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A Spatial version of the Shang method
TFS-17852; No of Pages 9 Technological Forecasting & Social Change xxx (2013) xxx–xxx
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Technological Forecasting & Social Change
A Spatial version of the Shang method Simone Di Zio a,⁎, Barbara Staniscia b a b
“G. d'Annunzio” University, Viale Pindaro 42–65127 Pescara, Italy Sapienza University of Rome, Piazzale Aldo Moro 5–00185 Roma, Italy
a r t i c l e
i n f o
Article history: Received 19 July 2013 Received in revised form 16 September 2013 Accepted 18 September 2013 Available online xxxx Keywords: Shang Delphi Convergence of opinions Spatial decisions Environmental conflicts
a b s t r a c t This paper proposes a modified version of the Shang method, starting from the assumption that the convergence of opinions involves a spatial context in many applications. The Spatial Shang we present is based, like the classical Shang method, on judgments of a panel of experts, and is applicable when consultations and consequent decisions concern matters of spatial location. The experts are first asked to draw four points on a map while, in subsequent rounds, each panelist must locate a single point, representing her/his evaluation, in one of four rectangles drawn on the map. The method is very easy to be implemented and the whole procedure is very fast to be performed. The application presented in this paper concerns the Costa Teatina National Park (Italy) and the definition of its boundaries. We will here present the on-going conflict and the contribution to its mitigation offered by the Spatial Shang method. The application resulted in a convergence of opinions in a buffer of 550 m; that can be used as a decision support for the choice on the best location for the park's boundaries. © 2013 Elsevier Inc. All rights reserved.
1. Introduction The Delphi technique was developed at the Rand Corporation by Dalkey and Helmer [1] in the 1950s. In the scientific community it is commonly accepted as a method for achieving convergence of opinions in a group of experts. After about 60 years from its creation, the Delphi method has been so widely used that it is now considered to be the founder of a large variety of methods that are known as its variants. After the pioneering work of Dalkey and Helmer [1], Murray Turoff, in 1970, proposed the Policy Delphi [2], which is consensus-oriented and is used for the analysis of public policies. Soon after, in 1972, Olaf Helmer proposed the Mini-Delphi [3], a technique that speeds up the Delphi procedure as it is applied for face to face meetings, and in fact is also known as Estimate-Talk-Estimate (ETE) method.
⁎ Corresponding author at: The “G. d'Annunzio” University, Viale Pindaro 42 – Zip Code 65127 - Pescara, Italy. Tel.: +39 0854537978; fax: +39 0854537542. E-mail addresses: [email protected] (S. Di Zio), [email protected] (B. Staniscia).
Two years later the theoretical foundations of the Markov– Delphi were laid in a work of De Groot [4]; he provides important contributions in probabilistic terms tying the changes in the subjective evaluation of a forecaster to a linear combination of the remaining ones. In 1975 the Shang method was proposed [5]. Some characteristics of the Delphi method – such as the isolation of the participants (anonymity) — are kept in the Shang; moreover, the trouble of asking to rephrase the evaluations at each round is eliminated. The Shang method has the advantage of not anchoring the participants to a position and, then, urging them to depart from it. Afterward, other methods that can be included in the family of Delphi have been developed. We mention here the Nominal Group Technique [6], the Decision Delphi [7], the Abacus-Delphi [8–10], the Real Time Delphi by Theodore J. Gordon and Adam Pease [11] and, among the last ones, the Spatial Delphi [12]. The method we propose here, defined as Spatial Shang, is a variant of the Shang method, and stems from the same logic of a recent innovation of the Delphi method, called Spatial Delphi [12]. The authors of the Spatial Delphi start from a very simple idea: that many decision problems involve a choice of a place on a bounded space, and the territory becomes the basic element
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Please cite this article as: S. Di Zio, B. Staniscia, A Spatial version of the Shang method, Technol. Forecast. Soc. Change (2013), http:// dx.doi.org/10.1016/j.techfore.2013.09.011
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for the application of the Delphi logic. Experts are asked to border the decision problem within a certain area using a map; the result of the convergence is represented by a portion of territory small enough for the scope of the investigation [12]. The Spatial Shang arises from the same considerations which have led to the Spatial Delphi, with the added advantages of the Shang method; it is, therefore, applicable whenever the research problem involves issues related to the choice of a geographical location. The application we present here, is related to a protected area in a coastal region: the Costa Teatina National Park, in Abruzzo, Italy. The Spatial Shang has been applied as a tool for the definition of the park's boundaries. After the legal institution in 2001 — through the National Law 93/2001, art. 8 — its delimitation has not been defined yet. This is because of a severe conflict taking place in the area between the groups in favor and against the protected area. The Spatial Shang has been used as a methodology and tool to reach the convergence of opinions of the local stakeholders concerning the park's limits. In the remainder of the paper, after a description of the Shang method (Section 2), we illustrate the Spatial Shang in Section 3, while we present the application on a coastal park in Section 4. In Section 5 we conclude with a brief discussion the results of the application together with the strengths and weaknesses of the method. 2. The Shang method The Delphi method is an iterative process designed to achieve consensus in a group of experts on a particular topic. Originally developed by a research group at the RAND Corporation, the Delphi technique has seen many applications in the course of half a century [1,13,14]. The method consists of a number of iterations, or rounds, during which the administrator who manages the process, also called facilitator, provides participants with statistical summaries of the answers given by all the panel members. There are many versions of this method but the main steps of the classical version [14] can be summarized as follows: a) formation of the panel of experts and construction of the questionnaire; b) submission of the first questionnaire to the panel; c) calculation of a statistical summary of responses (typically the interquartile range containing 50% of the evaluations); d) submission of the second questionnaire. Panel members are asked to provide a second assessment, typically within the limits of the interquartile range, together with comments on their responses. In case of an external evaluation the expert is asked to argue the choice; e) calculation of a new interquartile range and inclusion in the questionnaire of the reasoning and comments, with preparation of specific spaces for any counter-arguments; f) iteration of steps b–e until the desired degree of consensus is achieved or, if consensus could not be achieved, crystallization of the reasons for disagreement. The Delphi can generate a convergence of opinions: starting from a decisional problem, it facilitates the achievement of a common solution, shared as much as possible. The convergence of opinions is considered a structured process, in which individual thoughts on issues under discussion lead to relatively shared conclusions. However, the objective of a Delphi process is not always consensus; according to each specific application,
