to
move the posterior in favor of the opposite action, so Agent 3 will choose the actions of
Agent’s 1 and 2, regardless of her signal. This logic will continue for all subsequent agents.
Therefore, for sufficiently high N , it can be shown that an information cascade will nearly
always occur.2
2
Since an imbalance of two consecutive, identical actions can trigger a cascade, the only turns in which
cascades will not occur are turns in which actions alternate for every player (e.g., for player 6, the probability
that a cascade has not formed is the probability that player 6 observes action sequences {0, 1, 0, 1, 0} or
{1, 0, 1, 0, 1}. Moreover, if players are updating their beliefs according to Bayes Rule, then the only way for
the action sequence to alternate for every player is if every player receives alternating signals. Therefore, it
n
can be shown for player n, the probability of not being in a cascade is [(1 ≠ p)p] 2 . Therefore as n goes to
infinity, the probability of not being in a cascade quickly goes toward zero.
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2.2
Extending the Information Cascade Model to Account for
Group Identity
Now we extend the information cascade model to allow for group identity. Specifically,
we now index agents by i as well as g œ {V, W }, where i still indexes the order of moves,
but g indexes membership in group V or W . In addition to the private signal and actions
of her predecessors, each agent also observes her own identity and the identity of all of her
predecessors. Group identity has no significance for payoffs or the reliability of information;
it is just a label. In a fully rational Bayesian world, group identity ought to play no role in
the updating process and the probability that a cascade occurs should be the same as in the
case where there is no group identity. However, previous work on out-group discrimination
suggests that group membership could affect the rational processing of information between
groups (see Hogg, 2013). The idea that group identity affects individual decision-making
helps us generate an alternative set of hypotheses about the likelihood that a cascade occurs
in rounds where group identity is revealed. Specifically, we can model the probability that
a cascade occurs as a function of the number predecessors with relevant signals who are
members of the in-group or the out-group.
To illustrate, suppose that Agent 2 now weighs Agent 1’s action differently depending
on whether Agent 1 is in Agent 2’s group; in other words, now there are “in-group” vs.
“out-group” weights on agent actions. Call ⁄I the in-group weight and ⁄O the out-group
weight. The posterior belief on ◊ is now a function of the agent’s signal, the agent’s group,
the agent’s predecessors’ actions, and the agents’ predecessors’ group membership:
µi (si , gi , x≥i , g≥i ) = Pr (◊ = 1 | si , gi , x≥i , g≥i )
We can compute the posterior probabilities for Agent 2 under four potential scenarios
using a weighted form of Bayes’ Rule. Note that we assume that x1 = 1, without loss of
generality. Also recall that Agent 2 can infer Agent 1’s signal from her action, so s1 = h
without loss of generality. However, we hypothesize that Agent 2 will over-weight or underweight Agent 1’s action depending on whether Agent 1 is a member of Agent 2’s group or
not. Therefore, we have the following scenarios:
1. Scenario 1: Same group, same signal:
µ2 = Pr(◊ = 1 | g1 = g2 , s1 = s2 )
p(⁄I p)
=
p(⁄I p) + (1 ≠ p)(1 ≠ ⁄I p)
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2. Scenario 2: Same group, different signal:
µ2 = Pr(◊ = 1|g1 = g2 , s1 ”= s2 )
p(1 ≠ ⁄I p)
=
p(1 ≠ ⁄I p) + (1 ≠ p)(⁄I p)
3. Scenario 3: Different group, same signal:
µ2 = Pr(◊ = 1|g1 ”= g2 , s1 = s2 )
p(⁄O p)
=
p(⁄O p) + (1 ≠ p)(1 ≠ ⁄O p)
4. Scenario 4: Different group, different signal:
µ2 = Pr(◊ = 1|g1 ”= g2 , s1 ”= s2 )
p(1 ≠ ⁄O p)
=
p(1 ≠ ⁄O p) + (1 ≠ p)(⁄O p)
By observing Agent 2’s actions under these different scenarios with and without group
identity, we can back out what the weights would have to be in order for Agent 2’s actions
to differ from the Bayes’ Rule optimum without group identity.
2.3
Group Identity with Many Agents
In an information cascade model with N agents, Anderson and Holt (1997) show that
the posterior for any agent is simply a function of the number of relevant signals. Relevant
signals are those inferred from decisions made before a cascade starts, from the two decisions
that start a cascade, and from non-Bayesian deviations from a cascade. Following Anderson
and Holt (1997), “in all cases, it takes an imbalance of two decisions in one direction to
overpower the informational content of subsequent individual decisions.”
