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The level of climate-change mitigation depends on
how humans assess the risk arising from missing the
2 °C target
Kristin Hagel ([email protected]) (Max Planck Institute for Evolutionary
Biology), Manfred Milinski, Jochem Marotzke
Supplementary information:
S.1 Methods
S.2 Frequency of selfish, fair-share, and altruistic individual investments
S.3 Experiment instructions
S.1 Methods
Experimental design. We tested 198 undergraduates from the Universities of Kiel (in
November 2013) and Hamburg (in December 2013). We divided the participants into
33 groups of six subjects each. We performed a computerized experiment using the
experimental software Z-Tree (Fischbacher, 1999). Our goal was to see whether they
would contribute their own money, which they had received as an initial endowment
of €40 each, to prevent simulated dangerous climate change in a collective-risk social
dilemma (Milinski et al., 2008). They were separated by opaque partitions and asked
to perform anonymously ten rounds of a climate game. In each round each subject
could choose to donate €0, €2, or €4 into a climate account; they were informed at the
beginning of the game that the money collected in this account would be used to buy
an advert in a German daily newspaper informing about the risks of climate change.
Donations into the climate account are hence a metaphor for investing into climate
change mitigation. The subjects received the ‘‘little-information’’ version from
Milinski et al. (2006) to explain the climate account, so that we could expect weak
motivation to invest in publishing the advertisement per se. If a group collected €120
or more in the climate account over the ten rounds (on average, €20 per subject and
thus half of each subject’s initial endowment), each subject was paid out in cash (after
the game and without disclosing the subject’s identity) the remainder of this subject’s
initial endowment.
The subjects received a print copy of the part of Fig. 1a, b or c that applied to
the specific risk curve of their treatment. After each round the decisions of the six
subjects were displayed on all computers simultaneously, allowing the subjects to
track their fellow group members’ decisions as well as the round sum in the climate
account. Additionally, pen and paper were provided for making notes. If a group
collected less than €120, the computer ‘‘threw dice’’ so that with a probability that
depended on treatment and group investment over ten rounds (Fig. 1a-c), all group
members lost all their savings or, if lucky, received the remainder of their endowment
as described above.
Identification of group contribution with climate change mitigation. Our
interpretation of our experiment design assumes not only that the group investment in
our game can be identified with mitigated warming but also that this relationship is
linear. In principle, effort in reducing greenhouse-gas emissions leads to a delayed
rather than a direct reduction in warming, because it is the accumulated emissions that
determine greenhouse-gas concentrations, and it is the accumulated radiative forcing
from greenhouse-gas concentrations that determines temperature (Sterman, 2008). In
practice, however, there is robust evidence that emissions reductions by the mid-21st
century are linearly related to cumulative CO2 emissions over the 21st century, which
in turn are linearly related to the total warming over the 21st century (Allen et al.,
2009; Matthews et al., 2009; Collins et al., 2013; Gillett et al., 2013; IPCC, 2013;
2014).
The simple linear relationship between emissions reductions by mid-century
and warming arises because of two counteracting processes of the global carbon cycle
(Matthews et al., 2009). At higher already-present CO2 concentrations, a certain
amount of CO2 emissions has a smaller radiative effect (radiative forcing is
proportional to the logarithm of CO2 concentration); on the other hand, at higher CO2
concentrations and hence higher temperatures a larger fraction of the CO 2 emissions
remains in the atmosphere, instead of being taken up by the oceans and by the land
biosphere.
Once we accept the proportional relationship between effort toward emissions
reductions and mitigated warming, the interpretation of the €80 focal point in T2 as a
focal point of 3 °C warming quantitatively works as follows. Any warming limit that
is based on comparing against the pre-industrial globally averaged temperature must
take into account that by now, nearly 1 °C of warming has already happened (“past
warming”); see, for example, IPCC (2013). Furthermore, a scenario without
mitigation is expected to lead to a 21st-century warming of about 4 °C (IPCC, 2007;
2013). But the more we mitigate, the further we reduce the 21st-century warming
against this no-mitigation case of 4 °C. If we mitigate by 3 °C, we have a 21 st-century
warming of only 1 °C, and we reach the 2 °C target exactly (the past warming of 1 °C
must be added to the 21st-century warming). Achieving 3 °C mitigation and hence
reaching the 2 °C target is mirrored in our experiment by the group of subjects
collecting €120. Collecting €80 constitutes two-thirds of the effort and hence
corresponds to 2 °C mitigation, assuming that the mitigation result is proportional to
the effort. Mitigation by 2 °C implies a 21st-century warming of 4 – 2 = 2 °C and
hence, because the past warming of 1 °C must be added, a warming of 3 °C above
pre-industrial. We thus interpret T2 such that the risk of dangerous climate change
decreases linearly from 90% to zero as mitigation increases from 2 °C to 3 °C.
In T3 we consider the case where loss probability decreases linearly with the
sum collected for any sum up to €120. Again we interpret this as 21st-century
mitigation of climate change that is proportional to effort, but we now assume that the
risk of dangerous climate change is proportional to the globally averaged warming
during the 21st century, for any amount of this warming.
