Slow Response of Societies to New Problems: Causes and Costs

A Mathematical Model of Opinion Shifts

Suppose that for each individual there are simply two modes of “opinion” or “attitude” with respect to a problem: active (+1) or passive (-1). It takes effort to be active, but activation also generates pressure on authorities in the direction of one’s own interest as well as a “warm glow” feeling (Andreoni 1998) that one is doing “the right thing.” Let Ũ(+) denote the perceived pay off or utility to being active and Ũ(-) the utility of being passive. These utilities have a random component to reflect idiosyncrasies across people: Ũ(a) = U(a) +ε(a) for action a = +1, −1, where U(a) is deterministic, ε(a) is a random variable, and s scales the variance. It turns out that if ε(a) is independently and identically distributed across people and action, we may apply the law of large numbers and compute the probability (P) of action a as a function of U(a), a, and s:

We now introduce peer group “social pressure” effects. We define n _t(a) as being the probability P of action a at time t, and overall tendency for action as

and assume the perceived utility for person i at time t of taking a certain action to be affected also by the cost c(a _i,t - A _t)² of deviating from the overall group tendency obtaining:

Then adapting the probability function Eq. (1) replacing U with V, we have

Details of this development in a different context are presented elsewhere (Brock and Durlauf 1999). Our figures of the response of public attitude to an increasing problem (Figures 1 and 2) were obtained by plotting the equilibrium action level [solving Eq. (4) for A _t = A _t-1] as a function of h _t.

Figure 1

In societies with little difference among individuals and high peer pressure, the response of public attitude to an increase in perceived problem size is predicted to be discontinuous. When the problem is perceived to be small (and the perceived pay off of taking action is low), the attitude of most individuals is passive with respect to the problem. Society abruptly shifts to a predominantly active attitude (creating political pressure to regulate the problem) when the perceived severity of the problem has grown sufficiently to reach a critical point (F ₁). If, subsequently, the severity of the problem is reduced, the active attitude towards regulation remains until another critical threshold point (F ₂) is reached where an equally abrupt transition to a passive attitude occurs. The graph is produced from our model (Appendix) by plotting h on the horizontal axis and on the vertical axis.

Figure 2

Modeled relationship between public attitude about the need to take action against a problem and the perceived severity of the problem. a If the cost of taking a deviating position (c = 0.1) is low, the average level of action smoothly increases with the perceived size of the problem and the net utility of taking action against it. b With increasing cost to deviating, the action level starts to rise more steeply around a critical perceived size of the problem at which the perceived net payoff of taking action becomes positive. c At higher costs of deviating from the rest of society, the equilibrium curve takes a sigmoidal shape. The figures are produced from the model (Appendix) by plotting on the vertical axis and h on the horizontal axis using c = 0.1, 0.5, and 1.0 for a, b, and c, respectively. Reducing variation among individuals (s) in the model has largely the same effect as increasing the cost of taking a deviating position.

Figure 3

The degree of hysteresis in public attitude towards the need to regulate a problem (see Figures 1 and 2) is predicted to be larger in situations with high peer pressure, lack of strong opinion leaders, complex problems, and relatively homogeneous populations.

Figure 4

The likelihood that an environmental problem becomes quickly (and effectively) regulated once it has been recognized is lower if resources or power are distributed unevenly between stakeholders (bottom panels) and if there is no centralized decision-making authority (right-hand panels).

Figure 5

The costs to society of a new activity that causes a “spillover” problem are initially very small but will grow as the intensity of this activity increases. There may be a long time lag before regulation of the problem in which three phases can be distinguished. Phase I:A period in which the problem goes undetected altogether; Phase II: A period in which general recognition of the problem is lacking; and Phase III: A delay before the onset of actual regulation.

Figure 6

New problems continuously arise and the total costs of all these problems to society depend on the ability to recognize and regulate problems in early phases. Some problems may be regulated relatively quickly (for example problem # 6) and eliminated almost entirely (for example #6 and #7), whereas others grow unregulated for a long time (for example # 10), or correspond to irreversible switches that cannot be solved (for example #2). The area below the curve of a specific problem represents its cumulative cost to society starting from the moment of its introduction. The sum of the costs of all individual problems at one instant of time is the total environmental spillover burden to society at that moment. The grand total of environmental spillover costs carried by society is the sum of the areas under all the curves.