To formalize this idea simply, assume p = 23 . If xi is the number of relevant h signals and
yi is the number of relevant l signals, then agent i uses Bayes Rule to calculate her posterior,
P r(xi , yi |◊ = 1)P r(◊ = 1)
P r(xi , yi |◊ = 1)P r(◊ = 1) + P r(xi , yi |◊ = 0)P r(◊ = 0)
pxi (1 ≠ p)yi 12
= x
p i (1 ≠ p)yi 12 + (1 ≠ p)xi (p)yi 12
µi = P r(◊ = 1|xi , yi ) =
7
=
=
2 xi 1 yi
3 3
x y
2 xi 1 yi
+ 13 i 23 i
3 3
xi
2xi
2
+ 2yi
To incorporate group identity, we modify this formula, so that it becomes a function of
the number of relevant signals from in-group and out-group members. Let ji be the number
of relevant h signals from in-group members and let (x ≠ j)i be the number of relevant h
signals from out-group members. Let ki be the number of relevant l signals from in-group
members and let (y ≠ k)i be the number of relevant l signals from out-group members.
Suppose wlog that agent i receives signal h.Then,
µig = P r(◊ = 1|ji , (x ≠ j)i , ki , (y ≠ k)i )
P r(ji , (x ≠ j)i , ki , (y ≠ k)i |◊ = 1)P r(◊ = 1)
=
P r(ji , (x ≠ j)i , ki , (y ≠ k)i |◊ = 1)P r(◊ = 1) + P r(ji , (x ≠ j)i , ki , (y ≠ k)i |◊ = 0)P r(◊ = 0)
=
=
2.3.1
p(⁄I p)ji (⁄O p)(x≠j)i (1 ≠ ⁄I p)ki (1 ≠ ⁄O p)(y≠k)i 12
p(⁄I p)ji (⁄O p)(x≠j)i (1 ≠ ⁄I p)ki (1 ≠ ⁄O p)(y≠k)i 12 + (1 ≠ p)(1 ≠ ⁄I p)ji (1 ≠ ⁄O p)(x≠j)i (⁄I p)ki (⁄O p)(y≠k)i 12
(x≠j)i ni
p (1
⁄jIi ⁄O
(x≠j)i ni
p (1
⁄jIi ⁄O
≠ ⁄I p)yi (1 ≠ ⁄O p)(y≠k)i
(y≠k)i yi
p (1
≠ ⁄I p)yi (1 ≠ ⁄O p)(y≠k)i + ⁄kI i ⁄O
≠ p)(1 ≠ ⁄I p)ji (1 ≠ ⁄O p)(x≠j)i
Predictions for Information Cascades
There are three general predictions that come out of the model with group identity. For
a given set of high and low signals ({si , xi , yi }),
1. When ⁄I = ⁄O = 1, then µig = µi . When the in-group and out-group weights equal
1, then there is no effect of group identity on individual decision-making.
ˆµig
ig
i
2. ˆµ
> ˆµ
> ˆ(x≠j)
for all ⁄I œ (1, 32 ] and ⁄O œ [ 34 , 1).3 As the number of h signals
ˆji
ˆxi
i
from in-group members increases, then agent i’s posterior increases more than it would have
if the same number of h signals came from out-group members or from agents without group
identity. Since agent i’s posterior increases, agent i is more likely to choose ◊ = 1 relative to
the case without group identity.
ˆµig
ig
i
3. ˆµ
< ˆµ
< ˆ(y≠k)
for all ⁄I œ (1, 32 ] and ⁄O œ [ 34 , 1). As the number of l signals from
ˆki
ˆyi
i
in-group members increases, then agent i’s posterior decreases more than it would have if
the same number of l signals came from out-group members or from agents without group
⁄I must be less than or equal to 32 because probabilities cannot be negative and ⁄O must be greater than
or equal to 34 because an out-group member’s action must still be more informative than the prior. These
are the bounds when p = 23 .
3
8
identity. Since agent i’s posterior decreases, agent i is less likely to choose ◊ = 1 relative to
the case without group identity.
These predictions have implications for the likelihood that information cascades form
in any given turn. By prediction (1), if agents do not over-weight or under-weight their
predecessors’ signals, then the probability that a cascade forms should be the same in models
with and without group identity. By prediction (2), as the relative number of in-group
predecessors increases, Agent i’s posterior increases relative to the model without group
identity. Holding constant the number of relevant signals, the probability of observing a
cascade for Agent i is then increasing in rounds with high shares of in-group predecessors.
Prediction 3 is the same as prediction 2, but with the signals reversed. Therefore, as the
share of in-group predecessors increases (decreases), cascades should be more (less) likely to
occur.
2.3.2
Examples
Now we will work through some examples for agents 2 and 3. In the original model when
Agent 2’s signal did not match Agent 1’s action, Agent 2 chooses Agent 1’s action with
probability 12 (i.e., she randomizes). This leads to an information cascade for Agent 3 in 3
out of 4 scenarios.
However, suppose that Agents 1 and 2 are members of the same group. Agent 1
plays action 1 and Agent 2 receives signal l. Then Agent 2 will over-weight Agent 1’s action
relative to her own signal, which will increase her posterior on ◊ to be greater than 12 . This
means she will always choose action 1, and similarly if the actions and signals are reversed.
So if Agents 1 and 2 are members of the same group and if 1 < ⁄I Æ 32 , then Agent 3 will
always observe action sequences {1, 1} or {0, 0}. This increases the probability that Agent
3 joins the cascade. Therefore, agents are more likely to trigger information cascades in
“tie-breaking turns” when the share of in-group predecessors is high.
