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航空武器技术美国兰德公司70年发展启示美国兰德公司（RAND Corporation）成立于1948年11月，是一家致力于通过研究与分析来改善政策和决策的非营利性研究机构，是世界上享有盛名和影响力的综合性智库之一。
70年来，兰德公司在国际关系、军事战略、科技装备等领域取得了一系列高水平研究成果，对二战后美国国际政治军事政策产生了重大影响，特别是兰德公司正确预测了美苏争霸历史进程中的多项重大事件，研究成果影响了朝鲜战争、越南战争的军事决策过程，围绕中美关系正常化向美国政府提出了灵活可行的措施建议。
同时，在精确制导武器应用研究、全球卫星监控与通信、无人机侦察与打击系统等武器装备层面，为美国军方提供了至关重要的决策服务，经常性地引领着学术研究的潮流。
美国兰德公司究竟为什么能够取得如此令人瞩目的成就？其发展运行有何独到之处？近些年又有哪些重量级的研究成果？在新的历史时期，这一系列问题值得深入思考。
本文从兰德公司的選题立题、聚能选才、方法工具、组织文化、前沿创新等多维度进行研判分析。
通过思考，希冀能对国内武器装备长远发展带来一些启示。
1 兰德公司的历史RAND是英文“Research and Development”（研究与发展）的缩写。
1946年3月1日，兰德计划依托道格拉斯飞机公司正式启动，其章程中写道：“兰德是永久性维持科技领域开发和制作工作的新生机构，旨在为美国空中作战领域开展广泛的科学研发，并为空军提供战略分析及战术储备”。
1948年11月，由福特基金会捐助，在兰德计划基础上正式成立了兰德公司。
兰德公司成立之后第一份研究报告是《实验性绕地空间飞行器的早期设计》，报告建议制造人造地球卫星，描述了今天看起来习以为常的空间活动，但这一研究成果当时被认为完全脱离现实。
1957年苏联发射了人类历史上第一颗人造卫星。
这一次，兰德再次发挥了“神预测”，其发布的研究报告详细预测出苏联发射第一颗人造卫星的具体时间，与苏联实际发射时间相差不到两周，预测能力震惊世界，从此确立了兰德作为高端智库的地位。
DECISION MAKING – THE ANALYTIC HIERARCHY AND NETWORK PROCESSES (AHP/ANP)Thomas L. SAATYUniversity of Pittsburgh saaty@Abstract This is the first part of an introduction to multicriteria decision making using the Analytic Hierarchy Process (AHP) and its generalization, the Analytic Network Process (ANP). The discussion involves individual and group decisions both with the independence of the criteria from the alternatives as in the AHP and also with dependence and feedback in the entire decision structure as in the ANP. This part explains the Analytic Hierarchy Process, with examples, and presents in some detail the mathematical foundations. An exposition of the Analytic Network Process and its applications will appear in later issues of this journal. Keywords: Decision making, Analytic Hierarchy Process (AHP), Analytic Network Process (ANP)1. Introduction (Saaty 1977, 1994,2000a, 2000b and 2001)Decision making involves criteria and alternatives to choose from. The criteria usually have different importance and the alternatives in turn differ in our preference for them on each criterion. To make such tradeoffs and choices we need a way to measure. Measuring needs a good understanding of methods of measurement and different scales of measurement. Many people think that measurement needs a physical scale with a zero and a unit to apply to objects or phenomena. That is not true. Surprisingly enough, we can also derive accurate and reliable relative scales that do not have a zero or a unit by using our understanding and judgments that are, after all,the most fundamental determinants of why we want to measure something. In reality we do that all the time and we do it subconsciously without thinking about it. Physical scales help our understanding and use of the things that we know how to measure. After we obtain readings from a physical scale, they still need to be interpreted according to what they mean and how adequate or inadequate they are to satisfy some need we have. But the number of things we don’t know how to measure is infinitely larger than the things we know how to measure, and it is highly unlikely that we will ever find ways to measure everything on a physical scale with a unit. Scales of measurement are inventions of a technological mind. Our minds and ways of understanding we have had with us and will always have. The brain is an electrical device of neurons whoseISSN 1004-3756/04/1301/1 CN11-2983/N JSSSE 2004JOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING Vol. 13, No. 1, pp1-35, March, 2004Decision Making – The Analytic Hierarchy and Network Processes (AHP/ANP)firings and synthesis must perform measurement with great accuracy to give us all the meaning and understanding that we have to enable us to survive and reach out to control a complex world. Can we rely on our minds to be accurate guides with their judgments? The answer depends on how well we know the phenomena to which we apply measurement and how good our judgments are to represent our understanding. In our own personal affairs we are the best judges of what may be good for us. In situations involving many people, we need the judgments from all the participants. In general we think that there are people who are more expert than others in some areas and their judgments should have precedence over the judgments of those who know less as in fact is often the case in practice. Judgments expressed in the form of comparisons are fundamental in our biological makeup. They are intrinsic in the operations of our brains and that of animals and one might even say of plants since, for example, they control how much sunlight to admit. We all make decisions every moment, consciously or unconsciously, today and tomorrow, now and forever, it seems. Decision-making is a fundamental process that is integral in everything we do. How do we do it? The Harvard psychologist Arthur Blumenthal tells us in his book The Process of Cognition, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1977, that there are two types of judgment: “Comparative judgment which is the identification of some relation between two stimuli both present to the observer, and absolute judgment which involves the relation between a single stimulus and someinformation held in short term memory about some former comparison stimuli or about some previously experienced measurement scale using which the observer rates the single stimulus.” When we think about it, both these processes involve making comparisons. Comparisons imply that all things we know are understood in relative terms to other things. It does not seem possible to know an absolute in itself independently of something else that influences it or that it influences. The question then is how do we make comparisons in a scientific way and derive from these comparisons scales of relative measurement? When we have many scales with respect to a diversity of criteria and subcriteria, how do we synthesize these scales to obtain an overall relative scale? Can we validate this process so that we can trust its reliability? What can we say about other ways people have proposed to deal with judgment and measurement, how do they relate to this fundamental idea of comparisons, and can they be relied on for validity? These are all questions we need to consider in making a decision. It is useful to remember that there are many people in the world who only know their feelings and may know nothing about numbers and never heard of them but can still make good decisions, how do they do it? It is unlikely that by guessing at numbers and assigning them directly to the alternatives to indicate order under a criterion will yield meaningful priorities because the numbers are arbitrary. Even if they are taken from a scale for a particular criterion, how would we combine them across the criteria as they would likely be from different scales? Our answer to this conundrum is to derive a relative2JOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING / Vol. 13, No. 1, March, 2004SAATYscale for the criteria with respect to the goal and to derive relative scales for the alternatives with respect to each of the criteria and use a weighting and adding process that will make these scales alike. The scale we derive under each criterion is the same priority scale that measures the preference we have for the alternatives with respect to each criterion, and the importance we attribute to the criteria in terms of the goal. As we shall see below, the judgments made use absolute numbers and the priorities derived from them are also absolute numbers that represent relative dominance. Among the many applications made by companies and governments, now perhaps numbering in the thousands, the Analytic Hierarchy Process was used by IBM as part of its quality improvement strategy to design its AS/400 computer and win the