Fiering, M.B.

International Institute for Applied Systems Analysis (IIASA)

Compressed Policy AnalysisFiering, M.B.IIASA Working PaperWP-74-0101974 Fiering, M.B. (1974) Compressed Policy Analysis. IIASA Working Paper. WP-74-010 Copyright © 1974 by the author(s). http://pure.iiasa.ac.at/161/ Working Papers on work of the International Institute for Applied Systems Analysis receive only limited review. Views or opinions expressed herein do not necessarily represent those of the Institute, its National Member Organizations, or other organizations supporting the work. All rights reserved. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage. All copies must bear this notice and the full citation on the first page. For other purposes, to republish, to post on servers or to redistribute to lists, permission must be sought by contacting repository@iiasa.ac.at COMPRESSED POLICY ANALYSISM. FieringMarch 1974Working Papers are not intended fordistribution outside of IIASA, andare solely for discussion and infor-mation purposes. The views expressedare those of the author, and do notnecessarily reflect those of IIASA.WP-74-10- 7 -5.4 Compressed Policy Analysis5.4.1 Objective(al Some DefinitionsThe objective of this portion of the analysis isto seek approximations to an optimal strategy of forestmanagement, and thereafter systematically to evaluateany such approximation in the hope that one or moremight be sufficiently reliable to preclude the enormouscomputing effort sUbtended by those more comprehensiveｭ ｡ ｴ ｨ ･ ｭ ｾ ｴ ｩ ｣ ｡ ｬ formalisms (linear and dynamic programming)which ure ｾ ｬ ｳ ｯ investigated in this study. CompressedPolicy Analysis (CPA), unlike its more formal counter-parts, does not identify an optimal solution, but ratherprovides a mechanism for rapid and fluent examination ofalternative solutions which are generated exogeneouslyＨ ｩ ｉ ｾ accordo:.nce vii th some systematic or ra:fldomized samplingprocedure), and then, by a comprehensive. display ofecc'!1oTLlic crite:cia and other relevant performace factors,ｳ ｵ ｧ ｧ ･ ｾ ｴ ｳ to the decision-maker(s) which alternative toadvpt.A ｓｏｊＮＱｊｴｪｏｾｾ is a set of decisions germane to forestmetnagc)L1ent. Certain options are available; these includea variety of ｴ ｩ ｮ ｾ ･ ｲ cutting and harvesting patterns, ratesof ｃ ｬ ｰ ｰ ｾ Ｎ ｩ ｣ ｩ ｬ ｕ Ｎ ｯ ｮ of insccticlde, and enhancement of vlild-life alld recreation facilities. The thrust of CPA isthe identj.ftcation of several policies. which are deemed .ｾＮﾣＮ｣ｩＨｬ｝ＮﾷＮ＿ＺＮ to b2 politically, socially and· institutionallyｦ ･ ｾ ｳ ｩ ｢ ｬ ･ Ｌ ｾ ｮ ､ the evaluation of these policies in wayswhich t:ake explicit account of the multi-dimensional andhiS!hly var iegC.t ted outputs of the forest ecosystem. Amongthe requirements of a feasible poJ.icy is that its actiondisplay a reasonable·mGasure of spatial and temporal homo-geneity. This tends to keep costs down, even though the- 8 -policy consequences might be inhomogeneity in systemresponse. Thus the richness of "the potential policyspace is compromized by practicality, and the fullpalette of a mathematically intact search for the optimalpolicy might prove too ambiti.ous.It is therefore proposed that CPA be applied to arelatively small set of policy options, including that onein current use, on the assumption that this set \'1111 besufficiently fertile to identify some policies which areclearly inappropriate, some which merit further detailedconsideration, and some to which system performance islargely indifferent. The point of the exercise is not toidentify a sharply-defined opt:imum which might be extremelysensitive to unanticipated climatic or ecological pertur-bations but to sharpen the focus of subsequent debate byexcising a small number of candidates for continuinganalysis, and thereby to advance a general methodologyfor decision-making in an environmental ｾ ｯ ｮ ｴ ･ ｸ ｴ Ｎ(b) A Formalism for Decision-MaJ:j.ngIt. would be ideal if mathematical programming couldroutinely be used to solve for the optimal policy undera variety of assumptions and conditions pertaining to ourforest ecosystem model, but it should be recalled thatpolj cy evaluation proceeds \'Ji.t.hin mul ti--diraensional space.lDe] thir; severly 1] 1111 lr.; the applicabi lity of techniquesfOL direct iQentification of optimal policy. The multi-dimensionality of system outputs, undertainty about whichoutputs to include und how to weight t.hem, and conflictsconcerning the priorities expressed by the several claimantson the resource all conspire to make mathematical pro-gramming un unlikely tool for identification of the optimalpolicy in this forest management problem. Three alter-native modes of analysis are suggested in this section;- 9 -all of them t:ogether are lumped under the rubricof Compressed Policy ａ ｮ ｾ ｬ ｹ ｳ ｩ ｳ Ｌ and all suffer several dis-｡ ､ ｶ ｾ ｮ ｴ ｡ ｧ ･ ｳ and imprecisions. ｂ ｕ ｾ Ｌ as in virtually everyreal problem of policy analysis, there is no unique solu-tion or method of analysis which clearly dominates thedecision-making ｰ ｲ ｯ ｣ ･ ｳ ｳ ｾ it is through the conjunctive useof exact and approximate solutions, computationally simpleor exotic, deterministic or stochastic, descriptive orprescriptive, that grudging progress is made.(c) Sa.mpling in Policy SpClceThe busic tool for evaluation of policy options issimulation or the budvmnn-forest ecosystem. Initi.al ap-plicCiti.ons used a short trace of meteorological inputs, \:J 1"\ hthe model .was· applied to a single plot and with no spatiallin};.agcs to simulate pest dispersal through the entireregion. Our l-lOrk generalizes the program to accommodatedispersal over all 265 plots,.'Simulation runs \-lere made, each signed to test analternative candidate for policy implementation. The can-didates were developed after consultation with ecologistcivil servants, representatives of recreat!on and wildlifegroups, i.ndustrial proponents, and others \',Thorri \-le couldidentify as having a vested interest in management of theforest ecosystem. Due to the fact that this study identifiesmethodology rather than definitive conclusions, we did notpursue em extellsive progrilm of sampling in the space ofpolicy options; restrictions on time and computing budgetmade tllis infeasible. Instead, we are concerned primarilywith the exposition of a methodology for decision-making,so we ｰ ｲ ･ ｳ ｾ ｮ ｴ here a highly abbreviated. examination of policy'options. \ve did not use systematic or random samplingtechniques for identification of policy ｯ ｰ ｴ ｩ ｯ ｮ ｳ ｾ for com-pleteness of exposition these are described below. Buti,- 10 -even a limited analysis can be extremely useful if itturns out t.hat system response, in terms of the outputvariables critical to the decision makers, seems to berelatively flat. That is, if it appears that response ｩ ｾnot highly sensitive to a wide range of reasonable policyoptions, we might begin to appreciate, even from a super-ficIal analysis, that it is unnecessary to undertake a.very large random or systematic sample of policy options.It might turn out that there is enough buffering, enoughnatural resilience or persistence, in the system to con-clude, or at least strongly to suggest, that the majorissues are those of political acceptability rather thansensitivity to small changes in decision variables.It is reasonable to ask how many policies or potentialsolutions should be investigated to be sufficiently certainthat. the sample from which our solution is drawn is bigenough. Of course, -in solution by mat.hematical programming,this question does not arise because the most commonly usedtechniques generate the optimal solution. But mathematicalprogrmnming is not likely to be able to embrace the numberof variables required for our forest ecosystem performanceindex; thus the generated policies are guidelines to the. ,selection of a few policy options which can be furthertested and refined by simulation. It is our intent thatthese few promising policies (or decisions) should formthe basis of a more penetrating investigation which wouldlead ultimately to a final decision.Techniques other than mathematical programming areavailable t.o identify candidates for simulation, and someof these are particularly powerful. For example, if thenumber of decision variables is small, and if each can bedivided into a small ｮ ｬ ｬ ｩ ｾ ｢ ･ ｲ of alternatives, then it isreasonable systematically to examine all the intersectionsor potential decisions in ｭ ｵ ｬ ｴ ｩ Ｍ ､ ｩ ｾ ･ ｮ ｳ ｩ ｯ ｮ ｡ ｬ space, to- 11 -･ｶｾｬｵ｡ｴ･ ench, and to pick the most promising few forfurther investigation. But it is in the nature of eco-logical systems that many ､ ｩ ｭ ･ ｮ ｾ ｩ ｯ ｮ ｳ are required, and itis unreasonable to divide all the decision variables intoa small number of steps, so an exhaustive search for po-tential decisions cannot generally be undertaken. Aparticularly powerful tool under these circumstances isthe use of random sampling techniques'to develop trialsolutions which can be improved by steepest ascent or"hill c1imb1ing" techniques now routinely used in appliedmathematics. For example, we know that if a random sampleof size n is taken, where each of the n points is anotherdecision vector, then the probability is 1 - (1-8)n thatthe best of all n trials, lies in the upper e-fractile ofall possible results. This simple but pOvlerfu1 result isindependent of the dimensionality of the decision and ofthe functional form of the distribution of any of thesystem outcomes. It requires only that the outcmnes berepresented on a continuum in multi-dimensional space, acondition which might sometimes be difficult to guaranteebecause of the potential lumpiness of system response.But experience with many resource investigations suggeststhat we can virtually always find reasonable and feasiblepolicies (or solutions) which closely approximate the re-quirement that all outputs be defined on a continuum.If we c1raH a random sample of size 30 and inquireabout the probability that the best of these lies in theupper 10% of all possible results, we determine that theprobability is 0.957. It should be ･ ｾ ｰ ｨ ｡ ｳ ｩ ｺ ･ ､ that de-fining a point to lie in the upper 8-fracti1e is differentthan asserting that. a point lies within e of the trueopt.imum. hIe make no s·tatement here abouL the quantitative､ ｩ ｦ ｦ ･ ｲ ･ ｮ ｣ ｅ ｾ between the best of an independent random sampleof outcomes and the true optimum; we define only the prob--ability that a particular output lies within any given- 12 -fractile. This probability, 0.957, is independent of thedimensionality of the decision vector.Moreover, if the few best results of the random castare ｳ ｹ ｳ ｴ ･ ｭ ｾ ｴ ｩ ｣ ｡ ｬ ｬ ｹ improved·by various hill climbing pro-cedures to promote them from their random positions in thedecision space t:o a local optimu.m (from which all smallchanges make the output worse), we reside (symbolically)on a set of local mountain peaks from which all directionsare down. From an operational point of view this is tant-amount to saying that we have a new set of local optima,the best of ｾ ..,hich is at least as good as the best of therundom draw because all movements vlere necessarily uphill"(in the direction of inc.reasing value of system output) .There is no general theory which describes how to calculatethe confidence and tolerance limits on the best of the localoptima because such a result would depend on the nature ofthe response surface and on statements about higher deri-vatives.The decision as to whether n, the size of the initialrandom sample, is large enough depends on the cost ofdrawing additional samples (that is, on the cost of ｣ ｯ ｭ ｾputing) and on the fertility of our imagination (becauseit is required that these policy options be feasible andit is oftentimes difficult to generate feasible randomcombinations of decision variables). Thus one should notbe misled by the apparent simplicity and elegance of randomsampling techniques but should recognize that the potentiallyhigh cost of identifying a random feasible candidate maymake the procedure unattracttve. Moreover, it i.s obviousthat the probu.bilit.y of identifying a feasible random solu-tion becomes painfully acute as the number of dimensions,and possible interactions among decision variables, increaseR.All this has been investigated by many theorists, and theresults are neither conclusive nor satisfactory; the best- 13 -that can be done here is to use currently availabletechniques, modified by the best advice we can obtainfrom consultants and practitioners.

Compressed Policy Analysis

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