Continuing with this example, suppose that Agents 1 and 2 are members of the same
group (V ) and they play the same action (1), but Agent 3 is a member of a different group
(W ) and has signal l. Then Agent 3’s posterior on ◊ is
µ3w = P r(◊ = 1 | s3w = l, x1v = 1, x2v = 1)
(1 ≠ p)(⁄O p)2
=
(1 ≠ p)(⁄O p)2 + p(1 ≠ ⁄O p)2
Suppose p = 23 as in the baseline model. Then under Bayes Rule when ⁄O = 1, µ3w =
0.666 > 0.5, so Agent 3 ought to play action 1 and join the cascade sequence, {1, 1, 1}.
9
Suppose, however, that Agent 3 under-weights the actions of her predecessors because her
predecessors are members of the other group. In that case, suppose that ⁄O = 0.8. Then
µ3w = 0.395 < 0.5, so Agent 3 ought to play action 0 and she will break the cascade,
which will result in action sequence {1, 1, 0}. This example demonstrates that if Agent
3 sufficiently discounts out-group member actions relative to her own private signal, then
she will be more likely to break cascades when her predecessors are out-group members.
Therefore, information cascades will be less likely to persist when the share of out-group
predecessors is high.
This logic easily extends to agents later in the sequence. For example, agents 4 and 6 will
often find themselves in tie-breaking turns similar to Agent 2. Agents 4, 5, and 6 can also
find themselves in cascades similar to Agent 3. Therefore, based on the sequence of actions
and signals, it is possible to construct “tie-breaking” and “cascade” turns to test the model’s
predictions empirically. We discuss this further in Section 4.
3
Experiment Design
To test the effects of group identity on individual decision-making, we use a lab experiment
similar to Anderson and Holt (1997), with additional experimental tasks designed to render
group identity salient. Previous economics experiments have shown that “minimal” groups
with mere labeling have little effect on social preferences, but instilling group identity through
team-building tasks results in a strong group effect (e.g., Eckel and Grossman, 2005; Charness
et al., 2007). Therefore, our team-building experimental tasks are designed to fulfill this
requirement.
The experiment has four parts, where the first part sorts participants into two equallysized groups based on painting preferences. The second part asks the participants to answer
trivia questions with their group members. The third part consists of the information cascades experiment, which is described below. In the fourth and final part, we assess group
salience with an allocation game. We believe this is a credible research design because it
incorporates many features of previous experiments in the literature.
We administer experiment sessions at the Columbia Experimental Lab for the Social
Sciences (CELSS). Participants are recruited in the weeks leading up to experimental sessions
using the ORSEE recruitment platform. Because we have N = 6 (six turns in a round), we
recruit either 12 or 18 participants, depending on the availability of recruits. Volunteers are
notified that they will receive a $5 show-up fee. If more volunteers arrive than needed, then
the excess volunteers receive $5 cash and they do not participate in the experiment.
Participating subjects are randomly assigned to computer terminals. Visual barriers are
10
Figure 1: Screenshot of Paintings Stage
used to prevent participants from seeing the screens of their neighbors. The instructions for
all stages of the experiment are recited from a script and presented in a slide presentation
(see appendix).
At the beginning of each session, participants are told not to use cell phones and not to
talk to other participants. They are told that the experiment will last for up to 75 minutes
and that they will earn between $5 and $27. They are told that there will be four parts to
the experiment.
The experiment is administered using the z-Tree economics experiment platform (Fischbacher, 2007). The terminals are Dell desktops with 16:9 displays running Windows Vista.
In between stages, participants are given a numerical pass code to proceed to the next stage.
The treatment and questionnaire programs for the experiment are available upon request.
In part one (i.e., the paintings stage), participants view a series of five pictures and
selected the picture that they liked the best. Figure 1 shows an example of what a participant
in our experiment would see at this stage. After each participant makes their choices, they
learn that the paintings are by Paul Klee and Wassily Kandinsky. Based on their painting
preferences, the computer divides subjects into two equally sized teams, with either six or
nine members. In the event of a tie at the margin, participants are randomly assigned to
11
Figure 2: Screenshot of Trivia Stage
one of the teams. “Team Klee” and “Team Kandinsky” correspond to groups V and W from
the model.
For the rest of the experiment, each participant’s team membership is salient on their
computer terminal, through the name of the team and a representative icon. This approach
to instilling group identity is popular in previous work in this literature, and has been shown
generally not to correlate with other participant characteristics (e.g. Chen and Li, 2009).4
In part two (i.e., the trivia stage), participants further solidify group identity through
a team trivia task. As in Masella et al. (2014), participants work together to answer
three multiple choice questions. These questions are chosen to be challenging enough that
none of the subjects would know them outright but they could through deliberation arrive at
informed guesses (the questions and answers are included in the appendix). Before answering
the questions, participants have 90 seconds to discuss with their team members (see Figure
2). While the chat box includes player labels, those labels have no relation to other parts of
the experiment. Players from the team with the most correct answers win $3 each, regardless
of each person’s individual answers. Players from the losing team get nothing from this part
4
In our data, we find small but statistically insignificant differences in the handful of participant characteristics variables available from ORSEE. Relative to the Kandinsky team, the Klee team has 9% more
women, 3% more STEM majors, and 2% more grad students.