different goals can be achieved, such as stability in estimations or, even, generation of alternatives [14]. The Shang method has been described for the first time by Ford [5], as an alternative to the traditional Delphi method. Like the Delphi, it consists of a series of questions directed to a panel of experts, with the scope of progressively facilitating a shared solution. The panel implies several interviews of the same persons at different times; both in Delphi and Shang the guarantee of the anonymity among the participants avoids a series of problems typical in a face-to-face group interaction. In face-to-face communication many mechanisms of distortion may occur and, generally, they affect the reached solution. The most important are the following ones: 1. The error of Leadership. When the highest-ranking person in a group (e.g. in military, political, academic or corporate hierarchies) expresses his/her opinion, the others usually tend to follow him/her. 2. The error of Spiral of Silence. Those whose opinions reflect the ideas of the majority are more likely to feel confident in expressing their opinions; on the contrary those whose opinions are in the minority, fear that expressing their views will result in social ostracism, and therefore remain silent. Those perceptions can lead to a spiraling process, in which minority's viewpoints are increasingly withheld and, therefore, underrepresented. 3. The error of Groupthink. It occurs when the pressure to conform within a group, interferes with the group's analysis of a problem and causes poor group decision making. Individual uniqueness and independent thinking are lost in the pursuit of group cohesiveness. When members strive for unanimity their motivation to realistically assess alternative courses of action is affected. A typical advantage of the Shang (with respect to Delphi) is that participants are not anchored to a position from which they are, later, asked to deviate; this is possible since, in the Shang, at each round, a different question is posed (as will be explained later, indeed, the expert is asked to give, at each round, an estimate above or below a value that is always different). As a consequence, the well known problem of abandon of the Delphi — due to the boredom of answering multiple times the same question — is a little reduced. Furthermore, according to Ford, the Shang — while preserving Delphi advantages — avoids problems derived from pressure toward convergence and response commitment [5]. Finally — since the evaluation interval is halved at each iteration — that method is much faster than Delphi. We now describe schematically the main steps of the Shang method. a) Selection of participants. Like in the traditional Delphi, the construction of the panel is a critical phase, the success of the study depending on it. The knowledge and cooperation of the panelists affect the results of the entire procedure. Generally speaking, the participants can be identified through literature searches (persons who have published on the subject under study), recommendations from institutions (e.g. heads of institutions, mayors, politicians) or recommendations from other, already known, experts. b) First round. Once the problem under study has been defined, the first questionnaire has to be set up; experts
Please cite this article as: S. Di Zio, B. Staniscia, A Spatial version of the Shang method, Technol. Forecast. Soc. Change (2013), http:// dx.doi.org/10.1016/j.techfore.2013.09.011
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will be asked to express their opinions about a minimum and a maximum regarding the value to be estimated. The questionnaire has to be equipped with all necessary information and instructions for drawing it up. c) First elaboration. After the collection of all the answered questionnaires, two groups of values can be found: one for the minimum and one for the maximum values. Denoting with n the cardinality of the panel, if all the participants respond to the questionnaire, we have: • m a vector of n elements for the minimums; • M a vector of n elements for the maximums. For each vector a statistical synthesis is calculated, which summarizes in a single value all the n subjective estimates. We denote these indices, respectively, with m0 and M0 and the interval [m0,M0] constitutes the initial range of assessments. From this range a central value is calculated: C0 ¼
M 0 þ m0 2
This number represents the basis for the construction of the second questionnaire. An important decision concerns the choice of the statistical synthesis. Depending on the objective of the study, it is possible to choose among one of the following criteria: 1. m0 = the maximum of m; M0 = the minimum of M; 2. m0 = the arithmetic mean of the vector m; M0 = the arithmetic mean of the vector M; 3. m0 = the median of the vector m; M0 = the median of the vector M; 4. m0 = the minimum of m; M0 = the maximum of M. It is evident that according to the chosen criterion, the interval will be more or less wide (see Fig. 1). For example, if we want to consider the widest range we will choose criterion 4, while if for the purposes of research a small interval is necessary the criterion 1 will be the most suitable one. In practical applications,
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it may happen that the maximum of m is greater than the minimum of M, therefore the option will be among criteria 2, 3 and 4. d) Second round. According to the object of the study a new question is formulated for the panelists. Now each expert has to answer if his/her evaluation is above or below the central value C0. Each participant is invited to compare the central value C0 with what he/she believes more plausible, simply answering “greater than” or “lesser than”. e) Second elaboration. After the second consultation, the majority of the estimates given by the experts can be greater than or lesser than the central value C0. In the first case the new range of assessment is the distance between the central value and M0, namely [C0,M0]. On the contrary, if the majority of the estimates is lesser than the central value, the new range is the distance between m0 and the central value, namely [m0,C0]. At this point a new central value — say C1 — is calculated. Depending on the two cases above, the central value C1 will be given by one of the following two formulas: C1 ¼
M0 þ C 0 2
C1 ¼
C 0 þ m0 2
f) Iterations. Further rounds are performed, calculating new ranges and new central values (…, C2, C3, …, Ck), until a sufficiently narrow range is obtained, and the convergence of opinions is considered reached (step k). Note that, from the second round on, the structure of the question is the same — namely each expert responds with a value either above or below the central one — but the central value is never the same; therefore, the question is different at each round. If the experts do not stiffen on opposite initial positions and behave in a consistent way in subsequent iterations, the
Fig. 1. Scheme of the different criteria for the construction of the first range.