prestigious Malcolm Baldrige National Quality Award (Bauer et al. 1992).2. Deriving a Scale of Priorities from Pairwise ComparisonsSuppose we wish to derive a scale of relative importance according to size (volume) of three apples A, B, C shown in Figure 1.Assume that their volumes are known respectively as S1 , S2 and S3 . For each position in the matrix the volume of the apple at the left is compared with that of the apple at the top and the ratio is entered. A matrix of judgments A = (aij ) is constructed with respect to a particular property the elements have in common. It is reciprocal, that is, a ji = 1/ aij , and aii = 1 . For the matrix in Figure 1, it is necessary to make only three judgments with the remainder being automatically determined. There are n( n 1) / 2 judgments required for a matrix of order n . Sometimes one (particularly an expert who knows well what the judgments should be) may wish to make a minimum set of judgments and construct a consistent matrix defined as one whose entries satisfy aij a jk = aik , i, j , k = 1,L , n . To do this one can enter n 1 judgments in a row or in a column, or in a spanning set with at least one judgment in every row and column, and construct the rest of the entries in the matrix using the consistency condition. Redundancy in the number of judgments generally improves the validity of the final answer because the judgments of the few elements one chooses to compare may be more biased.Pairwise ComparisonSize Comparison Apple A Apple B Apple CApple A Apple B Apple CS1/S1 S2/S1 S3/S1S1/S2 S2/S2 S3/S2S1/S3 S2/S3 S3/S3Figure 1 Reciprocal structure of pairwise comparison matrix for applesJOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING / Vol. 13, No. 1, March, 20043Decision Making – The Analytic Hierarchy and Network Processes (AHP/ANP)Assume that we know the volumes of the on any criterion. Note that in the (2, 3) position apples so that the values we enter in Figure 2 we can enter the value 3 because we know the are consistent. Apple A is twice as big in judgments are consistent as they are based on volume as apple B, and apple B is three times actual measurements. We can deduce the value this way: from the first row A = 2B and A = 6C, as big as apple C, so we enter a 2 in the (1,2) position, and so on. Ones are entered on the and thus B = 3C. diagonal by default as every entity equals itself Pairwise ComparisonSizeApple AApple BApple CSize ComparisonApple AApple BApple CRelative Size of Apples from Any Column Normalized 6/10 3/10 1/10PrioritiesApple A Apple B Apple C1 1/2 1/62 1 1/36 3 1A B CFigure 2 Pairwise comparison matrix for apples using judgments If we did not have actual measurements, we could not be certain that the judgments in the first row are accurate, and we would not mind estimating the value in the (2, 3) position directly by comparing apple B with apple C. We are then very likely to be inconsistent. How inconsistent can we be before we think it is intolerable? Later we give an actual measure of inconsistency and argue that a consistency of about 10% is considered acceptable. We obtain from the consistent pairwise comparison matrix above a vector of priorities showing the relative sizes of the apples. Note that we do not have to go to all this trouble to derive the relative volumes of the apples. We could simply have normalized the actual measurements. The reason we did so is to lay the foundation for what to do when we have no measures for the property in question. When judgments are consistent as they are here, this vector of priorities can be obtained in two ways: dividing the elements in any column by the sum of its entries (normalizing it), or by summing the entries in each row to obtain the overall dominance in size of that alternative relative to the others and normalizing the resulting column of values. Incidentally, calculating dominance plays an important role in computing the priorities when judgments are inconsistent for then an alternative may4JOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING / Vol. 13, No. 1, March, 2004SAATYdominate another by different magnitudes by transiting to it through intermediate alternatives. Thus the story is very different if the judgments are inconsistent, and we need to allow inconsistent judgments for good reasons. In sports, team A beats team B, team B beats team C, but team C beats team A. How would we admit such an occurrence in our attempt to explain the real world if we do not allow inconsistency? Most theories have taken a stand against such an occurrence with an axiom that assumes transitivity and prohibits intransitivity, although one does not have to be intransitive to be inconsistent in the values obtained. Others have wished it away by saying that it should not happen in human thinking. But it does, and we offer a theory below that copes with intransitivity.3. The Fundamental Scale of the AHP for Making Comparisons with JudgmentsIf we were to use judgments instead of ratios, we would estimate the ratios as numbers using the Fundamental Scale of the AHP, shown in Table 1 and derived analytically later in the paper, and enter these judgments in the matrix. A judgment is made on a pair of elements with respect to a property they have in common. The smaller element is considered to be the unit and one estimates how many times more important, preferable or likely, more generally “dominant”, the other is by using a number from the Fundamental Scale. Dominance is often interpreted as importance when comparing the criteria and as preferencewhen comparing the alternatives with respect to the criteria. It can also be interpreted as likelihood as in the likelihood of a person getting elected as president, or other terms that fit the situation. The set of objects being pairwise compared must be homogeneous. That is, the dominance of the largest object must be no more than 9 times the smallest one (this is the widest span we use for many good reasons discussed elsewhere in the AHP literature). Things that differ by more than this range can be clustered into homogeneous groups and dealt with by using this scale. If measurements from an existing scale are used, they can simply be normalized without regard to homogeneity. When the elements being compared are very close, they should be compared with other more contrasting elements, and the larger of the two should be favored a little in the judgments over the smaller. We have found this approach to be effective to bring out the actual priorities of the two close elements. Otherwise we have proposed the use of a scale between 1 and 2 using decimals and similar judgments to the Fundamental Scale below. We note that human judgment is relatively insensitive to such small decimal changes. Table 2 shows how an audience of about 30 people, using consensus to arrive at each judgment, provided judgments to estimate the dominance of the consumption of drinks in the United States (which drink is consumed more in the US and how much more than another drink?). The derived vector of relative consumption and the actual vector, obtained by normalizing the consumption given in official statistical data sources, are at the bottom of the table.JOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING / Vol. 13, No. 1, March, 20045Decision Making – The Analytic Hierarchy and Network Processes (AHP/ANP)Table 1 The Fundamental scale of absolute numbersIntensity of Importance 1 2 3 4 5 6 7 8 9 Definition Equal importance Weak or slight Moderate importance Moderate plus Strong importance Strong plus Very strong or demonstrated An activity is favored very strongly over another; its dominance importance Very, very strong Extreme importance If activity i has one of the above Reciprocals of above assigned nonzero to it numbers