12
Figure 3: Virtual Jars
of the experiment. The outcome is not announced until the end of the session.
The third and main part of the experiment is the jars task based on Anderson and Holt
(1997). Before the incentivized rounds, participants receive comprehensive instructions,
played two practice rounds, and had to correctly answer a quiz on the key features of the
task. There are 32 incentivized rounds.
As depicted in Figure 3, the game centers around two virtual jars, one red and one blue
(this image was included in the instructions slide deck). The red jar has two red balls and one
blue ball; the blue jar has two blue balls and one red ball. In terms of the model notation,
p = 23 . In each round, participants are randomly assigned to sets of six (N = 6), which can
have any composition of the teams. The computer randomly selects a jar for each set, which
players do not observe directly.
Participants are ordered in a random sequence for play. On their turn (see Figure 4),
players observe a ball drawn from the jar as well as the jar choices of the preceding players
(but not subsequent players). These are informative about the color of the jar, as discussed
in Section 2.
The 32 rounds are divided between 24 treatment rounds and 8 control rounds, with the
treatment and control rounds randomly determined. Control rounds and treatment rounds
are identical with one exception. In treatment rounds, the team identity of predecessors is
revealed (through the team icon and in parentheses in the text, as shown in Figure 4). In
control rounds, that information is not revealed.
Participants have up to one minute to select a jar; the game moves forward once all
13
Figure 4: Screenshot of Jars Stage
participants in a turn selected a jar. At the end of a round, the sets are reshuffled, new jars
are selected, and a new round begins. Participants earn $0.50 for guessing the correct jar, and
$0.00 for incorrect guesses. However, participants receive no feedback during the task and
only learn about their earnings at the end of the session. We emphasize in the instructions
that payoffs do not depend on what other players choose or the team membership.
In the fourth and final part, participants play an allocation game based on Chen and
Li (2009). This is illustrated in Figure 5. For each of 3 rounds, participants are asked to
allocate $1 between two other players, in 25-cent increments. The other players are selected
randomly – their individual identities are not observed, only their team membership. In
the three respective allocation decisions, the recipient players are two members of one’s own
team, two members of the other team, and one of each team. This is designed to assess
whether the group identity treatment is still working at the end of the session. In our data,
participants favor their in-group member with an unfair allocation 61% of the time.
After the experiment, participants answer a brief questionnaire and then are paid privately in cash.
14
Figure 5: Donation Game
4
Empirical Predictions
The purpose of our experiment is to test the predictions of the modified model outlined
in Section 2. Ideally, our experiment could measure the precise values of the posterior
probabilities given a set of parameters {N, ”, p, ⁄O , ⁄I }. However, posteriors are unobservable
for all agents, so instead, our experiment tests whether adding group identity affects behavior,
holding the parameters and signals constant. In Anderson and Holt (1997), cascades occurred
in 73 percent of the rounds where theory would predict a cascade to occur. We expect that
cascades will occur with comparable frequency in our control rounds.
We test the degree to which group identity affects individual decision-making in two ways.
First, we compare how players make decisions in rounds where group identities are revealed
compared to rounds in which group identities are not revealed. Second, we focus on rounds
in which group identities are revealed and then test whether players make different decisions
when they receive more information from in-group versus out-group members. Specifically,
we create a variable that measures the share of the player’s predecessors who are in-group
members.
Next we focus on two outcomes Y . One outcome is simply the probability that the player
chooses the correct jar in each round (P r(Correct = 1)). The probability that the player
15
chooses correctly measures the player’s welfare because players only receive compensation
when they choose correctly. The second outcome is the probability that the player’s choice
matches her own signal (P r(Own Ball = 1)). The frequency with which a player follows
her own signal as opposed to the choices of predecessors reveals how much she weights her
private information relative to information she learns from predecessors.
Our regression framework for estimating the net effect of group identity on individual
decision-making is as follows. We model the probability that Yijst = 1 for player i in set j
in round s in session t as
P r(Yijst = 1) = – + —T reatijst + uijst
(1)
for Yijst œ {Correctijst , Own Ballijst }. The indicator variable T reatijst equals one during
treatment rounds and equals zero during control rounds. This is randomly assigned as part
of our lab experiment design. The coefficient — measures the average effect of group identity
on the two outcomes. We estimate model (1) with all players in all rounds in all sessions, so
N = 1, 728.