Please cite this article as: S. Di Zio, B. Staniscia, A Spatial version of the Shang method, Technol. Forecast. Soc. Change (2013), http:// dx.doi.org/10.1016/j.techfore.2013.09.011
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procedure generally converges. Like in the classical Delphi, there is not a standard rule to define the number of iterations a priori. The amplitude of the ranges certainly leads, in real applications, to operational guidance to understand when the procedure should be stopped. The convergence speed of the Shang is greater than in Delphi, given that at each iteration the range of evaluations is halved. Note that, at each round, the expert is not asked to change his/her previous estimate (like in Delphi), but simply to compare it with a reference value. As explained by Ford [5] this is an advantage with respect to Delphi, because it avoids pressures toward consensus. Finally, it is worth noting that if n is even, then ties are possible, when 50% of experts respond “above” and 50% “below”. This is a stalemate, difficult to overcome, and remains an open question. It suffices to say that Ford himself proposed to go on a coin toss as a possible solution [5]. 3. The Spatial Shang The Spatial Delphi is applicable when the research problem involves issues related to the choice of a geographical location. In literature, a wide range of possible applications are proposed; they range from the problem of choosing an optimal site to place goods or services or to act for a specific intervention, to the problem of selecting the best area for deforestation, the best field for crops, the best location for drainage, the best place for nuclear waste storage, and so on. Forecasting problems can be approached as well since it is possible to ask a group of experts where a future event will be most likely to happen [12]. In Spatial Delphi the opinions are expressed by placing a series of points on a map. Following the Delphi logic, at each round the experts can revise their previous evaluations and, consequently, move their points. The interquartile range of the classical Delphi is replaced by a circle containing 50% of the points and the radius of the circle tends to decrease at each iteration, indicating in the space the convergence of opinions [12]. Here we propose the Spatial Shang; it starts from the same consideration that gave rise to the Spatial Delphi but takes advantage of the additional benefits of the Shang. Many problems involve decisions made on a map. The map can be on paper or on a computer screen and, in the context of shared choices, the space is an important element to be considered. In real application, the method must be considered as a support to the decisions to be made in a spatial context: a decision support that is the result of the convergence of different (spatial) viewpoints. The main steps of the Spatial Shang are the following: a) Selection of participants. Like in the classical Shang, the construction of the panel is the first phase. Let's denote with n the number of participants. b) First round. The first questionnaire must be constructed using a map. The decision problem must be formalized according to a spatial logic. Therefore, the question(s) for the panelists must contain expressions such as “the most appropriate location for …”, “the most appropriate location where …” or “the place where most likely a future event will occur”. The experts are invited to draw 4 points on a map containing the territory under study. Two
points are the extreme positions along the direction North–south and two are the extreme positions along the direction East–west. In other words, given expert i, one point expresses the upper limit, in the direction of latitude, beyond which the expert considers that the phenomenon will not occur or will not be located (in symbol Ni with i = 1, …, n). A second point expresses the lower limit in the direction of latitude (in symbol Si). Similarly, in the direction of longitude two points represent the leftmost limit (Wi) and the rightmost limit (Ei) of the phenomenon. Thus, those points identify four imaginary lines that surround the area with a rectangle, representing the boundaries of the spatial problem. There will be n different rectangles, one for each expert. c) First elaboration. After having collected the results of the first round, there will be four groups of values (points): one for North, one for South, one for East and one for West. In symbol we have1: g) N a vector of n points for the North limits; h) S a vector of n points for the South limits; i) E a vector of n points for the East limits; j) W a vector of n points for the West limits; These vectors define n different rectangles on the map. Like in the classical Shang, a statistical synthesis must be calculated for each vector; it summarizes in a single value all the n subjective estimates. We denote those indices, respectively, with N0, S0, E0 and W0. One of the criteria used for the classical Shang can be applied for the indices (see Fig. 1). Let's now consider that “maximum” is the latitude/ longitude of the farthest point from the center of the map and “minimum” is the latitude/longitude of the closest point to the center of the map. More precisely, for the calculation of N0 and S0 the values of the latitudes of the points contained in the vectors N and S are used, while for the calculation of E0 and W0 the values of the longitude of the points contained in the vectors E and W are employed. These four values define a rectangle of convergence (ABCD in Fig. 2) with the following vertices: A(W0,N0), B(E0,N0), C(E0,S0), D(W0,S0); it represents a statistical synthesis of the n rectangles. From the four indices two central values are calculated, one for the latitude: C 0;LAT ¼
N 0 þ S0 2
and one for the longitude: C 0;LONG ¼
E0 þ W 0 2
which define the center of gravity of the rectangle. The initial geographical area of evaluations is therefore bounded by a rectangle, with area A0 = (|E0 − W0|) ⋅ (|N0 − S0|) and with center of gravity having geographical coordinates G0(C0,LONG,C0,LAT). By drawing a vertical line and a horizontal line passing through this center of gravity, the rectangle ABCD is divided in four sub-rectangles each having a quarter of its area, namely A1 = A01/4 (see Fig. 2). For 1 Note that each point is defined by two values: one for the latitude and one for the longitude.
