model consists of only one resource stock with one inflow and one outflow, i.e. the basic building block of all dynamic systems. If subjects systematically.
Moxnes: Misperceptions of Basic Dynamics 139 Misperceptions ofErling basic dynamics: the case of renewable resource management
Erling Moxnes*
Erling Moxnes is a professor in System Dynamics at the University of Bergen. Here he teaches traditional system dynamics, experimental methods, and optimization in the university’s International Master Program in System Dynamics. His research is mainly concerned with studies of misperceptions of dynamics and uncertainty in connection with sustainable development in areas such as renewable resources and energy.
Abstract Previous laboratory experiments, using quite complex resource simulators, suggest that renewable resources are over-utilised because of a general tendency for people to systematically misperceive the dynamics of bioeconomic systems. Here, similar experiments with simplified simulators involving the management of reindeer rangelands are carried out. Sufficient information is given for the subjects to construct perfect mental models. Misperceptions persist for a simulator containing only the basic building block of all dynamic systems: one stock and two flows. Results deteriorate in a second treatment where a two-stock model is used. Compared to earlier studies using questionnaires, where subjects do not benefit from repeated outcome feedback, the experiments show that, even in these simple systems, information feedback is not sufficient to make up for misperceptions. Simulations are used to test two hypothesised decision rules: the optimal policy is rejected; a simple feedback rule is not. Altogether, the experiment and the simulations provide both a motivation for and an introduction to studies of system dynamics. Copyright © 2004 John Wiley & Sons, Ltd. Syst. Dyn. Rev. 20, 139–162, (2004)
There are numerous examples of overexploitation and at times extinction of renewable resources, think of, for example, whales, forests and fish, as well as some reindeer pastures. A prominent theory for why this happens is the “tragedy of the commons” (Hardin 1968; Gordon 1954; and others back to Aristotle). However, overexploitation has also taken place for privately owned renewable resources and for shared resources with policies in place to tackle the commons problem. An alternative or supplementary theory for overexploitation is misperception of dynamics. Laboratory experiments show overinvestment and overutilisation even when the subjects (students and professionals) have full property rights and monetary incentives to behave optimally (Moxnes 1998a,b; 2000). These results are consistent with experimental studies of other complex dynamic systems (e.g., Sterman 1989a,b; Funke 1991; Brehmer 1992), showing, with few exceptions, considerable deviations from normative standards. The laboratory experiments used thus far have been characterised by considerable complexity and ambiguity about model structure and parameters. Here we construct similar experiments, but reduce the complexity to a minimum. In the present experiments it is possible to reconstruct perfectly the underlying model and its parameters from the instructions. Consequently, ∗ Correspondence to: Prof E. Moxnes, Dept. of Information Science, University of Bergen, PO Box 7800, N-5020, Bergen, Norway. E-mail: Erling.Moxnes@ifi.uib.no Thanks to the editors and referees for valuable comments and to the students for participating in the experiments and for ensuing discussions. System Dynamics Review Vol. 20, No. 2, (Summer 2004): 139–162 Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/sdr.289 Copyright © 2004 John Wiley & Sons, Ltd.
Received March 2003 Accepted July 2003
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observed subject behaviour can be compared to optimal normative behaviour. There are two treatments with different levels of complexity. The simplest model consists of only one resource stock with one inflow and one outflow, i.e. the basic building block of all dynamic systems. If subjects systematically misperceive such a simple dynamic system, it should motivate further studies of dynamic systems and signals a need for improved education in dynamic systems in general. From a methodological point of view it is interesting to note that a development towards more and more simple experimental designs parallels tendencies seen in the investigations of judgement under uncertainty. According to Edwards (1982, p. 361): “The simple example . . . didn’t occur to us; instead we were sure that we would need to use a fairly complex situation in order to get non-Bayesian behaviour.” Other attempts at testing misperceptions of simple dynamics have been made by Booth Sweeney and Sterman (2000), Kainz and Ossimitz (2002), and Ossimitz (2002). These investigations show systematic misperceptions of perfectly described, simple open-loop dynamic systems. The three studies contribute importantly to our knowledge about how people misperceive the basics of dynamic systems. They all use an experimental design different from ours, asking subjects to project consequences over time of certain actions; the subjects are not asked to manage simulators with information feedback and repeated decisions. When we choose the latter design, we allow the subjects to benefit and learn from feedback. Hence, errors made at an early stage can be corrected at later stages. An important question is: will the available feedback be sufficient to avoid serious effects of misperceptions in our simple dynamic systems? Compared to the more complex experiments of renewable resources, we find that the basic tendency towards misperception remains when the experiment is simplified to one stock with two flows. Compared to the simple experiments asking for projections, the basic misperceptions remain when feedback and repeated decisions are allowed. A second treatment with a two-stock model shows that complexity matters. Finally we use model simulations to examine subject policies. An optimal strategy (constant target escapement1) is rejected while a simple feedback rule is not.