when A reasonable assumption The evidence favoring one activity over another is of the highest possible order of affirmation demonstrated in practice Experience and judgment strongly favor one activity over another Experience and judgment slightly favor one activity over another Explanation Two activities contribute equally to the objectivecompared with activity j, then j has the reciprocal value when compared with iRationalsRatios arising from the scaleIf consistency were to be forced by obtaining n numerical values to span the matrixTable 2 Relative consumption of drinksW Which Drink Is Consumeded o the U.S.? U.S.? c s Co su More in e eDrink Consumption Coffee Wine in the U.S. Coffee Wine Tea Beer Sodas Milk Water 1 1/9 1/5 1/2 1 1 2 9 1 2 9 9 9 9An Example of Estimation Using JudgmentsTea 5 1/3 1 3 4 3 9 Beer 2 1/9 1/3 1 2 1 3 Sodas 1 1/9 1/4 1/2 1 1/2 2 Milk 1 1/9 1/3 1 2 1 3 Water 1/2 1/9 1/9 1/3 1/2 1/3 1The derived scale based on the judgments in the matrix is: Coffee Wine Tea Beer Sodas Milk Water .177 .019 .042 .116 .190 .129 .327 with a consistency ratio of .022. The actual consumption (from statistical sources) is: .180 .010 .040 .120 .180 .140 .3306JOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING / Vol. 13, No. 1, March, 2004SAATYIf the objects are not homogeneous, they may be divided into groups that are homogeneous. If necessary additional objects can be added merely to fill out the intervening clusters to move from the smallest object to the.07 Cherry Tomato .08 Small Green Tomatolargest one. Figure 3 shows how this process works in comparing a cherry tomato with a water melon, which appears to be two orders of magnitude bigger in size, by introducing intermediate objects in stages..28 Lime .22 .70 .65LimeGrapefruitHoneydew.08 =1 .08.65×1=.65 .10.22 = 2.75 .08.65×2.75=1.79 .30.70 = 8.75 .08.65×8.75=5.69 .60HoneydewSugar Baby WatermelonOblong Watermelon.10 =1 .105.69×1=5.69.30 =3 .105.69×3=17.07.60 =6 .105.69×6=34.14This means that 34.14/.07.487.7 cherry tomatoes are equal to the oblong watermelon.Figure 3 Clustering to compare non-homogeneous objects4. Scales of MeasurementMathematically a scale is a triple, a set of numbers, a set of objects and a mapping of the objects to the numbers. There are two ways to perform measurement, one is by using an instrument and making the correspondence directly, and the other is by using judgment. When using judgments one can either assign numbers to the objects by guessing their value on some scale of measurement when there is one, or derive a scale by considering a subset of objects in some fashion such as comparing them in pairs, thus making the correspondenceindirect. In addition there are two kinds of origin; one is an absolute origin as in absolute temperature where nothing falls below that reading; and the other where the origin is a dividing point of positive and negative values with no bound on either side such as with a thermometer. Underlying both these ways are the following kinds (there can be more) of general scales: Nominal Scale invariant under one to one correspondence where a number is assigned to each object; for example, handing out numbers for order of service to people in a queue. Ordinal Scale invariant under monotoneJOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING / Vol. 13, No. 1, March, 20047Decision Making – The Analytic Hierarchy and Network Processes (AHP/ANP)transformations, where things are ordered by number but the magnitudes of the numbers only serve to designate order, increasing or decreasing; for example, assigning two numbers 1 and 2, to two people to indicate that one is taller than the other, without including any information about their actual heights. The smaller number may be assigned to the taller person and vice versa. Interval Scale invariant under a positive linear transformation; for example, the linear transformation F = (9/5) C + 32 for converting a Celsius to a Fahrenheit temperature reading. Note that one cannot add two readings x1 and x2 on an interval scale because then y1 + y2 = (a x1 + b) + (a x2 + b) = a ( x1 + x2 ) +2b which is of the form ax + 2b and not of the form ax + b . However, one can take an average of such readings because dividing by 2 yields the correct form. Ratio Scale invariant under a similarity transformation, y = ax , a > 0 . An example is converting weight measured in pounds to kilograms by using the similarity transformation K = 2.2 P. The ratio of the weights of the two objects is the same regardless of whether the measurements are done in pounds or in kilograms. Zero is not the measurement of anything; it applies to objects that do not have the property and in addition one cannot divide by zero to preserve ratios in a meaningful way. Note that one can add two readings from a ratio scale, but not multiply them because a 2 x1 x2 does not have the form ax . The ratio of two readings from a ratio scale such as 6 kg/ 3 kg = 2 is a number that belongs to an absolute scale that says that the 6 kg object is twice heavier than the 3 kg object.The ratio 2 cannot be changed by some formula to another number. Thus we introduce the next scale. Absolute Scale invariant under the identity transformation x = x; for example, numbers used in counting the people in a room. There are also other less well-known scales like a logarithmic and a log-normal scale. The fundamental scale of the AHP is a scale of absolute numbers used to answer the basic question in all pairwise comparisons: how many times more dominant is one element than the other with respect to a certain criterion or attribute? The derived scale, obtained by solving a system of homogeneous linear equations whose coefficients are absolute numbers, is also an absolute scale of relative numbers. Such a relative scale does not have a unit nor does it have an absolute zero. The derived scale is like probabilities in not having a unit or an absolute zero. In a judgment matrix A , instead of assigning two numbers wi and w j (that generally we do not know), as one does with tangibles, and forming the ratio wi / w j we assign a single number drawn from the fundamental scale of absolute numbers shown in Table 1 above to represent the ratio ( wi / w j ) /1 . It is a nearest integer approximation to the ratio wi / w j . The ratio of two numbers from a ratio scale (invariant under multiplication by a positive constant) is an absolute number (invariant under the identity transformation) and is dimensionless. In other words it is not measured on a scale with a unit starting from zero. The numbers of an absolute scale are defined in terms of8JOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING / Vol. 13, No. 1, March, 2004SAATYsimilarity or equivalence. The (absolute) number of a class is the class of all those classes that are similar to it; that is they can be put into one-to-one correspondence with it. But that is not our complete story about absolute numbers transformed to relative form – relative absolute numbers. We now continue our account. The derived scale will reveal what wi andw j are. This is a central fact about the relativecondition for thinking about the world in a scientific way, but it is not sufficient because a mentally disturbed person can think in a perfectly consistent way about a world that does not exist. We need actual knowledge about the world to validate our thinking. But if we were always consistent we would not be able to change our minds. New knowledge often requires that we see things in a new light that can contradict what we thought was correct before. Thus we live with the contradiction that we must be consistent to capture valid knowledge about the world but at the same time be ready to change our minds and be inconsistent if new information requires that