To test whether group identities within treatment rounds affect individual decisionmaking, we estimate
P r(Yijst = 1) = – + “InGroup + uijst
(2)
for Yijst œ {Correctijst , Own Ballijst }, and where we have defined
InGroup =
Number of in-group predecessors
,
Total number of predecessors
which is randomly assigned by virtue of the lab experiment design. The coefficient “ measures
the effect of in-group identity on player i’s choices in treatment or control rounds
We estimate model (2) on two subsets of data: treatment rounds and control rounds.
In control rounds, group identity is obscured so we expect that “ = 0 for both Correct
and OwnBall. In treatment rounds where predecessors’ group identities are salient, an
increased share of in-group predecessors may increase the motivation to conform to predecessors’ choices, rather than following ones’ own observed ball. That is, an increased in-group
share may reduce P r(OwnBall = 1; in regression notation, we hypothesize “ < 0. Similarly, because player i will be more likely to conform to the choices of in-group predecessors
in treatment rounds, she may discard important information and reduce her probability of
being correct P r(Correct = 1. This also corresponds to “ < 0.
Our third and final model focuses on the probability of selecting one’s own ball in special
16
situations:
P r(Yijst = 1) = – + ”InGroup ú T reat ú Dif f Ball + ÂDif f Ball ú T reat
+ “InGroup ú T reat + ◊Dif f Ball ú InGroup + —T reatijst
+ ⁄Dif f Ball + ŸInGroup + uijst
(3)
for Yijst œ {OwnBallijst , Cascadeijst , Breakijst }. Cascadeijst is defined to equal one in
rounds where a cascade occurs. Breakijst is defined to equal one in rounds where an existing
cascade is broken. InGroup and T reat, both randomly assigned in the lab experiment, are as
before. Dif f Ball equals 1 if player i’s signal differs from the consensus of her predecessors’
choices, and 0 otherwise. The coefficient ” measures the effect of in-group identity on player
i’s choices in treatment rounds, in the case where player i’s ball differs from the jar chosen
by most predecessors. We estimate model (3) on players that make choices in two subsets of
turns, “tie-breaking turns” and “cascade turns,” which we describe presently.
Players in tie-breaking turns can be players numbered 2, 4, or 6, depending on the
sequence of earlier choices. We say that player i has a different ball (i.e., a different signal)
in tie-breaking turns if more than 12 of her predecessors chose the jar that does not match her
ball (e.g., player 4 draws a red ball after players 1 and 3 chose the blue jar). Tie-breaking
players with high shares of in-group predecessors may be less likely to follow their own
ball and more likely to follow the dominant choice of predecessors – but only in treatment
rounds where group identities are salient. In the regression notation, this corresponds to the
hypothesis that ” < 0. This is a crucial outcome because conforming to predecessors can
initiate an information cascade (P r(Cascade = 1)).
Cascade turns can occur for players 3, 4, 5, or 6, and refer to those turns where an
information cascade would have already begun for rational Bayesian agents. Specifically,
a cascade turn is any turn where at least two consecutive previous players made the same
choice. For example, player 3 faces a cascade if players 1 and 2 both chose the blue jar.
Players in these turns have different balls if their balls do not match the dominant jar choice
in the round (i.e., player 3 draws a red ball when there is a cascade on the blue jar). In cascade
turns, players “break” the cascade if they guess the jar that matches their signal rather than
the jar that matches their predecessors’ choices For example, P r(Break) = 1 if player 3
chooses the red jar when players 1 and 2 have chosen the blue jar. We hypothesize that
players with different balls in treatment rounds with high shares of in-group predecessors
will be less likely to break cascades. Again, this corresponds to ” < 0 in the regression
notation.
17
5
Results from the Experiment
This section reports our estimates for the coefficients described in Section 4 using the
experiment design described in Section 3. We test for aggregate effects first, followed by an
analysis of how the share of in-group members affects behavior in treatment rounds. In general, our results support the view that in-group biases increase the frequency of information
cascades, while out-group biases decrease the frequency of information cascades.
Table 1 reports the aggregate treatment effects of revealing group identity in the informationcascades task. The reported coefficient is — from model (1). As shown in Column 2, there is
no aggregate effect of group revelation on the probability of selecting the correct jar. Column
1 shows a small negative effect on the probability of following one’s own signal, but it is only
marginally significant. These small/zero effects in the aggregate are due to the countervailing effects of in-group and out-group bias within treatment rounds, as we endeavor to show
in the subsequent tables.
Table 2 reports estimates for “ from model (2). These are the effects in OwnBall and
Correct, within treatment rounds (Columns 1 and 3) or within control rounds (Columns 2
and 4), of a higher in-group predecessor share. First consider Columns 2 and 4, which show
that, as expected, when the group identities of predecessors are obscured (control rounds),
there is no effect of in-group share on the outcome variables. When group identities are
revealed (Columns 1 and 3), however, there are statistically significant effects. As the share
of in-group predecessors increases, players are less likely to follow their own signals (Column
1). Moreover, they are less likely to choose the correct jar (Column 3), meaning that payoffs
are lower on average when there is a higher in-group predecessor share. The coefficient in
Column 3 means that in turns with all in-group predecessors, payoffs are 15% lower relative
to turns with zero in-group predecessors. In the information cascades task, in-group bias
reduces welfare on average.