The experimental design Treatment T1—one stock The task faced by the subjects is one of managing a renewable resource, a reindeer rangeland. The most important dynamic factor for reindeer management is lichen, the plant providing the main source of winter fodder for the reindeer. Figure 1 shows how the stock of Lichen is increased by Growth (total
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Fig. 1. The stock and flow structure of the simple design, T1
growth minus decay) and reduced by Grazing. Grazing in turn depends on Grazing_per_animal and the Herd_size. The Herd_size is the decision variable, to be set once each year. The subjects are told that the herd size can be varied freely (as if animals can be sold and bought in a market). Growth depends on the stock of Lichen as described by the solid line in Figure 2. Fig. 2. Growth curve with calculated data points. The + signs denote historical grazing rates
The subjects in the experiment do not get to see the structure of the problem as depicted in Figure 1. The stock and flow diagram is one of the tools of system dynamics and has typically not been available to decision makers thus far. Consequently, a structuring of the problem by this tool has not been available either. Therefore, the subjects get verbal descriptions. However, the descriptions (Appendix 1) are sufficient to construct the model in Figure 1. Regarding the growth curve, the subjects learn that there will be no growth when the lichen thickness equals zero (the “seed” is missing) and when it equals 60 mm (due to crowding). They are also told that growth reaches a maximum somewhere between these extremes. They do not get to see the growth curve in Figure 2 since such growth curves have not been estimated until recently for lichen ranges (Moxnes et al. 2002). Consequently such growth curves have not been used in policy discussions. The subjects get exact information about the parameter Grazing_per_animal (0.004 mm/year). In addition
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they receive perfect information (figures and tables) about the development of the herd size and the lichen thickness over the last 15 years—the most recent period before they take over the management of the range. Real decision makers deal with less precise information, implying that they face a somewhat more complex problem. If the structure of the model is known, the time series can be used to estimate the growth curve from the time-series data. We measure the stock of lichen Lt by its average thickness (mm) and write the equation:2 L t+1 = L t + gt − hNt
(1)
where Nt is the herd size, gt is the growth rate for lichen, and h is grazing per animal. Rearranging the equation with gt on the left-hand side: gt = L t+1 − L t + hNt
(2)
we get data points for growth as a function of the lichen thickness; see the open squares in Figure 2. The data points for the last two years of the historical period provide data points to the left of the peak of the curve; hence the location of the maximum growth is found at a lichen thickness of 30 mm. This is the lichen thickness that gives the maximum sustainable yield (gmax = 5 mm/ year) and that represents the desired sustainable situation. Knowing that h equals 0.004 mm/year, we find the maximum sustainable herd size equal to Nmax = gmax/h = 1,250. If one is able to perform the above calculations, one has a perfect model to work with after spending just a few minutes on calculations. In the base treatment, T1, the task faced by the subjects is to reach the maximum sustainable herd size (and the maximum sustainable growth of lichen) as quickly as possible. The initial condition is one of overgrazing, with a lichen thickness L0 = 24.4 mm, i.e. less than the desired 30 mm. Figure 2 shows that initial growth g0 is slightly lower than gmax, while the initial grazing rate (hN0) is 50 percent higher than g0 (shown by the far left + sign in Figure 2). The optimal policy is to reduce the herd size to zero in the first year, increase the herd to 1,056 in the second year, and then reach the maximum sustainable herd of 1,250 and the corresponding lichen thickness of 30 mm in the third year (recall that the subjects are allowed to sell or buy any quantity of reindeer in the market). Given that Figure 2 has been properly constructed by the subject, an approximate solution is intuitively simple. First, the figure makes clear that grazing must be brought below the current growth rate to rebuild lichen. Second, three years with around 50 percent overgrazing since the growth peak was passed implies that three years with about 50 percent undergrazing is needed to return to the growth peak. Third, to reach the desired situation as quickly as possible, however, the herd should be reduced to zero in the first year. Then feedback about the development could be used to fine tune the herd size to the maximum sustainable state. The optimal policy is consistent with the constant target escapement policy known from resource economics (e.g., Clark 1985).
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Since it is possible to get very close to the optimal policy with simple means, we choose the optimal policy as our benchmark to judge observed subject behaviour. This is different from earlier, more complex experiments where underlying simulators have not been fully explained and where there has been ambiguity about both models and parameters. Hence in our case there is no need for learning and thus the problem is in principle much simpler than the previous experiments requiring learning. In practice, the difference may be of little importance if the subjects are not able to perform the above calculations. Then they have to rely on learning-by-doing anyway. Treatment T2—two stocks The second treatment, T2, is equal to T1 except that animals cannot be varied freely; the growth of the herd size is limited by recruitment from the existing herd (animals can be slaughtered but not bought), see Figure 3. Thus, in addition to lichen, also the livestock of reindeer Nt is modelled by a stock variable: Nt+1 = Nt + Rt − max(0, Nt + Rt − DNt)
(3)
where Rt is the recruitment of livestock and the expression in parentheses denotes the slaughtering of livestock. Since the livestock consists of 90 percent females and 10 percent males, all male calves in excess are excluded from Rt. DNt is the desired herd size, the decision variable. We see that if DNt is larger Fig. 3. The stock and flow structure of the complex design, T2
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than Nt + Rt, no livestock is slaughtered and the population growth is limited by the recruitment. Also note that compared to the model in T1, there will be a one-year delay after the desired herd DNt is changed until the lichen stock is affected. The subjects receive exact information about all parameters needed to calculate Rt; see Appendix 2. Thus, also in T2, subjects have perfect knowledge about the model such that learning-by-doing is in principle not needed. The optimal solution is more complicated than in T1, although the same logic applies regarding the lichen dynamics. In T2 one must take into consideration that if the herd size is reduced too much in the first year, there will be a shortage of reindeer at the time lichen reaches the desired level (30 mm). A rough estimate of the maximum growth rate for the herd could be used to indicate an appropriate first-year level for the herd size and to get quite close to the optimal solution. The optimal solution or the benchmark shown in Figure 5 is found by trial and error. Subjects and design details For both treatments, subjects were recruited among students with varied backgrounds entering the international Masters degree programme in System Dynamics at the University of Bergen. T1 was run in September 2002 (n = 16) and 2003 (n = 18), while T2 was run in September 2000 (n = 16) and 2001 (n = 15). In all runs except the one in 2000, each subject had three trials with the same simulator. The T1 simulator was programmed in Excel3 while T2 was programmed in Powersim.4 The person in each group and each trial getting closest to the maximum sustainable situation in the shortest time was promised and received a small prize. Each subject was situated at a separate PC with no communication allowed with other subjects. Importantly, each subject was granted private property rights to his or her lichen pastures and herds. Thus, the commons problem was ruled out by the design.