Please cite this article as: S. Di Zio, B. Staniscia, A Spatial version of the Shang method, Technol. Forecast. Soc. Change (2013), http:// dx.doi.org/10.1016/j.techfore.2013.09.011
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simplicity, we call these sub-rectangles with NE (the north-east one), NW (the north-west one), SW (the south-west one) and SE (the south-east one). d) Second round. The center of gravity G0 — together with the horizontal and vertical lines passing through it — is drawn on the map that is then submitted to the panel for the second consultation. Sub-rectangles are not shown to the panelists; they are only used internally, during the elaboration phases. Each expert is asked to choose one of the four sub-areas defined by the two lines, to indicate where he/she feels the true value falls with respect to the center of gravity. This is analogous to the question posed in the classical Shang that is “above or below the central value”. Note that the answer is very easy and fast to be given. e) Second elaboration. In this step, the objective is to choose one of the four sub-rectangles as new rectangle of convergence, together with its center of gravity and its sub-rectangles. After the second consultation, the number of preferences of each sub-areas is counted and this is equivalent to having “votes” for each sub-rectangle. If one of the four sub-rectangles receives the majority of votes, it becomes the new rectangle of convergence which — once calculated a new center of gravity G1 — will be divided in four sub-rectangles. Each sub-rectangle has a sixteenth of the area of the initial rectangle ABCD, namely A2 = A01/ 16. On the contrary, if two or more sub-rectangles receive the same (maximum) number of preferences, there is a problem of stalemate. One possible solution is to consult once again those experts who chose the sub-areas with maximum number of preferences, and ask them to locate a point on the map, representing her/his evaluation, somewhere in the selected sub-area. The point represents the opinion of the expert about the spatial problem under investigation; therefore, following Di Zio and Pacinelli [12], we can define it as opinion-point. The choice will fall on the sub-area (and, then, the sub-rectangle) which contains the farthest points from the center of gravity. That sub-area can be found by calculating the sum of distances from each point and the center of gravity.2 This procedure can solve any situation of tie while, as seen before, in classical Shang it is still an open problem. In this particular situation, it is useful to ask the experts reasoning of their choices. As known [1,11,14], reasoning is an essential aspect of the original Delphi process and in our case the reasons (together with the sum of distances) can provide valuable hints in choosing a sub-area. More generally, reasons constitute valuable material for the purposes of ongoing research. Let's take an example. If the sub-rectangle NW is chosen — because the sub-area NW received the majority of preferences or because the points are the furthest away from the 2 If the points in a sub-area are very close to the center of gravity, it means that the preferences of those experts are not far from those located in the other three sub-areas. It is like saying that there is not much difference between the chosen area and the others. If, on the contrary, the points are very far from the center of gravity, this means that the estimates of the panelists are far from the remaining rectangles; that sub-area is much more important than the other three. Therefore, if two sub-areas receive the same number of points, the one whose points are farther from the center will be chosen. We can state that the sum of the distances of the points from the center represents a weight of importance of the sub-area.
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Fig. 2. Representation of the result of the first elaboration.
center — the new center of gravity G1 has the following coordinates: C 1;LONG ¼
C 0;LONG þ W 0 N0 þ C 0;LAT ; C 1;LAT ¼ : 2 2
The new center of gravity G1 and its vertical and horizontal lines are drawn on the map, and submitted to the panel for the third consultation. Note that sub-rectangles are used only during the elaborations, while the experts see only the center of gravity with both the horizontal and the vertical lines, delimiting the four sub-areas. In general, from this moment the sub-areas have different sizes but their union always covers the whole study area. f) Iterations. Further rounds are performed, selecting new sub-rectangles and new centers of gravity, until a sufficiently small portion of territory is delimited. If we denote with k the iterations (with k = 0 the iteration in which the first rectangle is obtained), at each iteration the area of each sub-rectangle, say Ak, is reduced by a factor of 1/4k, namely k
Ak ¼ A0 1=4 : This means that the process of convergence is very fast. The procedure can be stopped after a certain predetermined number of rounds or when the area of the rectangle reaches a given value. One can, for example, establish that the rectangle should have an area below than a certain percentage (say P) of the area of the initial rectangle. In symbols the stopping criterion could be: when Ak ≤ P ⋅ A0. Like in the classical version, in subsequent rounds of the Spatial Shang the question is always different, because while the structure of the question is the same, the central value is never the same. In the Spatial Shang, the procedure does not require a change of opinion — right as in the classical Shang — and there is no pressure toward convergence. If an expert has an estimate in mind from the beginning of the procedure, he/she can keep that value throughout the duration of the survey, and simply compare it with the central value (each time different) that is proposed from time to time. This is one of the advantages of Shang with respect to Delphi and, similarly, of Spatial Shang with respect to Spatial Delphi. In Spatial
Please cite this article as: S. Di Zio, B. Staniscia, A Spatial version of the Shang method, Technol. Forecast. Soc. Change (2013), http:// dx.doi.org/10.1016/j.techfore.2013.09.011
