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‘Everybody’s doing it’: on the persistence of bad social norms

Abstract

We investigate how information about the preferences of others affects the persistence of ‘bad’ social norms. One view is that bad norms thrive even when people are informed of the preferences of others, since the bad norm is an equilibrium of a coordination game. The other view is based on pluralistic ignorance, in which uncertainty about others’ preferences is crucial. In an experiment, we find clear support for the pluralistic ignorance perspective . In addition, the strength of social interactions is important for a bad norm to persist. These findings help in understanding the causes of such bad norms, and in designing interventions to change them.

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Notes

  1. 1.

    The arguments for the negative welfare effects of restricting female labor participation on growth have been long discussed in economics; e.g. Goldin (1986).

  2. 2.

    Recent alternative approaches to modeling social norms include Michaeli and Spiro (2017), who focus on pairwise interactions in a coordination game, and Acemoglu and Jackson (2015), who investigate an intergenerational context.

  3. 3.

    Pluralistic ignorance has been linked to the propagation of various damaging social issues, such as college binge-drinking (Prentice and Miller 1996; Schroeder and Prentice 1998), tax avoidance (Wenzel 2005), school bullying (Sandstrom et al. 2013), the spread of HIV/AIDS due to stigmas against condom usage (Gage 1998) and the lack of female labor force participation in Saudi Arabia (Bursztyn et al. 2018).

  4. 4.

    We think that our results also shed light on situations where utility is derived from conforming to one’s group identity instead of from a material payoff (Akerlof and Kranton 2000; Tajfel and Turner 1986, 1979). A raft of recent empirical evidence has demonstrated that social identity can influence individual decision-making and behavior in a wide range of respects, such as group problem-solving (Chen and Chen 2011), polarization of beliefs (Hart and Nisbet 2011; Luhan et al. 2009), preferences over outcomes (Charness et al. 2007), trust (Hargreaves Heap and Zizzo 2009), redistribution preferences (Chen and Li 2009), punishment behavior (Abbink et al. 2010), discrimination (Fershtman and Gneezy 2001), self-control (Inzlicht and Kang 2010), competitiveness (Gneezy et al. 2009) and time horizons for decision-making (Mannix and Loewenstein 1994). Several studies have successfully induced group identity directly in the lab to test for different effects; e.g., Chen and Chen (2011), Charness et al. (2007), Eckel et al. (2007), among others.

  5. 5.

    It appears to be very hard to avoid bad outcomes in minimum effort games, but there are some reliable factors that help subjects coordinate on better outcomes (Anderson et al. 2001; Brandts and Cooper 2006, 2007; Cachon and Camerer 1996; Cason et al. 2012; Chaudhuri et al. 2009; Chen and Chen 2011; Kopanyi-Peuker et al.2015; Riedl et al. 2015; Weber 2006).

  6. 6.

    Their design also differs in terms of the matching structure: in each round, matches are pairwise with external payoffs for group conformity, rather than group coordination.

  7. 7.

    In Brock and Durlauf (2001) the authors assume that shocks follow an extreme value distribution. The convenient properties of this distribution allow for analytical computation of rational expectations equilibria from the symmetry of N expectations equations.

  8. 8.

    Proofs are discussed in detail in (among others) Brock and Durlauf (2001) and Rothenhäusler et al. (2015).

  9. 9.

    Recall that \(\rho ^*\) is the expected proportion of the group choosing \(\omega _i=-1\). Due to the continuous distribution of the private shocks across all possible values on the real axis, there is always a positive probability of a private difference \(|d_{i}|>2J\), and so the expected equilibrium proportions are never exactly at the poles 0 and 1. With some abuse of terminology, a ‘mixed-proportions’ equilibrium \(\rho _=^*\in (\rho ^*_-,\rho ^*_+)\) also exists. In a setting where the parameter space is such that three equilibria exist, the equilibria at the poles are stable whereas the mixed-proportioned equilibrium is unstable. Small perturbations in players’ expectations will move players away from this equilibrium.

  10. 10.

    This result depends on the linear payoff function used in our and Brock and Durlauf’s (2001) model. To derive the condition for risk dominance in our game, we used the procedure described in Sect. 3.1 of Keser et al. (2012), who apply Harsanyi and Selten’s (1988) tracing procedure to a technology-adoption game.

  11. 11.

    Recent examples that have been studied include the role of social media and the internet in the 2011 ‘Arab Spring’ uprisings (Lim 2012) and in promoting women’s empowerment in India (Loiseau and Nowacka 2015).

  12. 12.

    Andreoni et al. (2017) find a positive effect of communication on equilibrium selection in a similar environment. Choi and Lee (2014) find that coordination is enhanced by allowing communication in networks. However, in their experiment the roles of implicit agreement and punishment from deviations are necessary for improving coordination. Ochs (2008) shows that the effect of communication can differ in different coordination games; interestingly, this paper also highlights the role of past precedent, a mechanism that in our experiment corresponds to the strength of the bad norm.