Results Figure 4 shows 95 percent confidence intervals for average herd sizes and lichen thicknesses for trial one in T1. Optimal paths are shown with dashed lines. Graphs are shown separately for the classes of 20025 and 2003. In the early years, the average herd size is significantly higher than the optimal one and, in later years, it is significantly lower. Hence, on average the subjects in T1, the simplest case, are not successful in reaching the maximum sustainable herd size within 15 years. The lichen thickness is significantly lower than the optimal lichen thickness in all years after the initial one. There is no significant difference between the classes of 2002 and 2003, with respect to neither herd size nor lichen.
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Fig. 4. Optimal and 95 percent confidence intervals for the average first trial results for herd size and lichen thickness; T1-2002 (thick lines) and T1-2003 (thin lines)
Figure 5 shows 95 percent confidence intervals for average herd sizes and lichen thicknesses for trial one in T2. Graphs are shown separately for the classes of 2000 and 2001. Optimal paths are shown with dashed lines; it takes three more years to reach the desired situation in T2 than in T1 because of the recruitment limitations for the reindeer. When the 95 percent confidence intervals for the average herd sizes and lichen thicknesses are considered, there are almost perfect overlaps between the experiments in 2000 and 2001. When the results of T1 and T2 are compared, the patterns are largely the same. However, the distance from the optimal situation seems larger in the complex case with two stocks, T2. To see if the differences are statistically significant at the 5 percent level, we compare lichen thicknesses relative to optimal lichen thicknesses for the two treatments. Figure 6 shows confidence intervals for the pooled results of T1 (2002 and 2003) and for T2 (2000 and 2001). T2 appears to produce better results in year one and two, but this is only because the subjects in T2 cannot influence lichen in the first year and hence cannot deviate from the optimal response. After that, the average relative lichen thickness is lower in T2 than in T1. Comparing the results year by year,
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Fig. 5. Optimal and 95 percent confidence intervals for average trial results for herd size and lichen thickness; T2-2000 (thick lines) and T2-2001 (thin lines)
Fig. 6. 95 percent confidence intervals for average lichen thicknesses for treatments T1 (thin lines) and T2 (thick lines)
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we find the p-values shown by the dashed line in Figure 6.6 The difference is statistically significant in the time interval from 4 to 13. Next we look at how the results improve over repeated trials. Such improvements are at times referred to as learning. However, one should be aware that improvements over trials could also be the result of trial-and-error with no deeper learning involved. A probably less biased test of learning is to investigate how new insights are transferred from one case to another (Bakken 1993; Paich and Sterman 1993; and Jensen 2004). When that is said, lack of improvement over repeated trials with the same case does signal lack of learning. Hence, what we present here indicates an upper limit for learning. Radical and sudden shifts in individual strategies may also indicate learning and we report the frequency of such events. However, before we consider learning, we have to address another problem: the subjects’ interpretation of the term sustainable. In the introduction to the experiments we say: “Note, however, you should make sure that your operation is sustainable.” We took for granted that all subjects interpreted this to mean that the herd size they ended up with could be sustained forever, without destroying the food resource lichen. Later discussions with subjects have revealed that some of them interpreted the term sustainable otherwise. They seem to have interpreted sustainable to mean that the lichen resource should last for the 15 years of the experiment, but no longer than that. This is an interesting finding in itself. Furthermore, it implies that we have to remove these subjects as outliers when we investigate improvements towards a truly sustainable maximum herd size over trials. We define this subgroup to be those who in both of the two last trials approximately deplete lichen in the last year or those who approximately deplete lichen in the third trial while not depleting lichen in the second trial. We find the following frequencies of misperceived sustainability: T2-2001 none out of 15, T1-2002 four out of 15, T1-2003 four out of 18. When these subgroups are removed, improvements over trials are as shown in Figure 7. In T1 the average lichen thickness moves quite rapidly towards the optimal level from trial one to trial two. Then the improvement is considerably smaller from trial two to trial three. In the complex case, T2, improvements are slower. Even after the third trial there is a considerable improvement potential. Finally, we show results indicating learning over time during the first trial. The example in Figure 8 is from treatment T1-2002. For most subjects the development of lichen is nearly linear over time. Three major exceptions are highlighted by thick lines. The subject with a lichen level closest to the optimal one seems to realise by the second year what is needed to get a favourable development in lichen. The two others make sudden and large reductions in the herd size in year 9. In the group T1-2003 one subject is doing it right from the very beginning, two make sudden and large reductions in the herd size around year 4 and one makes a strong reduction in year 8. In the
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Fig. 7. Optimal and average lichen development over three trials. Treatments from above: T1-2002, T1-2003, and T2-2001
group T2-2001, one subject does it nearly right from the very beginning and two make strong reductions in the herd size around year 5. In the T2-2000 group one subject makes a drastic reduction around year 6. To summarise, for the pooled results (T1 and T2) for trial one, 17 percent either do it quite right
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Fig. 8. Indications of learning during the first trial, treatment T1-2002
from the very beginning or make rather drastic reductions in the herd size after a while.