we think differently than we thought before. It is clear that large inconsistency unsettles our thinking and thus we need to change our minds in small steps to integrate new information in the old total scheme. This means that inconsistency must be large enough to allow for change in our consistent understanding but small enough to make it possible to adapt our old beliefs to new information. This means that inconsistency must be precisely one order of magnitude less important than consistency, or simply 10% of the total concern with consistent measurement. If it were larger it would disrupt consistent measurement and if it were smaller it would make insignificant contribution to change in measurement. The paired comparisons process using actual measurements for the elements being compared leads to the following consistent reciprocal matrix:measurement approach. It needs a fundamental scale to express numerically the relative dominance relationship by using the smaller or lesser element as the unit of each comparison. Some people who do not understand this and regard the AHP as controversial, forget that most people in the world don’t think in terms of numbers but of how they feel about intensities of dominance. They think that the AHP would have a greater theoretical strength if the judgments were made in terms of “ratios of preference differences”. I think that the layman would find this proposal laughable as I do for its paucity of understanding, taking the difference of non-existing numbers which one is trying to find in the first place. He needs first to see a utility doctor who would help him create an interval scale utility function so he can take values from it to form differences and then form their ratios to get one judgment!5. From Consistency to InconsistencyConsistency is essential in human thinking because it enables us to order the world according to dominance. It is a necessaryJOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING / Vol. 13, No. 1, March, 20049Decision Making – The Analytic Hierarchy and Network Processes (AHP/ANP)A1 w1 A1 A2 M An w1 w1 w w 2 1 wn w1A2 w2L LAn wnw1 w2 L w1 wn w2 w2 L w2 wn M wn w2 L wn wn We note that we can recover the vector w = ( w1 ,..., wn ) by solving the system of equations defined by: w1 w1 w1 w 2 K w1 w n w 2 w1 w 2 w 2 K w 2 w n Aw = M w n w1 w n w 2 K w n w n w1 w1 w2 w2 = n = nw M M wn wn We said earlier that an n by n matrix A = (aij ) is consistent if aij a jk = aik , i, j , k = 1,..., n holds among its entries. We have for a consistent matrix Ak = n k 1 A , a constant times the original matrix. In normalized form both A and Ak have the same principal eigenvector. That is not so for an inconsistent matrix. A consistent matrix always has the formw A= i wj . Solving this homogeneous system of linear equations Aw = nw to find w is a trivial eigenvalue problem, because the existence of a solution depends on whether or not n is an eigenvalue of the characteristic equation of A. But A has rank one and thus all its eigenvalues but one are equal to zero. The sum of the eigenvalues of a matrix is equal to its trace, the sum of its diagonal elements, which in this case is equal to n. Thus n is the largest or the principal eigenvalue of A and w is its corresponding principal eigenvector that is positive and unique to within multiplication by a constant, and thus belongs to a ratio scale. We now know what must be done to recover the weights wi , whether they are known in advance or not.Of course, real-world pairwise comparison matrices are very unlikely to be consistent. In the inconsistent case, the normalized sum of the rows of each power of the matrix contributes to the final priority vector. Using Cesaro summability and the well-known theorem of Perron, we are led to derive the priorities in the form of the principal right eigenvector. Now we give an elegant mathematical discussion, based on the concept of invariance, to show why we still need for an inconsistent matrix the principal right eigenvector for our priority vector. It is clear that no matter what method we use to derive the weights wi , we need to get them back as proportional to the expressionj =1∑ aij w jni = 1,..., n ,that is, we must solvej =1 n∑ aij w j = cwi i = 1,..., n .nOtherwise ∑ aij w jj =1i = 1,..., nwould yield another set of different weights10JOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING / Vol. 13, No. 1, March, 2004and they in turn can be used to form new expressions11,...,nij j j a w i n ==∑,and so on ad infinitum. Unless we solve the principal eigenvalue problem, our quest for priorities becomes meaningless.We learn from the consistent case that what we get on the right is proportional to the sum on the left that involves the same ratio scale used to weight the judgments that we are looking for. Thus we have the proportionality constant c. A better way to see this is to use the derived vector of priorities to weight each row of the matrix and take the sum. This yields a new vector of priorities (relative dominance of each element) represented in the comparisons. This vector can again be used to weight the rows and obtain still another vector of priorities. In the limit (if one exists), the limit vector itself can be used to weight the rows and get the limit vector back perhaps proportionately. Our general problem possibly with inconsistent judgments takes the form:12111222121...1/1...1/1/...1n n n nn a a w a a w Aw cw a a w==MM This homogeneous system of linear equations Aw cw =has a solution w if c is the principal eigenvalue of .A That this is the case can be shown using an argument that involves both left and right eigenvectors of A . Two vectors 11(,...,), (,...,)n n x x x y y y ==are orthogonal if their scalar product11...n n x y x y ++is equal to zero. It is knownthat any left eigenvector of a matrix corresponding to an eigenvalue is orthogonal to any right eigenvector corresponding to a different eigenvalue. This property is known as biorthogonality (Horn and Johnson 1985). Theorem For a given positive matrix A, theonly positive vector w and only positive constant c that satisfy Aw cw =, is a vector w that is a positive multiple of the principal eigenvector of A, and the only such c is the principal eigenvalue of A.Proof. We know that the right principaleigenvector and the principal eigenvalue satisfy our requirements. We also know that the algebraic multiplicity of the principal eigenvalue is one, and that there is a positive left eigenvector of A (call it z ) corresponding to the principal eigenvalue. Suppose there is a positive vector y and a (necessarily positive) scalar d such that Ay dy =. If d and c are not equal, then by biorthogonality y is orthogonal to z , which is impossible since both vectors are positive. If c and d are equal, then y and w are dependent since c has algebraic multiplicity one, and y is a positive multiple of w . This completes the proof.6. An Example of an AHPDecisionThe simple decision is to choose the best city in which to live. We shall show how to make this decision using both methods of the AHP which conform with what Blumenthal said. We do it first with relative (comparative) measurement and second with absolute。
世界著名的咨询公司——兰德公司(Rand)兰德公司是当今世界最著名的独立咨询机构。
“兰德”的英文名称是“Rand”，是英文“研究与发展”(ResearchandDevelopment)两词的缩写。
1948年11月，由福特基金会和银行联合出资组成了兰德公司，当时有21名工商界、学术界和代表机构的著名人士组成的托管理事会，任命公司的负责人进行决策咨询。
兰德公司成立初期，主要为空军服务。
从事研究各种武器系统的改善、军队经营管理的改善和战略概念的重新界定等工作。
随着冷战时代的结束，兰德的服务对象扩大到政治、司法、经济、外交、城市管理、环境保护、能源、保健、教育及计算机信息等许多方面。
兰德公司通过分析在许多领域中的问题及发展情况来帮助所有层次的政策制定者、许多组织蚱秘密部门的领导者和公众，以增强国际经济的活力，保证美国安全，改善生活的质量。
这些领域包括国际防御、教育和培训、健康护理和国内司法、劳工和人口、科学和技术、社团发展、国际间关系以及区域性研究。
兰德研究院可以培养决策分析的博士；，并且还可以为实施其他高级培训计划提供场所。
50年代，朝鲜战争前夕，兰德公司就组织大批专家对朝鲜战争进行评估并对“中国是否出兵朝鲜”进行预测。
得出的结论只有7个字：“中国将出兵朝鲜”。
当时兰德公司欲以200万美元将研究报告转让给五角大楼。