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Shang, at each consultation, the experts have the same whole initial area to make their choices. At each round, there is only a shift of the center of gravity (and of the relative two lines) and each expert contributes to this movement. Convergence is not requested in this method and, in general, is not the main objective of the techniques that fall within the Delphi family. However, the researcher can use the calculation of the areas of subsequent sub-rectangles as a measure of convergence. Table 1 summarizes the main steps of the Spatial Shang method and compares it to the classical Shang. 4. A Spatial Shang application to localize the boundary of a coastal park In the year 2001, through the Italian National Law L. 93/2001, art. 8, the Costa Teatina National Park was established in central Italy. It involves eight municipalities along the Adriatic coast, from Ortona to San Salvo and has a length exceeding 60 km. It is a coastal park — not a marine one — thus protection concerns the coast and its natural (animal and plant) species [15]. Already in 1985, the Abruzzo Region had considered those areas worthy of protection through the Regional Landscape Plan (Piano Regionale Paesistico, L. 431/85). Later on, the Italian Ministry of the Environment considered that area as meriting preservation for its environmental, landscape and cultural values. In a working document [16] that territory was described as “winning and varied, with the alternation of sandy and gravelly beaches, cliffs, rivers' mouths, areas rich in spontaneous vegetation and cultivated lands (mainly olives), dunes and forest trees”. The above mentioned Law established the park but did not define its boundaries. That is why a very heated debate has been developed since then about that issue. Which portions of the territories of the eight municipalities should be included within the park boundaries? What are the criteria the definition should be based on? What are the procedures to be adopted? In 2001 the orientation was towards a top-down approach: the Italian Ministry of Environment had the task to define the park's boundaries in agreement with the Abruzzo Region, where the park is
located. In 2007 the Abruzzo Region issued a special law (L.R. 5/2007) to protect that territory. The Region created a “System of Protected Areas of the Costa Teatina”, including six natural reserves. Since the park's boundaries had not been defined yet, the Ministry transferred to the Abruzzo Region the task to solve the problem, in agreement with the local authorities. An agreement was not reached, that is why the process of definition is still in act. In recent years a bottom-up approach has been preferred: the decisional process should include local stakeholders, including local public authorities, local communities, enterprises, NGOs and associations. The Abruzzo Region started a formal consultation procedure but, so far, has not obtained the consensus about the park's boundaries. Given the situation, our task was to provide a tool to support the local stakeholders in the decisional process. Our aim was to provide a scientific methodology that could guarantee the convergence of opinions among the stakeholders. The spatial problem we posed to them concerned the definition of the park's boundaries or, at least, a territorial buffer small enough to define the boundaries. We've involved representatives of all the stakeholders, able to give voice to a plurality of opinions and interests. 62 were the stakeholders involved in the process, representing the whole community from different perspectives. Among them there were representatives of the local public bodies (mayors, city and provincial councilors), of national institutions (MPs), of political parties, of the church (parish priests and representatives of the bishop's court), of the trade unions (general secretaries of the provincial bodies), of entrepreneurs and producers' associations (in the agriculture, handicraft, commerce, tourist sectors), of entrepreneurs operating in the environmental field and in the third sector, of the citizens' associations and NGOs, of the environmental and cultural associations, of the local media, of the local development agencies, of schools and universities. The selection of the stakeholders was based on three main criteria: (i) deep knowledge of the territory and awareness of the on-going conflict; (ii) capacity to represent a clear and transparent position in the conflict; (iii) capacity to give voice to the general interest of the specific category they represent.
Table 1 Comparison of Shang and Spatial Shang. SHANG
Spatial SHANG
1. Formation of the panel (n experts) and construction of the first questionnaire. 1. Formation of the panel, construction of the questionnaire and preparation of the maps together with explanatory documents of the area of interest. 2. Submission of the first questionnaire. Panelist must give 2 values: 2. Submission of the first questionnaire/map. Panelists have to indicate 4 one minimum and one maximum. Two vectors of values are obtained. points on the map: two extreme locations along the direction north–south and two extreme locations along the direction east–west. Four vectors of points are collected. 3. Calculation of two synthetic values (m0 and M0), which summarize the 3. Calculations of four synthetic values (N0, S0, E0 and W0), which summarize maximums and the minimums estimated. Calculation of the first central the four vectors containing each n subjective estimates. Calculation of the value: C0 = (M0 + m0)/2 first center of gravity: G0. This produces four sub-rectangles. 4. Submission of the second questionnaire. Panel members are asked to 4. Submission of the second questionnaire, consisting in the initial map with provide an assessment above or below the central value C0. the center of gravity and the horizontal and vertical lines passing through it. Panel members are asked to choose one of the four sub-areas. 5. According to the results of the second consultation a second range is 5. According to the results of the second consultation a sub-rectangle is calculated ([C0,M0] or [m0,C0]). The second central value C1 = (M0 + C0)/2 chosen. Its center of gravity — G1 — is then calculated. By using this point the or C1 = (C0 + m0)/2 derives from this range. Panelists have to give a new initial area is divided in four new sub-areas, generally having different sizes. Panelists have to choose one of these sub-areas. assessment, above or below this central value. 6. Steps 4 and 5 are iterated until the range will be sufficiently small. 6. Steps 4 and 5 are iterated until the rectangle will be sufficiently small.