Table 3 offers additional robustness checks for how Column 3 of Table 2, showing how
in-group share affects the probability of choosing the correct jar in treatment rounds. The
columns show that the result is robust within participants across rounds (participant fixed
effects), within rounds across sessions (round fixed effects), and with different methods of
calculating standard errors (clustering the standard errors within participants). These additions hardly change the estimate.
Further expanding on this point, Figure 6 shows how the probability of choosing the
correct jar varies across turns in a round (again, limited to treatment rounds). The red line
plots the probability of choosing the correct jar when the share of her in-group predecessors
is less than or equal to 0.5. The blue line plots the probability of choosing the correct jar
18
All Rounds
Treatment
Mean Dep Var
Turn Fixed Effects
(1)
Pr(Own Ball=1)
(2)
Pr(Correct=1)
-0.0324+
(-1.65)
-0.0208
(-0.82)
0.82
X
0.68
X
N
1,728
1,728
Robust standard errors, t-statistics in parentheses
Table 1: The Effect of Group Identity Treatment on Individual Decision-Making
Share In-Group
Mean Dep Var
Turn Fixed Effects
Treatment Rounds
Control Rounds
(1)
Pr(Own Ball=1)
(2)
Pr(Own Ball=1)
(3)
Pr(Correct=1)
(4)
Pr(Correct=1)
-0.074*
(-2.33)
0.095
(1.83)
-0.153***
(-3.90)
-0.006
(-0.08)
0.81
X
X
0.85
X
0.68
X
X
0.70
X
X
N
1,080
360
Robust standard errors, t-statistics in parentheses
X
1,080
360
Table 2: The Effect of Group Identity Within Treatment and Control Rounds
19
Treatment rounds
Share In-Group
Turn Fixed Effects
Subject Fixed Effects
Round Fixed Effects
Cluster std errors
(1)
Pr(Correct=1)
(2)
Pr(Correct=1)
(3)
Pr(Correct=1)
(4)
Pr(Correct=1)
-0.153***
(-3.84)
-0.158***
(-3.91)
-0.158***
(-4.22)
-0.141***
(-3.86)
X
X
X
X
X
X
X
X
X
X
N
1,080
1,080
1,080
Robust standard errors unless otherwise noted; t-stats in parentheses
1,080
Table 3: Robustness: The Effect of Group Identity Within Treatment Rounds
Probability of Choosing the Correct Jar
.6
Pr(correct=1)
.65
.7
.75
.8
Treatment Rounds
2
3
4
Turn Number
In−Group
5
6
Out−Group
®
Figure 6: Probability of Choosing the Correct Jar: Majority In-group Versus Majority Outgroup Predecessors
20
(1)
Tie-Break Turns
Pr(Own Ball=1)
(2)
Tie-Break Turns
Pr(Cascade=1)
(3)
Cascade Turns
Pr(Break=1)
Treatment*Different Ball*
Share In-Group
-0.256*
(-2.12)
0.313**
(2.60)
-0.796***
(-3.86)
Mean Dependent Variable
0.92
0.57
0.12
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
439
695
Treatment*Different Ball
Treatment*Share In-Group
Different Ball*Share In-Group
Treatment
Different Ball
Share In-Group
Turn Fixed Effects
N
439
Robust standard errors, t-statistics in parentheses
Table 4: In-Group Identity Triggers Information Cascades
when the share of her in-group predecessors is greater than 0.5. The figure shows that, across
all turns in the game, players are 7-15% less likely to choose the correct jar when they receive
more information from in-group vs. out-group members.
Now we turn to understanding why a higher in-group predecessor share is decreases the
probability of choosing the correct jar. It turns out that the key reason is that pro-in-group
bias increases the frequency of information cascades. In particular, the welfare decrease in
turns with more in-group members can be traced to two components. First, in tie-breaking
turns where conforming (rather than following one’s own signal) will trigger a cascade, players
are more likely to conform when predecessors are the same group. Second, in turns where
an information cascade has already begun, a player is more likely to break the cascade when
the predecessors in the cascade are members of the other group. This logic is discussed in
Section 4.
Table 4 reports regression estimates for the coefficient ” from model (3). Column 1
reports the effect on the probability of choosing one’s own ball in tie-breaking turns; Column
2 reports the effect on the probability of triggering a cascade in tie-breaking turns; Column
3 reports the effect on the probability of breaking a cascade that is already in progress. The
regressions includes all the other items in model (3), as well as turn fixed effects.
Begin with Column 1. The sample includes turns where Bayesian players ought to be
indifferent between guessing the Red and Blue jar. However, the estimate shows that the
higher the share of in-group predecessors, the more likely that players are to side with their
21
predecessors rather than with their own private signals (” < 0).
The consequences are highlighted in Column 2. As the share of in-group predecessors
increases, the probability that players trigger information cascades in tie-breaking turns also
increases. This is the first major reason for lower payoffs due to a higher in-group share.
