| A unit of Lasting Forests
evolving since March 30, 1999 |
|
A Total Forest Management Plan
|
|
|
You can never be sure in the wildlands, except about this statement.
If I am hungry and want an apple and I may select (blind folded) one or two from a basket that is known to be full of apples, exactly half of which are bad, I'd select two apples, not one. I need one but select two because the chance of getting a bad one is 0.50. This contrived example may be useful in elementary instruction about expected value, but it is limited in resource management. "Needs" of people are rarely so clear as for an apple; the amount needed is rarely so precise (one apple, an integer value, not 4.6 tablespoons of apple sauce); the boundaries of the selection are rarely so clear (the basket); the total population is usually unknown (apple packers know how many of each grade are in a bushel); and the proportion of defect or failure rate, itself, is usually uncertain.
Nevertheless, an estimate of the chance of failure (for example, the probability of selecting a bad apple, crop failure, or animal death) is needed. That probability subtracted from 1.0 (the chance of perfect success every time) becomes the expectation or chance of achieving an objective. Thus
E = 1.0 - r
Or expectation (E) is related to the risk of failure, r. A manager producing units (any desired resource unit, P) actually must produce p units because
P = pE.
Needing to produce P units to meet demand (or not be fired), the manager then finds that
p = P/E.
Needing 100 units and estimating the failure rate at 0.25, then
p = 100 / (1.0 - 0.25)
p = 133.
Nervous about the precision of the estimated risk, the manager raising r to 0.26 (instead of 0.25) computes a value of p of 135. He or she would produce 2 extra units, "just to be on the safe side." This is a reasonable strategy of the per-unit costs of production are low but otherwise ... lookout!
There are hidden premises in this brief introduction. One is that decisions can be improved and that understanding and accounting for failure rates might be of help. Another is that decisions are now based on estimates of failure and expected values and that the way such information is now used can be adequately formulated in the above manner. Another is that by seeing one approach to formulating expected values and expectation clearly, "cracks" in the procedures now used can be seen and an alternative method created to aid in making decisions. The work is not to improve the metrics of economic theory, only to clarify and thus improve wildland decisions.
The present procedure teeters on the ability of the manager or decision-maker to estimate r or some concept of failure of "being wrong." We allow the philosopher's proof that people cannot be certain…of anything ... and resort to discussing the odds of being wrong.
We believe that in natural resource work, timeliness of decisions is very important and affects risk taking more than in many other fields. The scope of decisions (thousands of acres) and the unlikely chance of seeing the payoff of a decision (100-year timber rotations) creates risk-taking situations unlike those encountered in most businesses.
As the time for making the typical natural resource decision approaches, there are well-known "deadlines", "bench-marks", and "mileposts", the willingness to take risks increases, requirements for confidence levels are reduced, and expected accuracy is reduced. This is held to be true for the novice as well as the experienced decision-maker.
As the costs of sample collection, analyses, and statistical work are realized as projects develop, levels of confidence and accuracy are usually surrendered.
Few people realize how slowly new samples add to confidence that a person can have in a conclusion and thus the risks of making decisions about things that often have a bell-shaped distribution. The general equation for a good sample is
n = s2 t2 / d 2 .
So since t (Student's "t" of the statistical test) expresses the confidence level, we can see that
t = (n d2 / s2 )0.5 .
As we change the number of samples collected in an hypothetical situation (where the variance is 9, mean is 21, and the desired accuracy is within 5 % of the mean) we can see that change comes slowly. At a point, it is clear that "the more, the better" is not a good rule since every sample has at least some cost and each new one may contribute little new information to the decision maker. (We are strongly in favor of auto-regression techniques.)
Samples can be used to assess risk. Risks are often expressions of frequency such as in "how many times out of 1000 will x happen?" We do not need 1000 studies to answer such a question. (Computing sample sizes needed to express such properties can be aided by CAPXXX.
All things in the wildlands are not bell-curve or normally distributed. Many are binomial, reflective of success or failure, dead or not. Others are Poissonal, the mean equaling the variance. Others have names describing the distributions but they can often be described generally as "skewed" and fitted with a Weibull distribution that skews both left and right. Increasingly the median of these skewed curves (not the mean) is used by decision-makers.
Time, costs, and distributions over-power the well-developed statistical aids which require knowledge, continual use to maintain expertise, data, software, and an appreciative audience…all of which are scarce.
Decisions are, and have always been, made under conditions of uncertainty. Risk r is usually assigned (guessed at). Often a "parametric approach" is taken. Three estimates of risk are made: high (a), low (c), and likely (b). Then analyses are made, one with each estimate.