Please cite this article as: S. Di Zio, B. Staniscia, A Spatial version of the Shang method, Technol. Forecast. Soc. Change (2013), http:// dx.doi.org/10.1016/j.techfore.2013.09.011
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To this group of stakeholders we applied the Spatial Shang methodology. Considering that the problem of the boundaries of the park is reduced to the definition of a line at a certain distance from the shoreline (more or less parallel to the coastline), the Spatial Shang is reduced from two to one spatial dimension in this application. In other words, given that the Adriatic coast extends from North to South, the analysis was conducted only in the direction of the longitude (East–west). 4.1. First round Using a map of the coast containing the eight municipalities involved in the park's area, we asked the stakeholders to indicate two values, representing the minimum and maximum distance of the park boundaries from the coastline. Therefore, for each respondent we collected two values in the direction of longitude, representing the left maximum limit (Wi) and the right minimum limit (Ei) of the park (i = 1, …, 62). In addition to the map on which drawing the points, we also provided supporting maps such as a map of the road network and a satellite image, in order to support the respondents in the evaluations. 4.2. First elaboration After the first questionnaire, we obtained two groups of points on the map, one group for East (representing the minimum evaluations) and one for West (representing the maximum evaluations). According to our notation we have a vector E containing 62 points for the East limits and a vector W containing 62 points for the West limits. For each point, we calculated the distance from the coast, therefore obtaining two distributions, respectively of the minimum and maximum distances from the coastline (see Table 2). Given the resolution of the map used for the survey, we approximated the values of the distances to values of 0.5 Km. The mean of the minimums is 2.0 and the mean of the maximums is 3.1. By looking at the variability of the two distributions, we can have a measure of the convergence of opinions after the first consultation. There was a greater consensus regarding the minimum values (st. dev. 4.7) with respect to the maximum values of the limit of the park (st. dev. 12.8). Table 2 Frequencies of responses of the first round. Distance (km)
Frequencies for E (minimum)
Frequencies for W (maximum)
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
1 15 10 6 9 4 3 3 3 3 5 62
0 4 6 7 6 5 5 5 1 3 20 62
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Note that, the smallest value for the maximum (0.5 km) is lower than the highest value of the minimum (5 km). In other words, the group of evaluations for the minimum and the maximum are overlapping. Probably, this can be read as a reflection of strong contrasts and disagreements involving the establishment of the park. As a synthesis of the two vectors of values we used the arithmetic mean of the distances, therefore according to our notation we have E0 = 2.0 and W0 = 3.1. These two values define two lines, parallel to the coastline, which delimit a first large area of convergence, having a width of 1100 m (see Fig. 3). Its central value is
C0 ¼
E0 þ W 0 ¼ 2:55 2
The eight municipalities interested by the coastal park are now crossed by an imaginary line at 2.55 km from the coastline (Fig. 3).
4.3. Second round and elaboration The stakeholders were asked whether the limit of the park should be fixed at a distance that is higher or lower than 2.55 km from the coastline. At the second consultation only 35 stakeholders responded to the questionnaire, so there was a large drop-out rate, also in this case due to the sharp conflicts which are still in progress on this issue. The 65.7% of the respondents set a limit that is above 2.55 km while 34.3% set a limit that is below that distance. Thus, according to the panel of respondents, the limit should be placed at a distance higher than 2.55 km from the shoreline. The new area of convergence is therefore a buffer of 550 m, included between 2.55 and 3.10 km from the coastline (see Fig. 3). The new central value within this range is:
C1 ¼
W 0 þ C 0 3:10 þ 2:55 ¼ 2:82: ¼ 2 2
Since the convergence area of 550 m is very little compared to the maximum area expressed by some stakeholders during the first consultation, we decided to conclude the consultation after the second round. In conclusion we can affirm that, according to the panel of stakeholders, the limit of the coastal park should be at about 2.8 km from the coastline or, more generally, in a buffer of 550 m between 2.55 km and 3.10 km from the coastline. These results do not represent the final solution to the strong on-going conflict in this territory, but a support to the mitigation of those conflicts. The buffer of 550 m is the result of the iterative consultation of the stakeholders; it can, therefore, be used as a decision support for the choice on where to set the limit of the park. Furthermore, the survey generated a debate in the area, among the main players of the conflicts; this is, anyhow, a positive fact for the solution of the problem.
Please cite this article as: S. Di Zio, B. Staniscia, A Spatial version of the Shang method, Technol. Forecast. Soc. Change (2013), http:// dx.doi.org/10.1016/j.techfore.2013.09.011
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Fig. 3. Diagram of the application.
5. Concluding remarks In this paper we have shown that, as much as in the Spatial Delphi [12], it is possible to reproduce the Shang method in a spatial context by using a map. We should, however, consider our method as an initial prototype since several questions are still open. First, the choice of the criterion for the construction of the rectangle in the first elaboration (minimum, maximum, arithmetic mean or median). Second, the rectangle could be replaced by another regular or irregular geometric figure, that may take account of the spatial constraints on the given territory. Other open questions concern the map used for the survey and its scale, as well as which kind of supporting maps are the most appropriate. We also believe that an evolution of this methodology, through the use of a Web GIS technology, could be a real-time version, in analogy to the Gordon's Real-Time Delphi [17,11]. Concerning the application, we are aware that this is only a preliminary experiment, and the applicative potentialities should be more in-depth analyzed; nonetheless our early results are encouraging. We can summarize as follows the main aspects emerged in this paper: • In real applications the method should be considered as a Spatial Decision Support System [18]. In our case study, for instance, the 550 m buffer is the result of the consultation of the stakeholders and can be used as a support for the decision on where setting the boundaries of the coastal park. • The stakeholders appreciated the fact that answering the questionnaire was very simple and intuitive: simply choosing one area on a map. • Because of the ease in giving responses, the total time of the application, including the elaborations, was very short, namely three weeks. • The Spatial Shang should be used only when the decision problem can be traced back to the location of a place on the territory. Otherwise, the method cannot be applied.