但军界的高级官员对兰德的报告不感兴趣。
在他们看来，中国刚经历了8年抗日战争，3年解放战争，无论人力财力都不具备出兵朝鲜的可能。
然而战争的发展和结局却不幸被兰德言中，美国军界一片哗然。
战争失败后，五角大楼为了全面检讨在朝鲜战争中的决策失误，还是花了200万美元重金买下兰德那份已经过时的研究报告。
然而，比之代价更为昂贵的却是成千上万美国军人丧生朝鲜半岛。
另一个确立兰德公司在美国乃至世界咨询业霸主地位的案例是对前苏联卫星发射的预测。
二战结束后，美苏两国形成了称雄世界的两极格局。
从陆地到海洋，从海洋到太空，双方都开展史无前例的军备竞赛。
《兰德决策》--机遇预策与商业决策CHAPT I：兰德理性管理决策我在兰德公司做社会研究工作时，同日后许多国家政府机关和许多大型企业所做的决策，其品质之差，使人难以相信，小者造成千万美元的损失，大者则造成社会灾难与动荡。
--本杰明?崔果哈佛大学社会学博士，兰德公司社会研究所最高主管，美国空军训练顾问§1、兰德式理性管理前提主题：对组织有效性的追寻第一号兰德决策元素专家团队一个专家团队的建立，主要是基于成员在追求特定目标上的技术能力。
团队的成员在各个方面都是专写。
他们都能以其独特的学识与经验，来做独特的贡献。
成功团队的条件：1、独特的技术能力（个人素质好）2、相互容忍对方。
3、追求一个共同目标。
4、遵守为实现这一目标所设定的程序（制度）《兰德案例》--一个建立管理团队的公司背景：某中型集团公司原来因集权领导，导致互不信任，互相离间，整个公司的生产力不高，这时提拔了一个新CEO，他采取了如下措施：决定让所有主管都能学习和使用兰德决策方法，把自己视为一个单一组织的管理者，而非一群分封采邑的诸侯。
1、这位新总裁和手下24名主管成为第一批学习和使用这些观念的人，一周之内，他们分析了近30个情况，这些情况中有许多被人避免触及，他们解决了某些问题，并做成决策。
2、24名主管的手下参加了同样的训练，他们学到了使用这些观念的方法，运用他们来找出分析那些具有重大关系的状况，并计划继续他们的分析，直到达成决议为止。
3、再下一层次的主管来接受同样的训练。
两个月内，有84名主管学到了处理及解决管理方面事项的共同方法，该组织亦建立了相应的新制度和程序，来支持这些方法的继续使用。
另外，这位CEO透过行动，又宣布如下信息：1、这是一个组织。
2、通过使用共同的处理及决策方式，身为组织，各组成部分的我们，能够亲密无间地在一起工作。
3、从我开始每个人都要使用这个方法。
4、你能够思考，你的知识和经验是重要的，你将会有效的运用你所学到的新方法。
兰德公司宗旨：兰德公司是一个非营利机构，这有助于通过研究和政策分析和决策。
在超过60年，在公共和私营部门的决策者已转向兰德公司的客观分析和解决该国面临的挑战和世界的有效的解决办法。
这些挑战包括关键在教育，贫困，犯罪的社会和经济问题，环境，以及对国家安全的一系列问题。
兰德公司的研究人员和分析师继续在各自领域的前沿，在公共和私营部门找到工作的决策者今天的困难，敏感和重要问题的解决方案。
我们的研究人员高素质，是众所周知的，正如许多诺贝尔奖获得者谁一直与兰德附属证明，或者作为雇员，顾问或提供咨询的能力。
我们致力于通过高品质的和客观的研究和分析，并与多年来开发了先进的分析工具，兰德公司从事客户创造知识，洞察力，信息，选择和解决方案将有效和持久。
正是在1948年5月14日，该项目兰德- 1第二次世界大战的产物- 道格拉斯飞机公司从圣莫尼卡，加利福尼亚，分离，成为独立的，非盈利性组织。
采用从它的名字一词收缩研究与发展，新成立的实体，是致力于推动和促进科学，教育，以及为公众福利和美国的安全慈善用途。
几乎马上，兰德开发了独特的风格，融入严谨，以事实为基础的分析一丝不苟nonpartisanship解决社会最紧迫的问题。
随着时间的推移，兰德公司的研究人员召集了一个独特的队伍，不仅为个人技能，而且也为跨学科合作，尤其显着。
到60年代，兰德公司是把它的经验，无党派，独立分析商标模式，许多紧迫的国内社会和经济问题的研究。
二战揭示了技术研究和开发，并在战场上的科学家和军内外谁提出这样的发展可能学术界广泛成功的重要性。
此外，随着战争接近尾声，但显而易见的是完整的和永久的和平可能无法保证。
其中包括了陆军部的人讨论，科学研究与发展办公室和行业谁看见了一个私人机构需要与军事研究和发展规划的决定。
在战争的局长，指挥官陆军空军架HH“的报告厦门”阿诺德说：“在这场战争的陆军，陆军航空部队，海军已经作出了科学和工业资源带来前所未有的使用。
KT决策法(KT Matrix)日期：[2008-12-5]什么是KT决策法KT决策法是最负盛名的决策模型，由美国人查尔斯·H·凯普纳(CharlesH．Kepner)和本杰明·特雷高(Benjamin B．Tregoe)二人合作研究发明的、把发现问题分为界定问题和分析原因两步的方法。
KT法是一种思考系统，即就事情各自的程序，按照时间、场所等，明确区分发生问题的情形和没有发生问题的情形，由此找出原因和应该决定的办法。
KT法共分四个程序：查明原因、决定选择方法、危险对策、掌握情况。
它是由美国兰德公司的凯普纳和本杰明·特雷高发明的一种训练法。
KT是凯普纳和特雷高两个英文字的字头。
如果是优秀的管理人员，就能够自然而然地实行这种方法，并把它当作教育程序加以系统化，这就是“KT法”。
有效决策的组成部分1958年,查尔斯·H·凯普纳(CharlesH．Kepner)和本杰明·特雷高(Benjamin B．Tregoe)成立了凯普纳——特雷高公司。
该公司是一间位于普林斯顿的国际管理咨询公司，主要致力于企业提供解决问题和决策制定方面的培训。
在出版于1965年的《理性经理人》一书中，凯普纳和特雷高提出了制定有效决策的三个主要组成部分：对所要完成的任务目标的认识程度；对备选方案进行评估的质量；对采用其他方法可能导致的后果的了解程度。
决策分析的主要因素他们使用了这一分析对决策分析方法论的主要因素进行了定义：制定决策声明；决策目标的确认，即：哪些是“必要目标”（必须被完成的目标），哪些是“理想目标”（最好能够完成，但不是最主要的目标）；备选方案的确认；对各种决策后果进行评估。
由此，我们可将凯普纳—特雷高的方法简洁地归纳如下：制定决策声明，明确决策制定的水平（他们认为，这一方法对一个集团企业来说最为有效）制定决策目标并明确“必要目标”和“理想目标”。
然后根据彼此之间的关系衡量“理想目标”的重要性（如：由1—10进行打分）；制定其他备选方案并进行评估。
我要再引一个案例，它就是兰德公司的七字报告：“中国将国兵朝鲜”。
大家一定知道，兰德公司1948年11月创办,源于美国空军1946年一项代号为RAND科研项目,部位于加州圣莫尼卡,兰德的译文是“研究和发展”(Research and Development )。
是美国最负盛名德决策咨询机构,美国兰德首先以介入政府决策，而名扬天下。
当时第二次大战刚刚结束，东西方两大阵营的对峙状态已经形成，为了在战略上取得优势，美国欲出兵朝鲜，但对中国是否出兵，一直难以判断。
就委托兰德公司对美国出兵朝鲜，中国将会怎样的战略咨询进行决策分析。
结果，兰德公司提交给美国杜鲁门政府，概括为七个字：“中国将出兵朝鲜”。
美国政府对兰德公司的咨询忠告半信半疑，因为，兰德公司索要260万咨询费，美国政府不愿为这七个字而付出高昂的咨询费，结果朝鲜战争一爆发，中国人民志愿军随之跨过鸭绿江，与美国在朝鲜战场上进行了三年多的浴血奋战，美国远东军司令长官麦克阿瑟将军讽刺美国政府：不愿花一架战斗机的价钱，却花掉了数艘航空母舰的代价打了这场预先可以避免的战争。
朝鲜战争结束三十年后，美国政府心悦诚服地从兰德公司手中，花巨额美金买下了咨询报告。
美军在朝鲜战场上的失败并没有失败在没做调研，而在失败于没有将调研的结果落到实处。
没做调研失败了是可恨，做了调研却没有用调研结果，这叫可悲。
[观点一] 税收优惠是政府与纳税人的交易税收优惠政策，就是能减轻企业税收负担的政策。
包括免税、减税、缓税、退税、税收抵免等十几种方式。
在对税收优惠作了一个简单介绍后，高金平话锋一转，提出了一个观点：税收优惠政策实际上是政府与纳税人的一项交易。
为何是“交易”？高金平阐述说，国家出台每一项税收优惠政策，都体现了一种导向：比如为了发展西部经济，国家就出台了多项减免税政策，鼓励企业到西部投资；为了吸引更多的外资到国内，国家就为外资企业提供了税收优惠政策；政府不能完全安置下岗失业人员、残疾人，那么政府就鼓励企业接纳这些人，但“条件”就是给这些企业一些减免税的优惠政策。
6Jump down to document Visit RAND at Explore RAND-Initiated ResearchView document detailsThis document and trademark(s) contained herein are protected by law as indicated in a noticeappearing later in this work. This electronic representation of RAND intellectual property is providedfor non-commercial use only. Permission is required from RAND to reproduce, or reuse in another form, any of our research documents for commercial use.Limited Electronic Distribution RightsFor More InformationCHILD POLICYCIVIL JUSTICEEDUCATIONENERGY AND ENVIRONMENTHEALTH AND HEALTH CAREINTERNATIONAL AFFAIRSNATIONAL SECURITYPOPULATION AND AGINGPUBLIC SAFETYSCIENCE AND TECHNOLOGYSUBSTANCE ABUSETERRORISM AND HOMELAND SECURITYTRANSPORTATION AND INFRASTRUCTURE The RAND Corporation is a nonprofit research organization providing objective analysis and effective solutions that address the challenges facing the publicand private sectors around the world.RAND-INITIATED RESEARCHThis product is part of the RAND Corporation occasional paper series. RAND occasional papers may include an informed perspective on a timely policy issue, a discussion of new research methodologies, essays, a paper presented at a conference, a conference summary, or a summary of work in progress. All RAND occasional papers undergo rigorous peer review to ensure that they meet high standards for research quality and objectivity.Problem Formulation and Solution ElementsMARTIN C. LIBICKI,SHARI LAWRENCE PFLEEGEROP-103-RCJanuary 2004This research in the public interest was supported by RAND, using discretionary funds made possible by the generosity of RAND’s donors, the fees earned on client-funded research, and independent research and development (IR&D) funds provided by the Department of Defense.ISBN: 0-8330-3561-4The RAND Corporation is a nonprofit research organization providing objective analysis and effective solutions that address the challenges facing the public and private sectors around the world. RAND’s publications do not necessarily reflect the opinions of its research clients and sponsors.R®is a registered trademark.© Copyright 2004 RAND CorporationAll rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from RAND.Published 2004 by the RAND Corporation1700 Main Street, P.O. Box 2138, Santa Monica, CA 90407-21381200 South Hayes Street, Arlington, VA 22202-5050201 North Craig Street, Suite 202, Pittsburgh, PA 15213-1516RAND URL: /T o order RAND documents or to obtain additional information, contactDistribution Services: T elephone: (310) 451-7002;Fax: (310) 451-6915; Email: order@PrefaceAcross a wide variety of endeavors—from homeland security to for-eign intelligence, criminal investigation, public health, and system safety—failure to anticipate disaster has been ascribed to the inability to “connect the dots.” This paper argues that to “connect the dots,”one must first “collect the dots.” All too often, the inability to foresee trouble has come about because pieces of information sit in this or that head. Were they combined, trouble would be easier to foresee, but when each stands alone, no compelling conclusions suggest them-selves. This paper investigates some of the barriers to circulating tell-tale information and describes some approaches—institutional, social, and technological—that would begin to bring information together in a meaningful way.This paper results from the R AND Corporation’s continuing program of self-sponsored independent research. Support for such research is provided, in part, by donors and by the independent re-search and development provisions of RAND’s contracts for the op-eration of its U.S. Department of Defense federally funded research and development centers. It is expected to be of interest to the broad policymaking community, particularly those who are concerned about how to recognize and thereby avert disastrous events.iiiiv Collecting the Dots: Problem Formulation and Solution ElementsRAND Science and TechnologyThe R AND Corporation is a nonprofit research organization pro-viding objective analysis and effective solutions that address the chal-lenges facing the public and private sectors around the world. RAND Science