Wednesday, October 26, 2005

Sunk-Cost Effects Made Ancient Societies Vulnerable to Collapse
Scheffer, Marten
Coauthors: M.A. Janssen, T. A. Kohler

Judging by the variety of explanations proffered in the literature, societies apparently collapse for a variety of reasons. In an influential review, Tainter (1988: 39-90) finds that published explanations for the famous collapses of the Classic Maya, the western Roman Empire, and many other less famous episodes such as the demise of the Chimu of Peru or the Chacoan system in the U.S. Southwest tend to fall into 11 major categories, with resource depletion or deterioration one of the most commonly adduced causes (see, for example, Hodell et al. 1997, 2001; Weiss and Bradley 2001). Another common explanation is insufficient response to circumstances, or “failure to adapt.” Tainter rejects both such explanations. Resource-degradation explanations beg the question as to why “societies sit by and watch the encroaching weakness without taking corrective actions…. As it becomes apparent to the members or administrators of a complex society that a resource base is deteriorating, it seems most reasonable to assume that some rational steps are taken towards a resolution…. If a society cannot deal with resource depletion (which all societies are to some extent designed to do) then the truly interesting questions revolve around the society, not the resource. What structural, political, or economic factors in a society prevented an appropriate response?” [1988:50; emphasis added].

As to the possibility that societies fail because they are inherently fragile, or static, or incapable of shifting directions, Tainter (1988:54-61, 89) considers this too not so much an explanation as something that, if true in particular cases, must be explained.

SUNK-COST EFFECTS: INDIVIDUALS AND GROUPS In this paper we seek to unite these two explanations in a model that suggests why and under what conditions societies faced with resource degradation might “fail to adapt.” We are not peddling a new universal theory for societal collapse; we do hope to insert into the anthropological conversation on collapse a mechanism—little noticed to date—making some societies more vulnerable to collapse under certain conditions. Our model, which we illustrate with a simple mathematical characterization, is based on a well-documented systematic deviation from rational decision-making known as the “sunk-cost effect” (Arkes and Ayton 1999). Rational choice theory tells us that prior investment should not influence one’s choice between options. Only the expected future costs and benefits of the current options should influence one’s decision. (Of course, prior investments may affect the knowledge and experience of the decision maker, but such effects can be included in the rational choice theory explanation of decision-making.) Numerous studies (Arkes 1996; Arkes and Ayton 1999; Teger 1980) nevertheless demonstrate that humans do consider prior investment in deciding what course of action to take.

Most sunk-cost research is focused on individual decision-making. The main explanation of observed escalation of commitment is self-justification (Brockner 1992). The idea of self-justification is that people do not like to admit that their past decisions were incorrect, and therefore reaffirm the correctness of those earlier decisions even in the face of evidence that the outcome was unsuccessful. One might expect that such irrational behaviour could be corrected in groups. Groups, however, actually tend to hang on to a given mode of behaviour even more than individuals. This may be largely due to a general tendency of individuals to agree with peers as demonstrated in classical experiments (Asch 1955) A SIMPLE MODEL FOR RESOURCE DYNAMICS UNDER HARVEST In conclusion, there is abundant empirical evidence that humans become increasingly unlikely to abandon a (failing) course of action to the extent that they have more existing investment in it, and that this effect tends to be amplified by group processes. We propose that this dynamic may lead to the postponing of small adaptive adjustments until more dramatic changes become necessary. To see how this effect might lead to collapse of settlements, suppose that the dynamics of the local renewable resources (R) used by a settlement of humans (H) can be described by a classic model of logistically regrowing resource exploited by a consumer such as:

We will not consider human population dynamics in detail, but simply assume that the population in the settlement tends to grow if resources are abundant, but decrease if the resource level falls below a certain critical limit (RC) when individuals quit the settlement in search of better opportunities. We may now analyse the dynamics graphically through a ‘slow-fast approach’ (Rinaldi and Scheffer 2000), if we consider the dynamics of human settlement size (H) to be slow relative to the dynamics of the resource. This appears to be a reasonable assumption for many agricultural societies where production may vary greatly from year to year, as they do in prehispanic Pueblo dry-farming regimes of southwestern North America (Van West 1993) from which our examples will come.