• While in classical Shang the stalemate is still an open question, here for the Spatial Shang we proposed a solution by using the opinion-points. • For an actual definition of the park's boundaries, it is clear that it is necessary to consider a boundary with a variable distance from the coast. The choice of a line equidistant from the coastline is only a first research hypothesis. Concretely, the Spatial Shang can be applied in each of the eight municipalities of the park (with local stakeholders), in order to obtain the boundary that best suits local diversity, and takes account of the constraints and specificities characterizing the different areas of the coast. • Strengths of the method. The proposed method has the advantage of being easily accessible and understandable, even for a non-specialized audience. The presentation of the map in a paper or on-line format gave the chance also to the older stakeholders to participate. Therefore, the method can be used both with a panel of experts and with a panel of general stakeholders. The experiment generated a debate in the area that, per se, was positive for the decisional process. While a well known weakness of the Delphi and Delphi derivative methods is the time that they take, we have seen that the simplicity of the responses in the Spatial Shang reduced enormously this problem. Moreover, like other Delphi methods, the Spatial Shang avoids the problems of face-to-face group interaction. As explained by Ford [5], the Shang method has some important advantages with respect to Delphi. In particular, Shang avoids “pressure toward consensus and individual commitment to an initial response” [5]. Similarly, we believe that the same benefits are worth for our Spatial Shang with respect to the Spatial Delphi. • Weaknesses of the method. The selection of the stakeholders was decided by the authors of this paper. It was based on the direct knowledge of the problem, of the territory, of the local stakeholders, after several years of research. Even if not biased by prejudices, the authors made a subjective assessment of who were the important stakeholders, crucial for the problem's solution. There is not objective counterproof that the results would have been the same choosing different
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representatives of the stakeholders. The risk that a silent minority (or majority) has been ignored because of its silence, cannot be ruled out. In literature there are various criticisms of the Delphi method that can be directed also to our method, like the fact that Delphi does not produce more accurate answers than other methods [19]. Even if this is still an open issue, it must be said that there are many papers that have refuted this criticism (see for example [20]). Finally, like other methods of the Delphi family, the drop out of participants during the process is an inevitable disadvantage. Acknowledgments The research leading to these results has received funding from the European Community's Seventh Framework Programme FP7/2007–2013 under grant agreement n° 244251. The authors would like to thank Angelo Staniscia for the valuable support he provided in all the phases of the research and the 62 stakeholders for their willingness to participate to the Spatial Shang. References [1] N.C. Dalkey, O. Helmer, An experimental application of Delphi method to the use of experts, Manage. Sci. 9 (1963) 458–467. [2] M. Turoff, The design of a policy Delphi, Technol. Forecast Soc. Change 2 (2) (1970) 149–171. [3] O. Helmer, Cross-impact gaming, Futures 4 (2) (1972) 149–167. [4] M.H. De Groot, Reaching a consensus, J. Am. Stat. Assoc. 69 (345) (1974) 118–121. [5] D.A. Ford, Shang inquiry as an alternative to Delphi: some experimental findings, Technol. Forecast Soc. Change 7 (1975) 139–164. [6] A. Delbecq, A. Van de Ven, D. Gustafson, Group Techniques for Program Planning: A Guide to Nominal Group and Delphi, Scott Foresman, Chicago, 1975. [7] W. Rauch, The decision Delphi, Technol. Forecast Soc. Change 15 (3) (1979) 159–169. [8] F. Régnier, Un Outil de Décision pour l'Entreprise, Cpe Bull. 27 (1986) 89–100. [9] F. Régnier, Du Principe de la Pratique de l'Abaque de Régnier, Institut de Métrologie qualitative, Nancy, 1987.
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[10] F. Régnier, Annoncer la couleur, Institut de Métrologie Qualitative, Nancy, 1989. [11] T.J. Gordon, A. Pease, RT Delphi: an efficient, “round-less” almost real time Delphi method, Technol. Forecast Soc. Change 73 (2006) 321–333. [12] S. Di Zio, A. Pacinelli, Opinion convergence in location: a Spatial version of the Delphi method, Technol. Forecast Soc. Change 78 (9) (2011) 1565–1578. [13] T.J. Gordon, O. Helmer, "Report on a Long Range Forecasting Study,", Rand Paper P-2982, Rand Corporation, Santa Monica, California, September 1964. [14] H.A. Linstone, M. Turoff, The Delphi Method: Techniques and Applications, Addison-Wesley Publ. Co., Reading, Massachusetts, 1975. [15] A. Montanari, B. Staniscia, Global changes, coastal areas and conflicts: experiences from Italy, in: A. Khan, Q. Le Xuan, E. Corijn, F. Canters (Eds.), Environmental Conflicts in Coastal Urban Areas. Towards a Strategic Assessment Framework for Sustainable Development, Casa Editrice Università La Sapienza, Rome, 2013, pp. 100–133. [16] Ministero dell'Ambiente, Progetto di istituzione del Parco Nazionale della Costa Teatina, working paper, Rome, 1998. [17] T.J. Gordon, The real-time Delphi method, in: J.C. Glenn, T.J. Gordon (Eds.), Futures Research Methodology Version 3.0, The Millennium ProjectAmerican Council for the United Nations University, 2009. [18] M.D. Crossland, B.E. Wynne, W.C. Perkins, Spatial decision support systems: an overview of technology and a test of efficacy, Decis. Support. Syst. 14 (1995) 219–235. [19] F. Woudenberg, An evaluation of Delphi, Technol. Forecast Soc. Change 40 (1991) 131–150. [20] G. Rowe, G. Wright, Expert opinions in forecasting: the role of the delphi technique, in: J.S. Armstrong (Ed.), Principles of Forecasting, Springer, New York, 2001. Simone Di Zio is Researcher in Social Statistics at the University G. d'Annunzio Chieti-Pescara (Italy). He is member of the World Future Society and of the Italian Statistical Society. He participated in the SELMA Project (Spatial Deconcentration of Economic Land Use and quality of Life in Metropolitan Areas) financed by the European Commission within the framework of the 5° European Union Research Programme. He has published 25 articles. His scientific activities deal with Spatial Statistics and IRT models. He is expert in GIS (Geographic Information Systems) and fractal geometry. Barbara Staniscia is member of the coordination and research team of the EU-FP7 funded project SECOA, at the Sapienza University of Rome. She is Scientific Secretary of the IGU Commission “Global change and human mobility”. She has been member of the research teams of the EU funded projects MIRE, ESPON 1.1.4, SELMA, EQUAL II-Celine, PLACE and TIGER. She has developed researches concerning urban dynamics and local development, spatial effects of EU policies, tourism and migration, environmental conflicts, rural development and geography of taste.