An alternative used is the so-called beta estimation procedure. It is used to estimate a median for decision making. The same three values above are used in:
m = (a + 4b + c) / 6.
The value, m, may be used as the best estimate of r.
Without an alternative, most decision makers that use r in their decision process will use m, perhaps along with a, b, and c.
President Truman is said to have yearned for one-handed advisors. They always said, he claimed, "on one hand this…but on the other hand ..." They did not include risk. That was for the President to include in his decision process. Including it is difficult for presidents as well as others. In complex systems it can quickly seem irrelevant. Risks (and expected values) must follow the product rule of probability. The probability of P, Q, and R is the product of the three values. When these values are small, the product can be very small, insignificantly small. The expected value, when the probabilities for success are as follows: P = 0.7, Q = 0.7, and R = 0.7, is 0.34. A decision-maker can be fairly certain about three major parts of a system but uncertain about the remainder and thus about the system itself. A single point of uncertainty or zero knowledge can leave a decision-maker in the cold and dark. The condition is not unusual because of the following conditions prevalent in wildland decision making:
1. The wildlands are variable. The decision-maker may know the range of possible states but which ones will exist when the decision is made can rarely be known. Narrowing the range and estimating the median value is not a bad idea.
2. Catastrophe occurs. Beyond normal ideas of variability, hurricanes, massive fires, volcanic action, and exotic insect events can have over-powering, system-changing effects.
3. Observers are limited. Some are dishonest or lazy.
4. Superior observers may be observing the wrong things or interpreting them improperly.
5. Observations may be inadequate in number or timing.
6. The wrong paradigm may be used and the data obtained (see 4 above) may not be useful.
7. Observations may be at the wrong scale. Causes of changes in systems may have their roots in other areas or in previous years.
8. Management action may have a partial effect, obscuring normal functions of the system.
9. The model selected and used (part of the paradigm) may be in error. We may not understand ecosystem or economic system mechanics well. Exact observations, tightly controlled action, and low environmental variations may yet produce erroneous results.
Any one of the above reasons is enough to explain the uncertainty in wildland decisions. If we were about 95 % confident of good results in all of these categories, we would only be justified in saying that we were about 63 % confident of the system about which decisions must be made (i.e., 0.95 9 = 0.63).
It has been experienced (and demonstrated in research) that different groups of people, for example, from different religions and socio-economic groups, are willing to take different risks. Some are conservative (risk-averse); others are inclined to take risks (risk-prone). This awareness allows people to see further the complicated nature of expectancy. It relates to:
1. The fear of being wrong (appearing to be or actually being wrong, and consequences to the psyche, family, or employment); the probability of dire personal consequences, self evaluated.
2. The actual probability of an event, describable in many cases using conventional statistics. The probability of a precise measure.
3. The probability of an error (or falsification) in measurement.
4. The probability of two known elements reacting negatively in an estimated way (a process probability).
5. The frequency of an event(s), probable occurrence in a period of importance.
6. The probability of an event or function, critical to an event.
7. The dire consequence of an event (e.g., given absolute certainty of an event, what is the probability of very bad consequences once the event occurs). This has parts:
Risk assessment is complex as well as tedious and difficult. Communicating all of the above seven dimensions as well as concepts of statistics and probability theory provide the challenges of risk assessment that increase with group size. Cleaves said that since the vast majority of uncertainties are not critical, numerical assessments should not be made unless precision is needed. We operate on the basis that precision is needed, especially for factors identified in sensitivity analyses. We recognize the costs and difficulties and strive for improved techniques, improved software, and for methods that compare actual occurrences with estimates ands allow methods to evolve. New rules in expert systems and auto-regression procedures may allow convergence of the estimate to the actual more rapidly than in the past.
We evaluated analyses of Kopp and Portney (1999:87-98) and find their ideas appealing. If impacts are translated into statements about the probable achievement of each of a long list of objectives then voters or decision makers can evaluate projects and decide on most desirable ones. The analytical work has to be that within a large multi-dimensional consequence table (with narrative) relating objectives (including amounts of demand to be met with project scale) and effects over time with different interest rates and effects in different locations (with GIS display).