Discussion First we discuss our main hypothesis about misperception of simple dynamic systems with feedback, then we examine policies that may explain behaviour by the use of simulations, and finally we discuss policy implications. Observed biases First we note that the observed mismanagement in both T1 and T2 is largely consistent with what has been found in experiments with more complex models and more experienced subjects, see Moxnes (1998b; 2000). This suggests that the simplest design, T1, captures the essence of the problem. People have difficulties in managing a system with one stock and two connected flows, i.e., the basic building block of all dynamic systems. The results from our simple design, T1, also seem consistent with the results from the studies where subjects are simply asked to project consequences over time of certain actions (Booth Sweeney and Sterman 2000; Kainz and Ossimitz 2002; Ossimitz 2002). Compared to these studies, which typically also deal with one stock and two connected flows, we find that precise outcome feedback each and every period is not sufficient to eliminate mismanagement even in a one-stock-andtwo-flows system. From all this follows that a priori one may suspect misperceptions to occur in all dynamic systems and that outcome feedback will not make up for wrong initial projections of consequences. While we think that is a sound suspicion, we cannot rule out that certain variants of the basic building block are easier to manage. Our version of the one-stock-and-two-flows system has a nonlinear
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growth function that complicates management (Figure 2). Without such a nonlinearity, people seem to benefit from outcome feedback in a one stock model (Moxnes and Saysel 2004). Renewable resources are also easier to manage if the catch-per-unit-effort drops with the stock (Moxnes 2000). There are also renewable resources that are of a “flow-type” rather than a “stocktype”. A simple example is the water flow in a river. For year-to-year management, pure flow-type resources are not complicated by stock-and-flow dynamics. On the other hand, most renewable resource systems are more complex than our one-stock model. Comparing treatments T1 and T2, we find that the average bias increases when one extra stock is introduced. This effect of increased complexity is consistent with findings in Paich and Sterman (1993) and Diehl and Sterman (1995). While we think that the one-stock representation in T1 captures the fundamental difficulty of the problem, the additional stock complicates the control of the system and typically slows down reactions. Furthermore, the second stock (in our case reindeer) plays a significant role for most renewable resources. For instance, in fisheries the fishing capacity (fleet and gear) represent this additional stock, while the fish represents the renewable resource comparable to lichen. The experimental analysis by Moxnes (1998a) shows strong tendencies towards overinvestment in capacity with implications for the fishing effort. A rough representation of the climate change problem has three major stocks: one for heat, one for greenhouse gases, and one for the capacity to emit greenhouse gases. Mental models and policies Then we turn to explanations of the observed behaviour. What mental models did the subjects employ and what policies did they use? Figures 4 and 5 show that we must reject the hypothesis that the average subjects used an optimal policy. The 95 percent confidence interval is far from the optimal path for lichen. It seems highly likely that the failure to behave optimally is due to an inability to formulate an appropriate model for the decision problem. We assert this because it is a common experience in the field of system dynamics that it is difficult to formulate appropriate dynamic models: it requires a language in which to represent dynamic systems and an ability to translate available normal language information into the modelling language. Furthermore, in our case, it does not seem logical that a subject who is able to formulate a perfect mental model will mismanage the resource. As suggested earlier, a near-to-optimal management strategy follows quite easily from the perfect model. Even without a perfect estimate of the growth curve, one should come close to the optimal solution, given that one has a qualitatively correct model. Whenever people know that they lack an appropriate mental model of a problem or they are uncertain about the relevance and precision of their mental model, they have to rely on outcome feedback to correct actions over time. Consistent with a view that most problems have an element of complexity and
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uncertainty, Forrester (1961) claims that: “Economic and industrial activities are closed-loop, information-feedback systems.” Hence we will investigate feedback policies. According to Kleinmuntz (1985): “. . . since the complexity of the environment far exceeds that of the information processing system, from the decision maker’s viewpoint the task has an essentially probabilistic character.” This implies that heuristics suggested in the literature on judgement under uncertainty (e.g., Tversky and Kahneman 1974) may be appropriate when feedback policies are operationalised. Since there are always many options with regard to the choice of policy, we start by discussing mental models that may have guided the choice among alternative policies (or heuristics). Only 6 percent in T1 and 3 percent in T2 choose a first year herd size lower than 1500. The three subjects involved may have had proper qualitative dynamic mental models, although none of them did behave fully optimally. Alternatively, these subjects, as well as some of those that reduced the herd towards 1500 in the first year, could have used the following simplified dynamic mental model: since lichen has decreased historically, the historical grazing must have exceeded the growth of lichen. From this dynamic mental model it follows that the herd size must be reduced. However, the model is too imprecise to say how much. Thus, even for this minority group a feedback policy is needed to stabilise lichen and to search for the maximum sustainable herd size. The observed behaviour suggests, however, that a vast majority had highly inappropriate mental models. One such mental model is a static one saying: “the more animals, the less lichen, and vice versa.”7 Figure 9 shows that this model is strongly supported by the data for the historical period provided in the instructions to T1 (a regression yields an impressive t-ratio = −63 for the slope). Choosing such a static model could be seen as consistent with the representativeness heuristic in cognitive psychology (Tversky and Kahneman