The second major reason is highlighted by Column 3. This regression includes turns
where an information cascade has already formed, and players make the choice whether to
join the cascade or to break it. The negative coefficient means that that players are less
likely to break cascades when the cascades were formed by their in-group members. That
is, out-group bias can reduce the frequency of welfare-reducing information cascades.
6
Conclusion
We have shown that group identity can interfere with Bayesian learning in a lab environment. These results suggest that group bias can affect social decision-making even when
decisions do not have a strategic component. Our results also suggest a new setting where
out-group bias may improve efficiency, by reducing the frequency of information cascades.
This is related to recent theory work on the advantages of disagreement in the provision of
expert advice (Che and Kartik, 2009).
Future lab work in this area could jointly analyze the strategic and informational components of intergroup bias. For example, in our set up, one could test whether observing
the group identity of successors (rather than just predecessors) alters behavior by lending
a strategic component to signal revelation. Further, one could analyze the role of group
identity in more complex strategic and informational environments, like the one reported in
Janssen et al. (2010). In that experiment, the authors found that costly punishment can induce cooperation in a common-pool-resource game, but only when players can communicate
with each other. An interesting addition to that study would be to induce group identity
in the players before the game, to assess whether group bias affects cooperation through
in-group favoritism, through communications distortions, or through both channels.
There are still open questions about the mechanisms underlying the differential learning effect. Does it come from (non)conformism, where people prefer to (dis)agree with
(out-)group members? Or does it come from beliefs about the competence of (out-)group
members? Satisfactory answers to these questions will have to await further research. Answering them will have important policy implications in light of, for example, Dee’s (2004)
evidence that students learn better from teachers of the same race.
22
References
[1] Anderson, Lisa and Charles Holt. (1997) “Information Cascades in the Laboratory.”
American Economic Review, 87 (5), 847-862.
[2] Becker, Gary (1957), The Economics of Discrimination.
[3] Bikhchandani, Sushil, David Hirshleifer, and Ivo Welch. (1992) “A Theory of Fads, Fashion, Custom, and Cultural Change as Informational Cascades.” Journal of Political Economy, 100 (51), 992-1026.
[4] Bikhchandani, Sushil, David Hirshleifer, and Ivo Welch. (1998) “Learning from the behavior of others: Conformity, fads, and informational cascades.” Journal of Economic
Perspectives, 12, 151-170.
[5] Bikhchandani, Sushil, and Sunil Sharma (2000), “Herd behavior in financial markets: A
review, IMF Staff Papers, 47 (3), 279-310.
[6] Charness, Garry, Luca Rigotti, and Aldo Rustichini (2007) "Individual behavior and
group membership." American Economic Review, 97, 1340-52.
[7] Che, Yeon-Koo and Navin Kartik (2009), “Opinions as incentives,” Journal of Political
Economy 117 (5).
[8] Chen, Y. and S. Li. (2009) "Group Identity and Social Preferences." American Economic
Review, 99, 431-57.
[9] Dee, Thomas (2004), “Teachers, race, and student achievement in a randomized experiment,” The Review of Economics and Statistics, 86(1), 195-210.
[10] Eckel, Catherine and Philip Grossman. (2005) “Managing diversity by creating team
identity.” Journal of Economic Behavior & Organization, 58, 371-392.
[11] Eyster, E. and M. Rabin. (2010) “Naive herding in rich-information settings.” American
Economic Journal; Microeconomics, 2, 221-243.
[12] Fischbacher, Urs (2007) “z-Tree: Zurich Toolbox for Ready-made Economics Experiments." Experimental Economics 10(20), 171-178.
[13] Fu, Feng, Corina Tarnita, Nicholas Christakis, Long Wang, David Rand, and Martin
Nowak (2012), “Evolution of in-group favoritism," Scientific Reports 2 (460).
23
[14] Goeree, J.K., T.R. Palfrey, B.W. Rogers, and R.D. McKelvey. (2007) “Self-correcting
information cascades.” Review of Economic Studies, 74, 733-762.
[15] Guarino, A. and P. Jehiel. (2013) “Social learning with coarse inference.” American
Economic Journal: Microeconomics, 5, 147-74.
[16] Hogg, Michael A. (2013), “Intergroup Relations," Handbook of social psychology,
Springer.
[17] Hung, A. and C. R. Plott. (2001). “Information cascades: Replication and an extension
to majority rule and conformity-rewarding institutions.” American Economic Review, 91,
1508.
[18] Janssen, Marco, Robert Holahan, Allen Lee, and Elinor Ostrom (2010) “Lab experiments for the study of social-ecological systems,” Science 328 (5978), 613-617.
[19] Landa, Dimitri and Dominik Duell (2014), "Social identity and electoral accountability,"
American Journal of Political Science.
[20] Loury, Glenn (1977) “A dynamic theory of racial income differences," in: Women, Minorities, and Employment Discrimination, ch. 8, Lexington, 1977.
[21] Masella, P., S. Meier, and P. Zahn. (2014) “Incentives and group identity,” Games and
Economic Behavior.