In summary, although we cannot completely mirror the risk of dangerous climate
change by means of an economic experiment, our design allows us to infer an important
aspect of climate-change mitigation – the influence of risk assessment on cooperative
behaviour.
Expected winnings. The average expected winnings per subject, as a function of
group contribution over ten rounds, are given in T1 by
,
in T2 by
(1)
,
(2)
and in T3 by
,
(3)
where E is the initial endowment of €40, s is the group investment over ten rounds, N
is the number of players within a group, and p is the maximum loss probability of
90% (see Figure 1d-f). T120 denotes a group investment of €120 over ten rounds and
represents the 2° C target; T80 denotes a group investment of €80 over ten rounds and
represents the 3° C focal point.
For T1 and T2, the maximum average expected winnings per subject are
readily read off the graphs (Fig. 1d,e); they occur at the target sum of €120 and
amount to €20 (equations 1 and 2, respectively). In T3, the maximum average
expected winnings per subject, smax, are readily found by setting the derivative of f(s)
in equation (3) to zero, yielding
.
For the parameters chosen here, smax= €113.3.
S.2 Frequency of selfish, fair-share, and altruistic individual investments
We find significant differences among treatments for the frequency of both selfish
investments (€0; Kruskal–Wallis test, nT1, nT2, nT3 = 11, χ2= 16.00, P< 0.001) and
altruistic investments (€4; Kruskal–Wallis, nT1, nT2, nT3 = 11, χ2= 10.30, P= 0.0058).
By contrast, the frequency of fair-share investments (€2) does not differ significantly
among treatments (Kruskal–Wallis, nT1, nT2, nT3 = 11, χ2= 4.02, P= 0.1341) (Fig.
S1.). In pairwise comparisons, selfish investments were significantly more frequent in
T3 than in T1 and in T2 (Wilcoxon rank sum test, n T1, n T2, n T3 = 11, WT1
PT1
vs. T3<
0.0005; WT2
vs. T3=
11, PT2
vs. T3=
vs. T3=
7.5,
0.0012; Fig. S1.), and altruistic
investments were significantly less frequent in T3 compared to each of the other
treatments (Wilcoxon rank sum test, n T1, n T2, n T3 = 11, WT1
vs. T3=
105.5, PT1 vs.
T3=
0.0032; WT2 vs. T3= 96, PT2 vs. T3= 0.021; Fig. S1.).
Fig. S1. Frequency of (a) selfish (providing €0), (b) fair-share (providing €2), and (c)
altruistic (providing €4) investments per group of six players for T1 (blue), T2 (green),
and T3 (brown).
S.3 Experiment instructions
Instructions for each of the 3 treatments (translated from German)
Welcome to this experiment in which you can earn money!
At the start of the experiment, €40 will be credited to your account as your personal
endowment. In the course of the game you can decide whether you want to invest
money from your endowment.
All decisions you make are anonymous. To ensure this, a pseudonym is assigned to
you by the computer, visible at the bottom left of the screen. These pseudonyms
correspond to names of moons in our solar system (Ananke, Telesto, Despina,
Japetus, Kallisto, or Metis).
For a successful experiment you must not talk to the other participants or make
yourself noticeable to them in any way.
You must confirm all information obtained during the course of the game by clicking
NEXT.
Over the course of this experiment you will play exactly 10 climate rounds.
In each of these rounds you can invest in an attempt to avoid dangerous climate
change. One of the consequences of dangerous climate change will be serious
economic loss, which is simulated in this game.
In each round of the game all six players will be asked simultaneously: How much do
you want to invest in climate protection? (Possible answers: €0, €2 or €4)
When every player has made his decision all six choices are displayed
simultaneously. Afterwards all contributions will be credited to an account for climate
protection.
Funded by the money that you may have paid into climate protection, we will place
an advertisement in a large daily newspaper. This will give general information about
simple methods for climate protection – methods that everybody can implement
without much effort to protect our climate and to assist in avoiding dangerous climate
change. The more money we collect, the larger and more conspicuous the
advertisement will be. If this promotion is successful, sponsors for international
advertising campaigns could be mobilized.
After reading please confirm by clicking NEXT.
Professor Jochem Marotzke, Director at the Max-Planck-Institute for
Meteorology in Hamburg will provide expertise about the state of the climate for the
advertisement. He will also give some recommendations on how to abate CO2-
emissions and how the climate can be protected; for example, energy can be saved by
decreasing ambient room temperature or by the use of public transportation instead of
private cars. Furthermore, the increased use of renewable energy sources contributes
to greenhouse-gas abatement.
After reading please confirm by clicking NEXT.
Continued climate round
After every round, the decisions of all players will be displayed.
Example: Four players have decided to invest into climate protection. Two of them
paid €2, and the other two of them paid €4.
Pseudonym
Leda
Triton
Portia
Sinope
Carpo
Galate
Decision
Yes
No
No
Yes
Yes
Yes
-2.00
0.00
0.00
-4.00
-2.00
-4.00
Change in
the player's
account
In total €12 were paid for climate protection and thus credited to the climate account.