Fig. 9. Data from the historical period before the subjects take over management and data for the (lower of two) median subject in the first trial of T12002
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1974): people tend to ignore prior (here: hard-to-represent structural) information and concentrate on the representativeness of data (here: the negative correlation indicated by the time-series data). According to the same literature, the impressive fit of the static model could cause over-confidence in such a model.8 Using this static model, the logical thing to do is to increase the herd further as long as there is lichen left. Close to one third of the subjects in each of the four treatments do that from the very beginning. However, those who increase the herd size or reduce it carefully, as the median subject in Figure 9 does, quickly receive confusing feedback: the lichen observations are no longer in accordance with the static model. In fact, when the new data (black squares) for the median subject is considered in isolation, the correlation becomes positive: “the more animals, the more lichen” (again, a t-ratio = 13 for the slope is impressive). A few subjects switch to this strategy after a short while, maybe rationalising that to begin with there were more animals and more lichen and that development could be reversed, as it could in a static model.9 Similar tendencies are seen in more complex experiments (Moxnes 2000). Most subjects, like the median subject in Figure 9, continue to reduce the herd size. A likely mental model says that there is no other alternative; lichen must be negatively influenced by more reindeer. To save this hypothesis in light of the conflicting observations, subjects may add auxiliary hypotheses including, for example, time delays, unknown external forces, nonlinearities such as the grazing per animal must increase when the herd size is reduced, etc. Such a revised mental model is highly likely to be perceived as ambiguous or uncertain such that outcome feedback is needed. We propose the following feedback policy for the herd size Nt: Nt = NTradt − α NTradt (DL − Lt)/DL
(4)
The policy is formulated as an anchoring and adjustment heuristic, consistent with what has been suggested in studies of judgements under uncertainty. The anchor is the traditional herd size NTradt, reflecting a certain faith in the appropriateness of the historical management or of the initial herd size. The adjustment has as its goal to close the gap between the desired thickness of lichen, DL, and the actual thickness, L t. The adjustment is set relative to NTradt. Thus, if the parameter α is set equal to 1.0 and L t equals zero, the adjustment will be equal to NTradt, implying that the herd size Nt will be reduced to zero. Lower values of α will lead to weaker adjustments and vice versa. The traditional herd size NTradt is likely to be updated by recent experiences. We choose a policy where NTradt is a smoothed version of the actual herd size Nt: NTradt+1 = NTradt + (Nt − NTradt)/AdjTime
(5)
As our a priori choice we will assume an adjustment time, AdjTime, of 10 years. According to Brekke and Moxnes (2003), random initial values can have
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effects that last for that many simulated years. The desired lichen thickness is set equal to 20.5 mm, assuming a certain erosion of the goal from the initial lichen thickness. The value is adjusted slightly from a first guess to improve the fit between actual and simulated development for the (lower) median subject in T1-2002; see Figure 10. We have no prior ideas about the value of the parameter α and adjust it to get a good fit, α = 0.9. Fig. 10. Simulated and actual development for the subject with the (lower of two) median lichen thickness in year 15 in T1-2003. Units: number of reindeer and mm lichen
The overall impression is that the simple feedback policy explains the major tendencies: a gradual decrease in the herd size and then a stabilisation. A simple statistical test suggests that we cannot reject the proposed model.10 As always, an apparently good fit does not prove that the proposed model is the correct one. One could for instance augment the model by assumptions about the relative change in lichen having an impact on the speed of the herd reductions (Moxnes 1998b), one could add assumptions about variations in the desired lichen thickness (e.g., a drift towards accepting a low standard);
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and one could add assumptions about implementation delays and about particular “wait-and-see” policies in the first few years to get more data and to become familiar with the task. Probably, none of these models would be rejected by the data after calibration of parameters. Thus, with these additional hypotheses, we could probably obtain fits for most subjects equally good to that shown in Figure 10. However, the main conclusion would remain, that behaviour is consistent with the use of some sort of feedback policy, a type of policy it is hard to imagine that the subjects could do without, given that they did not possess the perfect mental model. By variation of the parameter α, the feedback policy presented in Eqs 4 and 5 can produce developments that span the main area covered by observed developments. Figure 11 shows how the lichen thickness develops when α is Fig. 11. Simulated development with three different values of α: α = 0.9 (line 1), α = 0.4 (line 2) and α = 1.6 (line 3). Unit: mm
reduced to 0.4 and increased to 1.6 from its original value of 0.9. That α varies among subjects is to be expected. Different from the appropriate mental model, the applied mental models are not likely to give precise indications of needed herd reductions to close the gap between desired and actual lichen levels. Thus, the value of α is likely to vary with personal characteristics such as aggressiveness and risk aversion. Hence, one should not be very surprised that the results vary a lot, as shown in Figure 8. The explanatory power of the feedback policy suggests that the subjects abandon the static mental model. In fact, the static model predicts that a desired lichen thickness of around 20 mm is obtained by keeping the herd at a level slightly higher than the initial one and is therefore rejected by the data. However, another experiment with professional reindeer herders indicated that the static mental model is not abandoned for all purposes (Moxnes 2000). In each time period the subjects were asked to make forecasts of the next year’s lichen thickness. All gave projections that were biased in the direction of what the static model predicted. This suggests that for the “analytical” problem of