Plotting the critical resource level (RC) below which humans quit the place together with the resource equilibrium curve we can explore the expected effect of investment in fixed structures (either temples, other public structures, or housing) on the dynamics of settlements (fig. 2). The sunk-cost effect implies that the critical resource level (RC) tolerated before abandoning the site should decrease if more has been invested in fixed structures. Thus, if not much has been invested in local settlements this level will tend to be high (fig. 2a) resulting in a stable equilibrium at the intersection of the two zero-growth isoclines. If sunk-cost effects cause people to leave only at a lower resource level this equilibrium shifts to higher population densities (fig. 2b). At even stronger sunk-cost effects the intersection is in the unstable part of the resource curve (fig. 2c). In this case the settlement will grow until point F2 is reached and the resource crashes, followed by abandonment of the settlement. Eventually the resources will recover and new settlements may be set up in the same area, or nearby, resulting in a cyclic development. Inputs from outside the region denoted by parameter i in equation (1), for example by trade, will shift the curves in these figures to the right. The system may reach higher population levels due to such external inputs, but the qualitative impact of the sunk-cost effect remains the same.

Obviously, conditions are never constant and the deterministic model of equation (1) may exaggerate the importance of sunk costs in leading to settlement abandonment or more dramatically, societal collapse. One may alternatively interpret fig. 2c as a system that becomes vulnerable due to increasing settlement size. Disturbances such as floods, droughts, or conflict with neighbouring groups may push the system over the edge leading to a collapse. The effect of adverse events in this model can most intuitively be visualized by means of stability landscapes (fig. 3). Stochastic events that reduce resource abundance (e.g., pests, fires, droughts) may have little effect in small settlements but in large settlements can easily bring the system across the border of the attraction basin of the over-exploited state, resulting in a crash. Thus the model predicts that sunk-cost effects can lead to growth of settlements to a point where they are about to overexploit their resources. At this point resilience (the “basin of attraction”) becomes very small and adverse stochastic events will tend to induce collapse.

Evidently, the actual value of the parameters in such abstract models will be difficult to assess in practice, but analyses with various minimal models of this form (not shown) indicate that the behaviour occurs over a wide range of parameter values and alternative models. For instance, we analysed an alternative model in which human migration dynamics are included explicitly and the critical point for leaving a settlement depends on realized consumption (C) rather than resource level (R). This yielded the same qualitative results. We also obtained similar results from a more elaborate model including the economics of societies and the dynamics of investment in settlement structures (Janssen et al. 2002). It thus appears that the prediction is quite robust against details of the models used: societies that invest heavily in structures, monuments, or even equipment and facilities for very specific extractive activities become liable to collapse through sunk-cost effects from resource overexploitation.

IDENTIFYING SUNK-COST EFFECTS IN THE ARCHAEOLOGICAL RECORD In our original publication (Current Anthropology, 2003) we extensively scrutinize evidence for this effect from prehispanic Pueblo (Anasazi) populations, who constructed many hamlets of just a few households, but also much larger villages some of the largest non-earthen structures built in the U.S. before the Chicago skyscrapers of the 1880s (e.g., Pueblo Bonito, Chaco Canyon, New Mexico; Lekson 1984). The sunk-cost hypothesis predicts that people will continue to invest in construction at large settlements even into periods of scarcity, whereas construction at small settlements should be more confined to periods of relative abundance, given the slighter investment in local facilities. Using tree ring analysis data from wood recovered from the buildings at the archaeological sites, we showed that, as expectedpredicted by the sunk-cost effect, construction in hamlets is restricted primarily to years in which productivity is at or above the long-term mean, whereas construction in villages persists under highly variable (and even poor) conditions.

This and other observations we analysed strongly suggests that indeed people with large investments have, as a result of those investments, a tendency to rather rigidly attempt to maintain a previously successful way of life in areas and times when they are experiencing severely reduced returns on those investments—even to the point where they make additional investments in trying to maintain what perhaps ought to have been perceived as a lost case. As a result, local depletion becomes more severe than would have been the case, had they chosen to leave earlier, or otherwise changed the nature of their adaptation. In turn the final collapse appears all the more dramatic, given the more impressive nature of the final structures left behind in a desolate landscape.

Certainly, more archaeological records would need to be scrutinized to discover how general sunk-cost effects might be in inducing vulnerability to collapse in prehistoric societies with large structural investments. However, the strong empirical foundation in social psychological work and the fit to these Puebloan data encourage us to suspect that these effects are quite general. An attractive aspect of this model is that despite its simplicity it covers the three major ingredients that have been reappearing in the “collapse literature” for decades: the role of adverse events, the impressive size of collapsing settlements, and signs of overexploitation of resources during terminal occupations.