and Technology (S&T), one of RAND’s research units, as-sists government and corporate decisionmakers in developing options to address challenges created by scientific innovation, rapid techno-logical change, and world events. RAND S&T’s research agenda is diverse. Its main areas of concentration are science and technology aspects of energy supply and use; environmental studies; transporta-tion planning; space and aerospace issues; information infrastructure; biotechnology; and the federal R&D portfolio.Inquiries regarding RAND Science and Technology may be di-rected toStephen RattienDirector, RAND Science and TechnologyRAND1200 South Hayes StreetArlington, VA 22202-5050703-413-1100 x5219/scitechContents Preface (iii)Figures (vii)Tables (ix)Summary (xi)Acknowledgments (xvii)CHAPTER ONE Introduction (1)Dimensions of the Problem: Historical Failures (4)Methods and Scope of Inquiry (11)Dealing with Explicit and Tacit Knowledge (12)Examining New and Rare Phenomena (16)Dynamic Analysis of Large Communities (17)Putting the Pieces Together (19)Barriers to Collecting the Dots (20)Lack of Awareness (20)Lack of Attention (23)Misuse of Templates (25)Compartmentalization (30)CHAPTER TWOModeling Communication of Information (33)CHAPTER THREEElements of Potential Solutions (35)vvi Collecting the Dots: Problem Formulation and Solution Elements Networking (36)Roles and Responsibilities (39)Collaboration (43)Categorization (45)Hybrid Approaches (49)Defining Solution Frameworks (51)In-Box Monitor (53)Synthesizer (55)Analyzer (56)Decision Tool (56)Communicator (57)CHAPTER FOURFuture Directions: Outlining a Solution (59)Step 1: Investigating Relationships, Parameters, and Metrics (61)Step 2: Designing Tools to Support Each Subprocess (64)Step 3: Implementing and Assessing the Tools (64)CHAPTER FIVE Conclusions (67)References (71)Figures1.1.Generating Tacit and Explicit Knowledge (14)1.2.The Creation of Social Capital (19)1.3. A Framework for Recognizing and CommunicatingNotable Information (53)viiTables1.1.Meta-Matrix for Collecting the Dots (14)1.2.Types of Knowledge Management Systems (15)1.3.Relationship of Errors to Template Misuse (29)1.4.Correlating Barriers to Examples (31)3,1. A Framework for Addressing Barriers with SolutionElements (51)3.2.Detailed Questions Addressed by Each Subprocess (54)ixSummaryThe prevailing view in the intelligence and public safety communities is that forestalling major threats such as terrorist attacks or epidemics requires weaving together disconnected pieces of information to re-veal broader patterns; in more common terms, we call this “connect-ing the dots.” In this paper, we argue that connecting the dots is less likely to happen unless one takes a prior step: “collecting the dots,”that is, bringing scattered pieces of information into some proximity to each other to enable pattern recognition. This paper is intended to help decisionmakers understand the dimensions of solving the prob-lem of “collecting the dots.” Any solution involves identifying what information is important and improving its circulation within com-munities that are in a position to connect the dots so collected. The paper describes organizational and informational barriers to “collect-ing the dots” and explores the characteristics of potential solutions to overcoming them.Assumptions and MethodologyWe made three basic assumptions about the scope of the problem. First, we restricted the problem at hand to dealing with explicit in-formation rather than with knowledge management as a whole. Sec-ond, we focused on understanding how to collect and communicate dots on new or rare phenomena the existence of which is indicated by the dots (that is, by newly collected or reconsidered information).xixii Collecting the Dots: Problem Formulation and Solution ElementsAnd third, we looked primarily at how information is identified and shared in large communities. In this context, “large” means greater than the size (variously defined as between 50 and 200 people) at which everyone in the community knows one another.We analyzed several historical examples of well-known failures to “collect the dots” in order to identify those things that might en-courage or discourage collection. Next, we reviewed a subset of the literature on information networks, knowledge management, and in-stitutional communication, enhancing our understanding not only of what we know about aspects of our problem but also highlighting those areas where gaps in our understanding occur. We also created and ran a heuristic model that simulated the flow of information within an organization, in an attempt to understand variations in the flow of “useful” versus “misleading” information.BarriersThere are four major barriers to circulating the right kinds of infor-mation within communities.•Lack of awareness. People who possess notable information may not be aware of its notability and thus may not circulate it widely. As such, an important aspect of awareness may involve recognizing when one possesses some of the “dots” and therefore needs to circulate information to help others assemble the “big-ger picture.”•Lack of attention. Attention is the obverse of awareness. Whereas awareness leads to information flow, attention focuses on infor-mation received. Attention needs to be highly selective; paying attention to too many “dots” decreases the likelihood that sig-nificant items will receive needed attention.•Inadequate templates. Templates are generalized patterns based on experience that help people understand new situations. In some cases, past experience does not map usefully onto new in-formation. Observers may try to squeeze new information intoSummary xiii templates prematurely or to fit information into inadequate, in-appropriate templates, thus closing off potential avenues of in-terpretation.•Compartmentalization. Sometimes people in subcommunities tend (for security and bureaucratic reasons) to keep information to themselves. This careful guarding keeps information from cir-culating, thereby preventing dot collection.Some Solution ApproachesIn one sense, the problem of collecting the dots is one of promoting information-sharing in order to accelerate the detection of critical phenomena. To some extent, solutions that promote the sharing of information correspond to the barriers cited (e.g., networking helps to mitigate compartmentalization). In other respects, just as bio-chemical excitation agents do not simply suppress inhibiting agents, some solutions take the barriers as given and try to overcome them in other ways.NetworkingInformation-sharing requires some kind of networking. Physical net-working that connects machines can be a valuable tool in bringing disparate pieces of information into proximity. Social networks that connect people are just as important, but can be more difficult to in-stitutionalize. For one thing, communities may not be well-defined, and community boundaries may not always be clear. Individuals known as “connectors,” who know and speak with many people within an organization, may have an important role to play in bol-stering social networks.Roles and ResponsibilitiesIn any process that addresses the problems of circulating information, there are at least three types of roles: decisionmakers, perceivers, and connectors. Clarifying the responsibilities of each of them within or-ganizations or communities can improve communications.xiv Collecting the Dots: Problem Formulation and Solution Elements CollaborationCollaboration in this case means getting the right people together in the right situation. Mechanisms may be needed to overcome a built-in reluctance to collaborate. One of the biggest challenges to pro-moting collaboration is getting people to share information that they alone