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making forecasts, the static mental model is still relied upon, while decisions are made according to a feedback policy. A similar inconsistency is found in Broadbent et al. (1986), where an information treatment leads to better answers in a questionnaire while task performance is largely unaffected. Does the improved performance over trials in Figure 7 indicate that mental models also improve? As noted earlier, the improvements denote upper limits for learning. Furthermore, there exist quite compelling alternative explanations to learning in terms of mental model improvements. According to Figure 11, considerable improvements could be obtained by using a more aggressive version of the feedback rule; that is by using higher values of α. Adjustment of α could simply be motivated by poor results in previous trials and does not require any change in the mental model. Probably even more important, subjects learning towards the end of the first trial that the proper long-term herd size is around 1,250 could set the herd size to a corresponding level in the first year of the second and third trials. If so, what is learnt could be the near-tooptimal herd size for one specific district and not something that is useful for the management of other reindeer rangelands or other renewable resources. The difference between T1 and T2 suggests that it is easier to make quick adjustments of the first-year herd size when the herd can be varied freely. Comparison to observed real management The behaviour in both T1 and T2 is similar to what has been observed in many reindeer districts around the world, including districts where institutions have been in place to control the commons problem, see case data in Moxnes et al. (2002). Figure 12 shows one such case presented in a graph similar to the one in Figure 2. The data extends from 1944 (high lichen density) to 1967 (low lichen density). According to one anecdote, some experts started to warn against overgrazing just after the peak of the growth curve had been passed in the second half of the 1950s. These warnings were largely ignored by the Fig. 12. Herd size (+ signs) and an estimate of the (net) lichen growth curve measured in standard annual lichen takeouts per year.11 Source Moxnes et al. (2002)
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administration and the politicians until the mid 1960s, at which point the herd size had to be reduced to around one third of the maximum sustainable herd size. This was not a desired development for anyone involved. For purposes of comparison, data for the (lower) median subject in T12002 is presented in a similar graph in Figure 13. The figure includes both the Fig. 13. Herd size (+ signs) for the (lower) median subject in T12002 and the assumed (net) lichen growth curve. Lichen thickness in mm is converted to density measured in g/m2 by a factor of 20 g/m2/mm
historical period and the period managed by the subject. The overall pattern is the same. In both cases the decision makers spend many years on insufficient reductions in the herd size. For subjects who deplete lichen severely, the herd declines more or less in parallel with the decline in the growth rate. Decision makers do what they believe is correct, and the result is a steady decline in the lichen level. This causes frustration both to subjects in the experiment and those involved in real management. Policy implications The above anecdote suggests that experts need better tools for communication. In other cases of reindeer management experts have been known to give conflicting advice, indicating that there is also a need for better communication between experts. Furthermore, disagreements between experts imply an even greater need for appropriate communication tools such that policy makers can compare and evaluate the conflicting advice. Figure 14 may help clarify the information problem. On the left-hand side the client makes decisions. Complexity and uncertainty typically imply that information feedback is used when decisions are made. Normally the client is a dictator when it comes to making decisions; the analyst or modeller can only influence the client through information. On the right-hand side, the modeller builds a model of the problem, simulates and arrives at policy insights. The modeller may present these policies to the client without further explanation.
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Fig. 14. Illustration of client and modeller interactions (this is not a formal causalloop diagram)
However, clients responsible for decisions are not likely to substitute “black box” formulas for their own judgement. Experience tells them to be somewhat sceptical of experts, and particularly so if the experts give diverging policy advice. For these reasons the best alternative seems to be to present information that influence the client’s mental model of the problem. For this purpose the analyst may benefit from a “model” of the client’s mental model. In our case it seems that most subjects (clients) tend to think in terms of a static model (with some auxiliary assumptions) and to employ feedback strategies. They seem to lack proper dynamic representations. Depending on the time the client is willing to set aside, various options are available. The pedagogical tools and the principles of system dynamics (Sterman 2000) are known to help students in this discipline. Group model building (Vennix 1996) involves the clients directly in the model building. The more traditional approach is to present final model structures and simulation results. All approaches take considerable time. If only a short time is available, for instance a lecture or a media appearance, the presentation must be simple and focus on the essentials. Figures 2, 12 and 13 may represent such a simple representation. Once the figure is understood, it focuses attention on adapting the herd size to the lichen growth. The figure explains why a small reduction in the herd size can be insufficient to halt the decline in lichen. Such a result is not surprising with this model in mind; actually with this model in mind it is surprising that anybody could make the decisions portrayed in Figures 12 and 13. However, one should not take for granted that this graphical representation is easily understood. While Moxnes (1998b) found that the results improved with this graph as an information treatment, even researchers with considerable experience in formal analysis happened to misperceived the figure. A large fraction of the subjects did not consider the stock nature of lichen. More in accordance with a static model,
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they pictured that if the herd size was reduced to the maximum growth rate, the lichen stock would adjust accordingly and immediately. Hence it is a challenge to avoid this misperception when using the growth curve in short appearances.