  13. 13.

    As previously mentioned, actual payoffs were multiplied by 10 when presented to subjects. Instructions and an example screenshot are displayed in the “Appendix”.

  14. 14.

    The parametrization for \(J=4\) meant that Door A was the sole equilibrium in round 1.

  15. 15.

    Economics experiments involving the minimum-effort game have found a strong negative effect of group size on coordination, but this game is fundamentally different to our game in this respect, as discussed in Sect. 1. In the minimum-effort game, subjects are punished if one group member chooses a lower effort level, whereas in our game, punishment (a lower social value) depends on the proportion of others making the opposite choice. See also Weber (2006).

  16. 16.

    For instance, recent experimental evidence suggests that using Twitter as an intervention tool can be effective in combating norms of racial harassment (Munger 2017).

  17. 17.

    We thank an anonymous referee for these suggestions.

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Acknowledgements

We thank the editor, two referees, seminar attendees from the University of Nottingham, the University of East Anglia and the University of Amsterdam (Grant No. 201212170412), as well as Cars Hommes, Adriaan Soetevent, Swapnil Singh and Sabina Albrecht for helpful comments.

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Correspondence to David Smerdon.

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We acknowledge the University of Amsterdam Behavior Priority Area for providing funding for the experiment.

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Appendix

Appendix

Table of results

See Table 3.

Table 3 Key performance indicators by group

Proofs

Stage-game equilibria

It follows from the decision rule specified in Proposition 1 that, in equilibrium, we require that players prefer \(\omega _i=1\) at least as much as \(\omega _i=-1\) if \(d_i<c^*\), that players prefer \(\omega _i=-1\) at least as much as \(\omega _i=1\) if \(d_i>c^*\) and, in particular, that a player is exactly indifferent between \(\omega _i=-1\) and 1 if she draws private values with a difference equal to the threshold \(c^*\). We use this latter property of the equilibrium to endogenously calculate the threshold.

The threshold \(c^*\) depends both on an individual’s beliefs about group behavior as well as the (fixed) social factor. Solving for this threshold allows us to compute a general equilibria condition that holds for any given distribution of the private shocks. Then an individual i maximizing her expected utility chooses \(\omega _i=-1\) if \(d_i>2Jm^e_i\). To endogenously solve for an equilibrium, we first rewrite \(m^e_i\) as:

$$\begin{aligned} m^e_i=\displaystyle \frac{1}{N-1}\sum ^{N-1}_{k=0}\left( \left( {\begin{array}{c}N-1\\ k\end{array}}\right) p^k(1-p)^{(N-1-k)}(2k-N+1)\right) \end{aligned}$$
(7)

where p is the probability of a single draw of \(d_i<c^*\) so that i chooses \(\omega _i=1\). Then each term in the series is the expected value for each possible value of \(m_i\), which can be written in the form \(\frac{2k-N+1}{N-1}\) for each \(k\in \{0,N-1\}\).

Letting \(m_i^{e*}\) be the equilibrium expected average choice of the others in a group, corresponding to a threshold \(c^*\), we can rewrite \(c^*=2Jm_i^{e*}\) in (7). Then solving for an individual i drawing exactly \(d_i=c^*\) with \({\mathbb{e}}V_i(-1)={\mathbb{e}}V_i(1)\) allows us to solve endogenously for the expectation \(m_i^{e*}=m_j^{e*} \;\;\forall i,j\):

$$\begin{aligned} m_i^{e*} =\frac{1}{N-1}\sum \limits _{k=0}^{N-1}\genfrac(){0.0pt}0{N-1}{k}F(2Jm_i^{e*}-d)^k(1-F(2Jm_i^{e*}-d))^{(N-1-k)}(2k-N+1) \end{aligned}$$
(8)

At first sight, an individual’s expectations appears to depend on the size of the group, N. We perform the replacements \(M=N-1\) and \(F=F(2Jm_i^{e*}-d)\) for notational convenience to rewrite (8) as:

$$\begin{aligned} m_i^{e*} =\frac{1}{M}\sum \limits _{k=0}^{M}\genfrac(){0.0pt}0{M}{k}F^k(1-F)^{(M-k)}(2k-M) \end{aligned}$$
(9)

It can be shown that the sum of this series is independent of group size as follows: Let k be a binomially-distributed random variable with parameters \(n=M,p=F\). Then \(\mathbb {E}(k)=MF\) and so the right-hand side of (9) simplifies to \(2F-1\).

