Supplementary Materials for "Collective Action, Rival Incentives,
and the Emergence of Antisocial Norms"
Online Appendix B. Supplementary Figures (2b,2c,3b,3c,4b,4c)
The following document shows surface plots for enforcement behavior
corresponding to the surface plots for collective action shown in the
paper. Figures 2b, 3b, and 4b show the prosocial norms
(enforcement behavior promoting collective goods) corresponding to
Figures 2, 3, and 4 in the article. Figures 2c, 3c, and 4c show the antisocial
norms (enforcement behavior opposing collective goods) corresponding to
Figures 2, 3, and 4 in the article.
- Supplementary Figures
Online Appendix C. Sensitivity Analyses
Figures 2, 3, and 4 in the article are maps of equilibrium outcomes
("response surfaces") over ranges of experimentally manipulated
parameter values. Each experiment holds constant a set of other
parameters. Sensitivity analyses -- presented here as a series of
animated movies -- show robustness of my conclusions on the model's
qualitative behavior to variation in some of these other parameters.
Note that each movie is not an animation of the model's behavior over
time, but is a shifting map of the model's equilibrium response surface
as a third parameter is manipulated.
Movies are standard ".avi" format, and can be viewed with most
media players, such as Windows
Media
Player or
Apple QuickTime.
In Experiment 1, Figure 2 showed the response surface for productivity
with zero rivalness (λ=0) and Figure 3 showed this response
surface with maximum rivalness (λ=1). The animation of Figure
3 shows the changes in this response surface over the entire range of
rivalness, between these two extremes.
- Figure 3 (Productivity
x Cohesiveness x Incentive Value) animated with
rivalness increasing from λ=0 to λ=1
- Figure 3b (Promotion
x Cohesiveness x Incentive Value) animated with
rivalness increasing from λ=0 to λ=1
- Figure 3c (Opposition
x Cohesiveness x Incentive Value) animated with
rivalness increasing from λ=0 to λ=1
The animation of Figure 3c shows the appearance and expansion of stable
oppositional norms as rivalness increases from zero. The expansion of
prosocial norms as rivalness increases in Figure 3b seems
counterintuitive, but is due to second-order shirking at low rivalness:
When most actors are contributing to the collective good, individuals
may abstain from promoting work, but effective antisocial norms dampen
productivity and thus create an opportunity for prosocial norms to
emerge at high rivalness.
In the experiments presented in the article, enforcement is moderately
costly (e=2). The following animations show the changes in
model response surfaces as enforcement cost increases from perfectly
costless (e=0) to extremely expensive (e=5).
- Figure 3 (Productivity
x Cohesiveness x Incentive Value) animated with
enforcement cost increasing from e=0 to e=5
- Figure 3b (Promotion
x Cohesiveness x Incentive Value) animated with
enforcement cost increasing from e=0 to e=5
- Figure 3c (Opposition
x Cohesiveness x Incentive Value) animated with
enforcement cost increasing from e=0 to e=5
- Figure 4 (Productivity
x Rivalness x Incentive Value) animated
with enforcement cost increasing from e=0 to e=5
- Figure 4b (Promotion
x Rivalness x Incentive Value) animated with
enforcement cost increasing from e=0 to e=5
- Figure 4c (Opposition
x Rivalness x Incentive Value) animated with
enforcement cost increasing from e=0 to e=5
Increasing the cost of enforcement from 0 to 5 has an unsurprising
dampening effect on enforcement behavior, but the overall qualitative
patterns identified in the article (Figures 3 and 4) are robust over
this entire range. As mentioned, if enforcement is so costly or
difficult that no actor will ever enforce, we would obviously observe
no informal control and thus productivity will be a straightforward
function of selective incentives. This animation of Figure 3c shows the
reason for the surprising curvilinear relationship between incentive
value and antisocial norms, described in the article. As enforcement
cost rises, second-order free riding may in some cases be a solution to
the collective action problem identified in this article: Actors who
would prefer antisocial norms in the most highly competitive
environment nevertheless refrain from opposing work because the benefit
of doing so does not exceed the cost of enforcement in those
conditions.
In the experiments presented in the article, subjective scope of
influence is uniformly distributed in the range [0,9]. The following
animations assign the same influence scope value to all group members,
but vary the scope value from the minimum (θ=1) to the maximum
(θ=N-1).
- Figure 3 (Productivity
x Cohesiveness x Incentive Value) animated with
influence scope increasing from θ=1 to θ=9
- Figure 3b (Promotion
x Cohesiveness x Incentive Value) animated with
influence scope increasing from θ=1 to θ=9
- Figure 3c (Opposition
x Cohesiveness x Incentive Value) animated with
influence scope increasing from θ=1 to θ=9
- Figure 4 (Productivity
x Rivalness x Incentive Value) animated
with influence scope increasing from θ=1 to θ=9
- Figure 4b (Promotion
x Rivalness x Incentive Value) animated with
influence scope increasing from θ=1 to θ=9
- Figure 4c (Opposition
x Rivalness x Incentive Value) animated with
influence scope increasing from θ=1 to θ=9
As noted in the article, homogeneous θ<3 implies that no
actor will promote work, given the enforcement cost. We see no
promotion (and little opposition) in these conditions, where actors
believe that their influence efforts will have negligible effect. The
qualitative shape of the response surface presented in the article is
robust over the rest of the range of influence scope.