Conclusions Compared to earlier more complex experiments, the present experiments show that even minimal representations of a renewable resource are sufficient to cause severe mismanagement of the type observed in the real world. Compared to earlier studies using questionnaires, where subjects do not benefit from repeated outcome feedback, our experiments show that such feedback is not sufficient to achieve rapid learning over time and over repeated trials. At the heart of the problem lie people’s difficulties in formulating appropriate mental models of dynamic systems, even when the system only encompasses the basic building block of all dynamic systems—one stock with two connected flows. People’s mental models seem biased towards static, correlational representations and they tend to apply feedback rules when making decisions. On the other hand, once a simple, dynamic model is available, a quite simple heuristic could in our case lead to appropriate management. In this lies a considerable hope for improved management of renewable resources. Finally, our experience is that the simple experiment12 represents an efficient way to motivate students and others to study dynamic systems in general and renewable resources in particular. By constructing and using a simulation model to analyse the behaviour produced by the students themselves, the students get an introduction to the power of simulation models to study otherwise complex dynamic problems involving human decision making.
Notes 1. If the resource stock is greater than the target, the harvest reduces the stock to the target. If the stock is below the target, the harvest is set equal to zero. 2. Here we use the notation of a discrete time model. However, the model in Figure 1 can still be thought of as a continuous model, which is simulated with a time step of 1.0. This is acceptable since the implicit time constants are much longer than 1.0. 3. T1 is written in Excel 5.0/95 and is available from http://www.ifi.uib.no/ staff/erling/publications.htm 4. T2 is written in Powersim Constructor and is available from http:// www.ifi.uib.no/staff/erling/publications.htm 5. One outlier, who increased the herd size to 5,000 in the second year, has been removed, hence n = 15.
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6. We use the following formulae: tp = (11 − 12)/ s 1/n1 + 1/n2 , where tp is student-t distributed with n1 + n2 − 2 d.f. and where s 2 is the pooled sample variance. 7. By static model we mean a model without dynamics, e.g. Lichen = f (Herd_size). 8. Figure 9 gives a clear example of Tversky and Kahneman’s illusion of validity. It seems likely that people have more confidence in a static model when there are many rather than few data points (open squares) along the apparent straight line; p-values in regressions certainly improve with the number of data points. However, the model is erroneous independent of the number of data points one gets along the apparently straight line. Actually, when the model is simulated with a simple feedback policy, it produces cycles, which show up as a circling pattern in the phase diagram of Figure 9. 9. Also a gradient search would lead in the same direction. 10. We regress the deviation between Median_herd and Sim_Herd against the Median_herd and find that both the constant (p-value = 0.70) and the slope (p-value = 0.86) are statistically insignificant. 11. A standard annual lichen takeout, is what is eaten of lichen by one reindeer in one year under normal lichen conditions. 12. The experiment and the instructions can be downloaded from http:// www.ifi.uib.no/staff/erling/publications.htm
References Bakken BE. 1993. Learning and Transfer of Understanding in Dynamic Decision Environments. Ph.D. Dissertation. MIT Sloan School of Management, Cambridge, MA. Booth Sweeney L, Sterman JD. 2000. Bathtub dynamics: initial results of a systems thinking inventory. System Dynamics Review 16(4): 249–294. Brehmer B. 1992. Dynamic decision making: human control of complex systems. Acta Psychologica 81: 211–241. Brekke KA, Moxnes E. 2003. Do numerical simulation and optimization results improve management? Experimental evidence. Journal of Economic Behavior and Organization 50(1): 117–131. Broadbent D, FitzGerald P, Broadbent M. 1986. Implicit and explicit knowledge in the control of complex systems. British Journal of Psychology 77: 33–50. Clark CW. 1985. Bioeconomic Modelling and Fisheries Management. Wiley: New York. Diehl E, Sterman JD. 1995. Effects of feedback complexity on dynamic decision making. Organizational Behaviour and Human Decision Processes 62(2): 198–215. Edwards W. 1982. Conservatism in human information processing, in Judgment under Uncertainty: Heuristics and Biases, Kahneman D, Slovic P, Tversky A (eds). Cambridge University Press: Cambridge, UK, 69–83. Forrester JW. 1961. Industrial Dynamics. MIT Press: Cambridge, MA. (Now available from Pegasus Communications, Waltham, MA.)