Thus, (8) can be rewritten as \(m_i^{e*} =2F(2Jm_i^{e*}-d)-1\), which notably does not depend on N. Similarly, the researcher’s prediction of the expected average choice level of the whole group solves:

$$\begin{aligned} m^* =2F(2Jm^*-d)-1 \end{aligned}$$
(10)

Effect of group size

While group size does not influence the stage-game equilibria, it may still affect the probability of a group switching from a bad equilibrium to a good equilibrium in a given round. Consider a scenario in which the bad norm \(\omega _{it}=1\) is persistent on account of relatively large J and \(m^e_{it}\), such that in the majority of rounds \(\rho _{it}=0\). Ex-ante, the probability of an individual choosing \(\omega _{it}=-1\) in a given round t is \(\hat{\rho }_t\), regardless of the group size. Now consider the rounds in which \(0<\rho _{it}<0.5\); that is, the bad norm \(\omega _i=1\) is still in effect but at least one group member receives a private shock difference large enough to induce choosing \(\omega _{it}=-1\). This likelihood is not the same across group sizes. The probability that at least one group member chooses \(\omega _{it}=-1\) increases with N, and so we would expect a higher proportion of rounds with\(\rho _{it}\ne 0\) in larger groups while the bad norm persists. However, the marginal effect of a group member choosing \(\omega _{it}=-1\) on the overall group proportion \(\rho _{it}\) decreases with N, and so of those rounds where \(\rho _{it}\ne 0\) while the bad norm persists, we would expect that \(\rho _{it}\) is higher on average for smaller groups.

Now, assume there is some ‘tipping proportion’ \(\tilde{\rho }\) that, if reached after a previous equilibrium of full conformity to the bad norm (\(\rho ^*\approx 0\)), would result in a switch to the ‘good’ equilibrium \(\rho ^*\approx 1\) with almost certainty. The tipping proportion is greater than the predicted group proportion \(\hat{\rho }_t\) so that on expectation it should not be breached in a given round. Then, after a round in which \(\rho _{t-1}\approx 0\), the probability of reaching the tipping proportion in round t is the probability that at least \(N\tilde{\rho }\) individuals choose \(\omega _{it}=-1\). From the researcher’s perspective, the number of individuals choosing \(\omega _{it}=-1\) follows a binomial distribution so that \(N\rho _t\sim \mathcal {B}(N,\hat{\rho }_t)\) and hence:

$$\begin{aligned} \Pr \left( \rho _t\ge \tilde{\rho }\right)&=1-\Pr \left( \rho _t<\tilde{\rho }\right) \nonumber \\&=1-\sum ^{\lfloor N\tilde{\rho }\rfloor }_{j=0}\left( {\begin{array}{c}N\\ j\end{array}}\right) \hat{\rho }_t^j(1-\hat{\rho }_t)^{N-j} \end{aligned}$$
(11)

where \(\lfloor N\tilde{\rho }\rfloor\) is the largest integer less than \(N\tilde{\rho }\).

This function does not change monotonically with N. However, some idea can be garnered as to how the probability is affected across general size increases. The binomial distribution can be approximated by a normal distribution with mean \(N\hat{\rho }_t\) and variance \(N\hat{\rho }_t(1-\hat{\rho }_t)\) when \(N\hat{\rho }_t>5\). Assuming this is met, equation (11) can be approximated by:

$$\begin{aligned} \qquad \Pr \left( \rho _t\ge \tilde{\rho }\right)&=1-\Pr \bigg (\frac{N(\rho _t-\hat{\rho }_t)}{\sqrt{N\hat{\rho }_t(1-\hat{\rho }_t)}}<\frac{N(\tilde{\rho }-\hat{\rho }_t)}{\sqrt{N\hat{\rho }_t(1-\hat{\rho }_t)}}\bigg )\nonumber \\&\approx 1-\varPhi \Big (\sqrt{N}\frac{\tilde{\rho }-\hat{\rho }_t}{\sqrt{\hat{\rho }_t(1-\hat{\rho }_t)}}\Big ) \end{aligned}$$
(12)

which, for \(\tilde{\rho }>\hat{\rho }_t\), is a decreasing function of N.

When a bad norm is in effect, smaller groups are thus generally more likely to breach the tipping proportion in a given round. The effect of size on persistence increases slowly and not monotonically, although comparisons can be made for sizes that are not very close together. This is due to the discrete nature of the possible proportions and hence the upper sum limit \(\lfloor N\tilde{\rho }\rfloor\).

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Smerdon, D., Offerman, T. & Gneezy, U. ‘Everybody’s doing it’: on the persistence of bad social norms. Exp Econ 23, 392–420 (2020). https://doi.org/10.1007/s10683-019-09616-z

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Keywords

  • Social norms
  • Pluralistic ignorance
  • Social interactions
  • Equilibrium selection
  • Conformity

JEL Classification

  • C92
  • D70
  • D90
  • Z10