After reading please confirm by clicking NEXT.
Up to this point the introductions of the three treatments are identical. The following
text differs among treatments:
Treatment 1:
The end of the game
At the end of the game (after exactly 10 rounds), the computer compares the climate
account with the threshold amount of €120. This threshold amount has to be reached
to avoid dangerous climate change. It is reached if every player pays on average €2
per round for climate protection. In this case, €12 per round would be paid into the
climate account.
If this amount is reached in the climate account, every player will obtain whatever is
left over in his account. The payment will be paid anonymously by means of your
pseudonym.
If the threshold amount for the climate account is not reached, dangerous climate
change will occur with a probability of 90% (thus in 9 out of 10 cases), followed by
serious economic losses. This will be the probability of losing the savings in your
account, and no group member will receive a payment.
For instance: If your group invests less than €120 over 10 rounds, you will lose your
savings of the initial endowment with a probability of 90% (thus in 9 out of 10 cases).
There will be a probability of 10% (thus in 1 out of 10 cases) that you would keep
your savings. In this case your savings will be paid to you in cash anonymously after
the game. If your group invests at least €120, you will definitely receive the savings
from your account (see Fig. 1).
Fig. 1. Probability of losing savings from your initial endowment, dependent on the
total group investment over 10 rounds.
After the game the computer decides randomly by “throwing a dice” with this
probability.
After reading please confirm by clicking NEXT.
The experiment will start now.
After reading please confirm by clicking NEXT
Treatment 2:
The end of the game
At the end of the game (after exactly 10 rounds), the computer compares the climate
account with the threshold amount of €120. The threshold amount has to be reached
to avoid dangerous climate change. It is reached if every player pays on average €2
per round for climate protection. In this case, €12 per round would be paid into the
climate account.
If this amount is reached in the climate account, every player will obtain whatever is
left over in his account. The payment will be paid anonymously by means of your
pseudonym.
If the threshold amount for the climate account is not reached, dangerous climate
change will occur with a probability of 90% (thus in 9 out of 10 cases) if your
group has collected up to €80 over 10 rounds. Since dangerous climate change is
followed by serious economic losses, you will lose the savings in your account with
this probability, and no group member will receive a payment. The probability drops
linearly with further investments if your group invests an amount between €80
and €120 over 10 rounds. Finally, the probability equals zero at €120, and all players
will definitely receive their savings.
For instance: If your group invests €90 over ten rounds, you will lose your savings of
the initial endowment with a probability of 68%, thus in about 7 out of 10 cases
(accordingly you will keep your savings in about 3 out of 10 cases). If your group
invests €100 over ten rounds, you will lose your savings of the initial endowment with
a probability of 45%, thus in about 5 out of 10 cases (accordingly you will keep your
savings in about 5 out of 10 cases). And if your group invests €110 over ten rounds,
you will lose your savings of the initial endowment with a probability of 20%, thus in
about 2 out of 10 cases (accordingly you will keep your savings in about 8 out of 10
cases). If your group invests at least €120 you will definitely receive the savings in
your account (see Fig. 2).
.
Fig. 2. Probability of losing savings from your initial endowment, dependent on the
total group investment over 10 rounds.
After the game the computer decides randomly by “throwing a dice” with this
probability.
After reading please confirm by clicking NEXT.
The experiment will start now.
After reading please confirm by clicking NEXT.
Treatment 3:
The end of the game
At the end of the game (after exactly 10 rounds), the computer compares the climate
account with the threshold amount of €120. The threshold amount has to be reached
to avoid dangerous climate change. It is reached if every player pays on average €2
per round for climate protection. In this case, €12 per round would be paid into the
climate account.
If this amount is reached in the climate account, every player will obtain whatever is
left over in his account. The payment will be paid anonymously by means of your
pseudonym.
If the threshold amount for the climate account is not reached, dangerous climate
change will occur with a probability that drops such that higher group
investments linearly decrease the risk of losing savings over 10 rounds. Since
dangerous climate change is followed by serious economic losses, you will lose the
savings in your account with this probability, and no group member will receive a
payment.
For instance: If your group invests €30 over ten rounds, you will lose your savings of
the initial endowment with a probability of 78%, thus in about 8 out of 10 cases
(accordingly you will keep your savings in about 2 out of 10 cases). If your group
invests €60 over ten rounds, you will lose your savings of the initial endowment with
a probability of 45%, thus in about 5 out of 10 cases (accordingly you will keep your
savings in about 5 out of 10 cases). If your group invests €90 over ten rounds, you
will lose your savings of the initial endowment with a probability of 23%, thus in
about 2 out of 10 cases (accordingly you keep your savings in about 8 out of 10
cases). If your group invests at least €120, you will definitely receive the savings in
your account (see Fig. 3).
Fig. 3. Probability of losing savings from your initial endowment, dependent on the
total group investment over 10 rounds.
After the game, the computer decides randomly by “throwing a dice” with this
probability.
After reading please confirm by clicking NEXT.
The experiment will start now.
After reading please confirm by clicking NEXT.
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