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Funke, J. 1991. Solving complex problems: exploration and control of complex systems, in Complex Problem Solving: Principles and Mechanisms, Sternberg R, Frensch P (eds). Lawrence Erlbaum: Hillsdale, NJ. Gordon HS. 1954. The economic theory of a common property resource: the fishery. Journal of Political Economy 62: 124–142. Hardin G. 1968. The tragedy of the commons. Science 162 (13 December): 1243–1248. Jensen E. (Mis)understanding and learning of feedback relations in a simple dynamic system. Scandinavian Journal of Psychology (forthcoming). Kainz D, Ossimitz G. 2002. Can students learn stock-flow-thinking? An empirical investigation, in The International System Dynamics Conference. System Dynamics Society: Palermo. Kleinmuntz DN. 1985. Cognitive heuristics and feedback in a dynamic decision environment. Management Science 31(6): 680 –702. Moxnes E. 1998a. Not only the tragedy of the commons, misperceptions of bioeconomics. Management Science 44(9): 1234–1248. ——. 1998b. Overexploitation of renewable resources: the role of misperceptions. Journal of Economic Behavior and Organization 37(1): 107–127. ——. 2000. Not only the tragedy of the commons: misperceptions of feedback and policies for sustainable development. System Dynamics Review 16(4): 325–348. Moxnes E, Danell Ö, Gaare E, Kumpula J. 2002. Reindeer husbandry: a practical decision-tool for adaptation of herds to rangelands. R59/02. Bergen, Norway: SNF. Available at http://www.snf.no/Meny/IndPubl.htm Moxnes E, Saysel AK. 2004. Misperceptions of basic climate change dynamics. WPSD 1/04. Bergen: Information Science, University of Bergen. Available at http:// www.ifi.uib.no/sd/wp.html Ossimitz G. 2002. Stock-flow-thinking and reading stock-flow-related graphs: an empirical investigation in dynamic thinking abilities, in The International System Dynamics Conference. System Dynamics Society: Palermo. Paich M, Sterman J. 1993. Boom, bust, and failures to learn in experimental markets. Management Science 39(12): 1439–1458. Sterman JD. 1989a. Misperceptions of feedback in dynamic decision making. Organizational Behavior and Human Decision Processes 43(3): 301–335. ——. 1989b. Modeling managerial behavior: misperceptions of feedback in a dynamic decision making experiment. Management Science 35(3): 321–339. ——. 2000. Business Dynamics: Systems Thinking and Modeling for a Complex World. Irwin/McGraw-Hill: Boston. Tversky A, Kahneman D. 1974. Judgment under uncertainty: heuristics and biases. Science 185: 1124–1131. Vennix JAM. 1996. Group Model-Building: Facilitating Team Learning using System Dynamics. Wiley: Chichester.
Appendix 1 Instructions for the base treatment, T1 You will play the role of the owner of a reindeer herd. Your task is to produce as much reindeer meat as possible each year. Note, however, you should make
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sure that your operation is sustainable. This means that you should aim for the highest possible sustainable slaughtering rate. You should also try to reach this desired state as quickly as possible. For your information, sustainable meat production will be maximized when the sustainable herd size is maximized. Thus your focus should be on the maximum sustainable herd size. Each year your only decision is to set the desired number of reindeer for the next year. You get only 15 years to reach the desired state, and no new trial. Do the best you can. The subject who gets the best results will receive a symbolic prize. You are the sole owner of a given reindeer pasture. Nobody else has reindeer or other animals in your pasture. In summer, there is plenty of grass and herbs. The limiting resource is lichen to support the reindeer throughout the winter. Lichen is a small plant growing on the ground. Biologically it is a combination of fungus and algae. The lichen plant grows in the summer time, growth stops in the winter, and then the plant continues to grow “on top of itself” the next summer, and so on. When there is very little lichen present, there is only little growth. When there is a lot of lichen, the net growth of lichen tends towards zero, what grows up is just compensating for what rots at the bottom of the plant. In between these extremes, net lichen growth reaches a maximum. When the reindeer graze, they eat the top of the plant, and the plant continues to grow on top of what is left. As a way to keep track of how much lichen there is in the pasture, one can measure the average height of the plants, also referred to as the thickness of lichen. The size of the area is indicated by the following piece of information: In one year, the lichen eaten by 1,000 animals is sufficient to reduce the average lichen thickness for the entire pasture by 4 mm. We simplify and assume that the intake of lichen per animal does not depend on the amount of lichen, as long as there is lichen available. Still, lichen is vital for the survival of reindeer; if there is no lichen, all the animals will die. You do not have to think about the sex ratio, the number of calves, losses of animals, the age structure or whether the reindeer are slaughtered, sold or bought. You can vary the herd size freely. All measurements of the herd size and the lichen thickness are perfect and there are no random variations from year to year in the number of animals or the growth of lichen. Before you take over the pasture, the previous owner has increased steadily the number of reindeer from 1150 to 1900. As a consequence, the lichen thickness (mm) has dropped from 50 to 24.4 mm. This development is shown in the diagrams and table below. (Not shown here; however, the data can be inferred from Figures 2 and 13, or they can be seen in the downloadable version of T1, see Note 3).
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Appendix 2 Instruction for treatment T2 The instruction to treatment T2 deviates from the one to T1 primarily in the following addition: The number of animals that are slaughtered is given by your decision about the desired herd size. To maintain a fixed sex ratio of the livestock, all female calves and a few male calves become livestock each fall; the rest of the male calves are slaughtered at 5 months old. Livestock animals are slaughtered in order to obtain the desired herd size. Ten percent of the livestock is males. Each year 85 percent of the females gets a calf, which survives until the fall. 50 percent of the calves are females. It is assumed that the slaughter weight of male calves is 20 kg and that the slaughter weight of livestock is 40 kg.