possess.Categorization“Binning” similar pieces of information into consistent categories en-ables both machines and people to collect dots.Hybrid ApproachesAn approach that combines human and machine capabilities is promising, because it can exploit the unique capabilities of each. Solution FrameworksA formal process for collecting the dots should incorporate a signifi-cant role for human expertise, including heuristic tools for pattern recognition and relationships based on experience and knowledge. One possible framework would include five essential activities:1.An in-box monitor that captures and sorts information;2. A synthesizer that establishes contexts for messages and helps iden-tify candidate templates for categorizing them and adding infor-mation about relationships;3.An analyzer that picks out and juxtaposes related information,while assessing each component;4. A decision tool that interacts with the community’s decision-makers to determine and evaluate next steps; and5. A connector that takes output from the fourth stage and transmitsit to the right audiences.Connecting the dots requires collecting the dots. Ultimately, these two activities are not separate and distinct. Further research toSummary xv examine and refine the concepts introduced in this paper would look for a set of institutional and technological arrangements that would improve the likelihood of both successful collection and connection.AcknowledgmentsThis essay draws, in part, on NSF and NASA proposals, which we had considerable help in writing. Tora Bikson, Craig Martell, and Katherine Carley contributed immensely to the proposals and there-fore to this paper. Bill Butz, Jenny Preece, Ben Shneiderman, Felicia Wu, Charles Pfleeger, Ed Balkovich, Kevin O’Connell, and Ed O’Connell also contributed through their careful reading of earlier drafts and their insightful comments.xviiCHAPTER ONEIntroductionLife is a risky pursuit, and much of what we do is aimed at under-standing, mitigating, or avoiding risk. The understanding and conse-quent actions depend on gathering knowledge about situations and their elements, some of which are difficult to identify or describe. For example, understanding a new disease involves not only identifying the symptoms but also describing how the disease differs from other, similar illnesses. Nevertheless, we slowly build up our understanding from sometimes disparate pieces of information, some of which can change as our understanding grows. As we collect the information, we try to make sense of it in some way, so that we can interpret new or revised information in context.Often, the information available to us has no context when it first appears. We live in a sea of “dots” of information—events, facts, relationships, and/or interpretations thereof—and it is tempting to try to “connect the dots” to help us make sense of the world around us. For example, it is widely acknowledged that success at counterter-rorism (and other efforts to identify threats and avoid problems) re-quires that people “connect the dots”—that is, transform scattered and seemingly unrelated pieces of information into a complete pic-ture of some situation in order to prevent an attack or respond to a threat.In an ideal situation, the dots are sitting there, waiting to be connected—much like, say, U.S. census records, with data neatly in place and easy to find. In reality, data are seldom so neatly arranged and easily scanned; intervening steps are usually required between12 Collecting the Dots: Problem Formulation and Solution Elementsgathering raw intelligence and recognizing patterns that connect dis-crete bits of information. While the “dots” may exist—in the sense that they represent pieces of intelligence now possessed by various individuals within an organization or community of practice1 (hereaf-ter called a “community”)—they often exist widely separated from each other, in isolated locations or isolated from one another. Indeed, they can be particularly hard to recognize. And even when a dot’s ex-istence is known, its nature or importance may be difficult to recog-nize or understand. For example, when someone is first learning about an issue, a person, or an incident, much of the relevant infor-mation may lie in people’s heads and in various stages of articulation, difficult to divine or even describe. Those involved may recognize that something odd is nagging at them, but it is unclear whether the existence of that something is worth mentioning to someone else.In this paper, we argue that in order to “connect the dots,” one must first “collect the dots.” That is, substantial data recognition, gathering, and sorting are required to facilitate the eventual connect-ing of dots. The key to this initial but necessary stage is bringing re-lated but scattered facts into proximity with each other in order to help analysts detect significant patterns or connections. Admittedly, it is sometimes difficult to know which dots to collect and keep until we know their likely or actual connections to one another. That is, their connections may be what make them important, just as a link in a chain is important in supporting its adjacent links. Still, the recog-nition of the importance of a fact must precede its communication to others who need to know about it.There are three ways to think about bringing facts together: combinatorial, network, and spatial. Combinatorial proximity exists _____________1 An informal network of people who share similar roles working in a common context or with a similar perspective (Bieber et al., 2000). Also defined as a group of people who come together to learn from each other by sharing knowledge and experiences about the activities in which they are engaged (Wenger, 1998). The current definition, commonly used by re-searchers examining the dynamics of online communities, is more restrictive: professional or work-related groups that are often associated with a company or organization (Preece, 2003). We mostly use this narrower definition, because the types of problems we hope to solve gen-erally involve organizations that are formally chartered to address them.Introduction 3 when there are algorithms that can recognize that two facts may be meaningfully compared to each other (e.g., they share a keyword or a tag in common). Network proximity exists when two facts are known by two people who tend to share information with one another. Spa-tial proximity exists when two facts exist in the same location or community, so that one member of the community might come across and recognize both of them.Proximity can also be hybrid. For example, rules or algorithms can filter dots for presentation to an organization or community of practice (hereafter called a community), as when information is placed in a form (a table, or returns from a search query) or depicted in a graph or chart. Then, social processes or interactions make peo-ple aware of which dots merit attention. Exactly which approach or combination will work will vary by community and by problem.In most cases, it is hoped that the ultimate result of collect-ing—and then connecting—the dots will be the discovery of insights, understanding, and guidance that would have been less obvious from one dot alone. The problem is thus transferred to one of pattern rec-ognition, where the pattern is recognizable only when enough infor-mation of certain types and configurations is in place.Pointillism is one metaphor for the way in which pieces of in-formation are assimilated and viewed. In this style of painting, dis-tinct specks or “points” of color are arranged to represent distinct figures and objects, recognizable only from a certain distance and per-spective; the eye and the mind fill in the gaps between dots of color. Similarly, dots of