We often see equal choices being presented, those "with no significant difference." Risk assessment and estimating expectancy allows, as one other component of the decision process, to compare events, policies, practices, and programs. More information, no matter how compulsively collected, will not allow improved decisions where there are extreme differences in risks (of any of the types listed above.)
| Years | Percent |
| 0 to 25 26 to 75 76 to 300 301 - infinity |
3 - 4 2 1 0 |
We cannot assume that interest rate will be constant, people the same, resources per person the same, consumption or consumption per person the same. There are whole generations of people in some countries who hate past generations and have little regard, even hate, for future ones. In all of these topics, for every major wildland decision, there are thresholds for deep future effects. (Quantifying further (e.g., past 10%) the probability of holding my head above water is meaningless. There are integer values in effects of actions on resources including visual amenities, rare species, and pollution effects (e.g., badly crippled vs dead).)There will be corrective adjustments; costs will not be as high as they seem now; technology will flourish. The next generations will have resources if we can regulate populations, consumption, and retain fossil fuel long enough to set up energy conservation, rationing, and capture facilities.
Forestry, said to deal with a renewable resource, may work with a flawed premise. In our view, when working with hardwood forests, it is unlikely that a return to similar conditions after logging, even after 300 years is likely. There are irreversible consequences.
Societies invest and some are positive for the future, some negative, some indifferent. Over emphasis on " externalities" or pollution or secondary effects seems unwarranted and unfair unless a full accounting is done. Within The Trevey we provide as full analyses of primary and secondary effects of decisions as currently possible.
We believe that a positive rate of interest is likely and a good assumption, but it is based on observations of the past and a strong assumption about increasing technological advances. We doubt if it is prudent to postulate everlasting increases in per capita outputs. To do so would fly in the face of of declining oil availability and the observation that the rate of per capita income has been only slightly more than zero for a few thousand years.
We're experimenting with discount rates that may change annually (i.e., are not constant as in classical discounting). We have created from 100 simulations a mean annual rate allowing a pseudo-random fluctuation (grossly private or public -- a social rate of return) of interest rates from discontinuous rates over periods suggested by Weitzman (1999:29). Every project thus has
First, we compute conventional discounting using 50 years as a standard period. (most economist believe that within this period, classical discounting is appropriate). We use a rate, fluctuating randomly around 3% ranging normally with an assigned standard deviation of 1.6. When two whole negative standard deviations are computer-selected, the interest rate will be -0.02%. The maximum rate assigned will be 3% plus 3.29 or 6.2%. The negative discount rate arising from such computation, reflective of erosion, reduced air quality, etc. is unlikely. It may occur, however, and given past unwillingness and inability to measure it, we suspect it has and will occur again. Said to occur "by chance", we prefer to look first at mismanagement and accept natural catastrophe such as earthquakes and tornadoes (for which there is insurance protection). Thus we see preventing the negative rate as our objective, adapting the controls of management and rejecting a laissez-faire attitude to production (Dasgupta et al. 1999:71). We also lay out the above analyses.
We construct a simple ratio, dividing the estimated future value by the present value, giving, for ease, a relative measure (since we believe that most people compute this for them selves for they are "stunned" by the differences produced by time and the rate phenomena. We also compute the discounted future using Hunt and Overton's procedure.
We acknowledge studies that show that individual attach lower weights to distant benefits and that they seem to use a variable exponential discount rate, one that decreases with time to the effects of the project.
We are ashamed to doubt there is now or will be much concern for "intergenerational equity" We now have polluters, miners, and loggers operating without regard for their children, their towns, their watersheds, their state! We are forced to impose laws and threats and fines to gain actions seemingly apparent to this generation. Schelling (1999:101) is pessimistically realistic:
"I see little evidence, at least in the United States, that people want to make significant additional sacrifices to raise living standards among the people who live now in the developing world. It would surprise me if they would get excited about raising living standards in these same parts of the world at a time in the future when those living standards will be, we may both hope and expect, substantially elevated over where they are now."
Reference
Cleaves, D.A. 1994. Assessing uncertainty in expert judgements about natural resources. U.S. D. A. Forest Service, Southern Forest Experiment Station, Gen. Tech. Report SO-110, New Orleans, La.,17p.
Giles, R. H., Jr. 1979. Modeling decisions or ecological systems? p. 147-159, In J. Carins, Jr., G. P. Patil, and W. E. Waters (Eds.) Environmental biomonitoring, assessment, prediction, and management-certain case studies and related quantitative issues, International Cooperative Pub. House, Fairland, Md., 438 p.
Legg, Mark R. et al. 1976. US Building exposure (seismic risk), County Data USGS -OFR 80-1169 NTIS Lawrence, W.W. 1976. O acceptable risk: science and the determination of safety, Kaufmann, Los Altos, CA
Minnehan, R.F. 1967. Uncertainties and externalities in water resources investment decisions, PhD Diss, Univ. California, Berkeley
| Quick Access to the Contents of LastingForests.com |
|---|
This Web site is maintained by R. H.
Giles, Jr.
Last revision January 17, 2000.