A
Appendix Items
Experiment instructions slides and trivia questions are attached.
24
Experiment Instructions
Elliott Ash and Jessica Van Parys
Columbia Experimental Laboratory in the Social Sciences
December 10, 2014
1 / 30
Welcome
Welcome to our experiment!
We are happy to have you
Please sit at a computer
Today’s rules
Do not use your cellphones
Do not talk to other players
Please write your name and player ID # on your worksheet
2 / 30
Today’s Experiment
75 minutes long
You may earn $5-$27
There are 4 parts
After you complete each part, please sit quietly and await further
instructions
3 / 30
Part 1
You will see 5 pairs of pictures
From each pair, select the picture that you like the best
4 / 30
Part 1
Please enter the pass code “20” and click continue.
5 / 30
Part 1
(Part One in progress)
6 / 30
Part 1
You have been sorted into 2 teams based on your picture preferences
Your screen should say either “Klee” or “Kandinsky”
This is your team’s name
Your screen should show a picture
This is your team’s icon
7 / 30
Part 2
3 multiple choice trivia questions
90 second team text chat for each question
The team with the most correct answers wins
Winning team members receive $3
Losing team members receive $0
The outcome will be announced at the end of today’s session
8 / 30
Demonstration
9 / 30
Part 2
Please enter the pass code “65” and click continue.
10 / 30
Part 2
(Part Two in progress)
11 / 30
Part 3
There are 2 virtual jars
One is Red
One is Blue
We will play 32 rounds where the computer randomly selects a jar
Your objective is to choose which jar the computer selects
12 / 30
Part 3
At the beginning of each round,
The computer randomly selects a jar
The chosen jar is the same for every player in your round
The computer randomly assigns you a Turn Number, 1 through 6
Every player in the round chooses the jar in order according to their
Turn Number
13 / 30
Part 3
In each round you will be shown a marble from the selected jar
The marble will be Red or Blue
The marble color is a clue because
The Red jar contains 2 Red marbles and 1 Blue marble
The Blue jar contains 2 Blue marbles and 1 Red marble
14 / 30
Jars & Marbles
15 / 30
Part 3
Before choosing a jar, you will see the choices of players before you
In some rounds you will see the team membership of players before you
You will not see the marbles of players before you
You will not see any information about the players after you
16 / 30
Demonstration
17 / 30
Part 3
The objective of the game is to correctly choose the color of the jar in
each round
For each correct guess, you receive $0.50
For each incorrect guess, you receive $0
Your compensation does not depend on what other players choose
You may earn up to $16
We will reveal your earnings to you in private at the end of the session
18 / 30
Part 3
Please pay attention to the pace of the game
As the round progresses the computer will show you what other
players have chosen
When it is your turn to choose, the computer will show you a marble
You will have 1 minute to choose a jar
19 / 30
Practice Round & Questionnaire
We will now play 2 practice rounds
You will not be compensated for the practice rounds
After the practice round, you will respond to a questionnaire
The questionnaire reviews the rules of the game
20 / 30
Practice Round & Questionnaire
Please enter the pass code “15” and click continue.
21 / 30
Practice Round & Questionnaire
(Practice Round & Questionnaire in progress)
22 / 30
Part 3
Please enter the pass code “42” and click continue.
23 / 30
Part 3
(Part 3 in progress)
24 / 30
Part 4
3 rounds
You will receive $1 at the start of each round
You will allocate the $1 across two other players
You can allocate the $1 in denominations of 25 cents
You cannot keep any part of the dollar for yourself
The other players will receive the amount of the $1 that you allocated
to them at the end of the session
25 / 30
Part 4
Round 1: Two players from your team
Round 2: Two players from the other team
Round 3: One player from your team; one player from the other team
26 / 30
Part 4
Please enter the pass code “53” and click continue.
27 / 30
Part 4
(Part Four in progress)
28 / 30
Final Questionnaire
Thanks for participating :)
Before you leave ...
Please complete our questionnaire. It will not affect your earnings
Please write your earnings on your worksheet
See Elliott in the office to collect your earnings
Sign your worksheets to acknowledge that you received earnings
Then you are free to go!
29 / 30
Final Questionnaire
Please enter the pass code “34” and click continue.
30 / 30
Trivia Questions
1. Which year was the telephone invented?
a. 1876*
b. 1882
c. 1889
d. 1894
2. What is the population of California?
a. 20 million
b. 26 million
c. 32 million
d. 38 million*
3. Which country borders Somalia?
a. Sudan
b. Egypt
c. Ethiopia*
d. Tanzania
4. What is the state bird of Texas?
a. Cactus wren
b. Brown thrasher
c. Western meadowlark
d. Northern mockingbird*
5. Who was the 22nd President of the United States?
a. Chester Arthur
b. Grover Cleveland*
c. William McKinley
d. William Howard Taft
6. When was the last time that dinosaurs roamed the Earth?
a. 25 million years ago
b. 65 million years ago*
c. 300 million years ago
d. 1 billion years ago
*Indicates the correct answer