information may not actually be connected, and an individual may not be able to discern meaning or pattern without adding information from other sources. It is only when the dots are collected and connected and thus associated with some underlying phenomenon that people can identify the proper relationships and see the canvas as it is.Because the eye and mind play such an important role, the per-spective and context of the viewer influence what conclusions are drawn. That is, any one dot may contribute to the resolution of many different pictures; it may be interpreted differently depending on where it sits, where viewers sit, and what viewers see. And a particular4 Collecting the Dots: Problem Formulation and Solution Elementsindividual must be alert to the possibility of identifying and making sense of the dots; someone who is not looking is far less likely to see.2 Thus, the problem we address is how to identify and collect dots before we can consider connecting them. Our analysis is performed in four steps. First, we introduce dot collection as a phenomenon af-fecting large organizations and communities. We illustrate as much by exploring several examples of failures to collect the dots, in do-mains ranging from war and counterterrorism to crime, public health, space exploration, and even automobile manufacturing. Second, we characterize some of the obstacles to collecting the dots. Third, we contemplate systematic approaches to developing organizational ca-pabilities to collect the dots more efficiently; we also describe an in-formal model of how information might circulate within organiza-tions. The model’s implications suggest several next steps toward improving circulation effectiveness. Fourth, we outline a research agenda that proposes to further characterize the problem, to provide a basis for investigating each of the problem’s aspects—and possible solutions—in greater depth.Dimensions of the Problem: Historical FailuresDot collection examples abound, in that history provides many in-stances of the failure to identify and circulate important information (or at least in time to take needed action). These examples are instruc-tive both in illustrating why dots should be collected and in suggest-ing barriers to doing so. Although they are predominantly from the world of public policy, the examples we present span a variety of ex-perience, from war and crime to public health and systems perform-_____________2 Tools can encourage this identification. They can help by filtering information, highlight-ing dots of a particular type, using data mining techniques to flag unusual situations, and so on.Introduction 5 ance. The problem we address appears widely throughout modern complex societies.3We begin by nothing that there are two kinds of interactions among people or groups. The simpler kind, called symmetric, occurs when people have similar roles in solving a problem—and hence col-lecting or connecting the dots. They tend to have similar jobs, and often have corresponding worldviews, interests, or backgrounds; in a sense they speak the same language. The second kind, called asymmet-ric, involves people who have dissimilar roles in solving a prob-lem—and hence different responsibilities for collecting or connecting the dots. They tend to view the same things from a different perspec-tive and they often have different backgrounds or interests.Symmetric combinations of information characterize the first four examples: the terrorism, epidemic, sniper, and Pearl Harbor cases. In symmetric cases, the community of practice is composed of people with similar duties, in possession of comparable facts. Sym-metric cases present indications that are more parallel (e.g., patients presenting the same symptoms) or less parallel (e.g., the clues that would permit inference of a Japanese attack on Pearl Harbor). Here, it may be said that one fact is noise but two facts are signal. That is, a lone fact, by itself, may not be terribly indicative of anything but the normal range of human behavior or circumstance. Two facts, how-ever, may suggest that some underlying causal factor is at play, giving rise to a set of anomalies falling outside the range of statistical varia-tion (absent an underlying cause). Anomalies themselves do not lead _____________3 There is a reason that most of the examples are drawn from public policy. Modern societies tend to assign to government the task of protecting against certain types of unlikely but broad catastrophic events that no one individual can cover adequately. It is in the nature of military affairs, counterterrorism, and epidemiology to be dominated by the unexpected. Conversely, the fate of most other enterprises, especially commercial ones, is less likely to depend on the inability to spot a specific disaster in the making than it is on the inability to put related important dots together on a day-to-day basis. That Enron, Tyco, WorldCom and other companies laid low in the wake of accounting scandals suggests that this distinc-tion may be overdrawn insofar as commercial enterprises are also heir to disaster. But, in these cases, top management knew what was going on and made a concerted attempt to disguise important facts from others. These situations were largely not cases of failing to collect the dots; the dots were known but purposely kept out of sight.6 Collecting the Dots: Problem Formulation and Solution Elementsto detection; there may not be enough dots to infer anything mean-ingful from them. But they may well induce others to start searching for similar or related examples that help paint a fuller picture; in toto, the collection may possess explanatory value.The latter three examples—the Chinese embassy bombing, the Challenger disaster, and the airbag/security interactions—are asym-metric combinations, which characterize complex systems where changes in one facet create unexpected interactions with others. One dot is the change; the other dot is the knowledge of what a change might do. In these situations, not only are the dots dissimilar but so also are the people who know about the dots. That is, without some process for putting dots together, it is unlikely that the pieces of in-formation would be merged to form a bigger picture. For instance, in the Chinese embassy bombing example, the officials familiar with what was where in Belgrade did not usually travel in the same circles as the person determining targets; need-to-know often prevented them from finding out meaning and implication even if they had pos-session of isolated information. Similarly, the NASA space shuttle manager does not always communicate with the Morton Thiokol en-gineers building parts for the shuttle. When automobiles are designed and constructed, the safety engineer does not always communicate enough with the security engineer. Thus, dots of information (what we know, or “knowns”) can be mated to each other, or they can be mated to areas of relevance (what we need, or “needs”)—often the more difficult problem. For instance, the need, “Is this target pro-scribed?” requires the known “Yes, it’s the Chinese embassy.” Simi-larly, one dot may be a fault or a change to a program; the other dot is the context that establishes its dire consequences.Example One: Terrorism on September 11, 2001. In the months prior to September 11, 2001, one FBI special agent began to notice that there were many Arabs in flight school in the Phoenix, Arizona, area sporting strongly anti-American sentiments. Unbeknown to him, another agent in Minneapolis, Minnesota, was pondering why Zacarias Moussaoui had shown far more interest in piloting an air-craft than in taking off and landing it. Had these agents compared notes, they might have come closer to realizing what terrorists were。