Please cite this article as: S. Di Zio, B. Staniscia, A Spatial version of the Shang method, Technol. Forecast. Soc. Change (2013), http:// dx.doi.org/10.1016/j.techfore.2013.09.011
Contents lists available at ScienceDirect
Technological Forecasting & Social Change
A Spatial version of the Shang method Simone Di Zio a,⁎, Barbara Staniscia b a b
“G. d'Annunzio” University, Viale Pindaro 42–65127 Pescara, Italy Sapienza University of Rome, Piazzale Aldo Moro 5–00185 Roma, Italy
a r t i c l e
i n f o
Article history: Received 19 July 2013 Received in revised form 16 September 2013 Accepted 18 September 2013 Available online xxxx Keywords: Shang Delphi Convergence of opinions Spatial decisions Environmental conflicts
a b s t r a c t This paper proposes a modified version of the Shang method, starting from the assumption that the convergence of opinions involves a spatial context in many applications. The Spatial Shang we present is based, like the classical Shang method, on judgments of a panel of experts, and is applicable when consultations and consequent decisions concern matters of spatial location. The experts are first asked to draw four points on a map while, in subsequent rounds, each panelist must locate a single point, representing her/his evaluation, in one of four rectangles drawn on the map. The method is very easy to be implemented and the whole procedure is very fast to be performed. The application presented in this paper concerns the Costa Teatina National Park (Italy) and the definition of its boundaries. We will here present the on-going conflict and the contribution to its mitigation offered by the Spatial Shang method. The application resulted in a convergence of opinions in a buffer of 550 m; that can be used as a decision support for the choice on the best location for the park's boundaries. © 2013 Elsevier Inc. All rights reserved.
1. Introduction The Delphi technique was developed at the Rand Corporation by Dalkey and Helmer [1] in the 1950s. In the scientific community it is commonly accepted as a method for achieving convergence of opinions in a group of experts. After about 60 years from its creation, the Delphi method has been so widely used that it is now considered to be the founder of a large variety of methods that are known as its variants. After the pioneering work of Dalkey and Helmer [1], Murray Turoff, in 1970, proposed the Policy Delphi [2], which is consensus-oriented and is used for the analysis of public policies. Soon after, in 1972, Olaf Helmer proposed the Mini-Delphi [3], a technique that speeds up the Delphi procedure as it is applied for face to face meetings, and in fact is also known as Estimate-Talk-Estimate (ETE) method.
⁎ Corresponding author at: The “G. d'Annunzio” University, Viale Pindaro 42 – Zip Code 65127 - Pescara, Italy. Tel.: +39 0854537978; fax: +39 0854537542. E-mail addresses: [email protected] (S. Di Zio), [email protected] (B. Staniscia).
Two years later the theoretical foundations of the Markov– Delphi were laid in a work of De Groot [4]; he provides important contributions in probabilistic terms tying the changes in the subjective evaluation of a forecaster to a linear combination of the remaining ones. In 1975 the Shang method was proposed [5]. Some characteristics of the Delphi method – such as the isolation of the participants (anonymity) — are kept in the Shang; moreover, the trouble of asking to rephrase the evaluations at each round is eliminated. The Shang method has the advantage of not anchoring the participants to a position and, then, urging them to depart from it. Afterward, other methods that can be included in the family of Delphi have been developed. We mention here the Nominal Group Technique [6], the Decision Delphi [7], the Abacus-Delphi [8–10], the Real Time Delphi by Theodore J. Gordon and Adam Pease [11] and, among the last ones, the Spatial Delphi [12]. The method we propose here, defined as Spatial Shang, is a variant of the Shang method, and stems from the same logic of a recent innovation of the Delphi method, called Spatial Delphi [12]. The authors of the Spatial Delphi start from a very simple idea: that many decision problems involve a choice of a place on a bounded space, and the territory becomes the basic element
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Please cite this article as: S. Di Zio, B. Staniscia, A Spatial version of the Shang method, Technol. Forecast. Soc. Change (2013), http:// dx.doi.org/10.1016/j.techfore.2013.09.011
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for the application of the Delphi logic. Experts are asked to border the decision problem within a certain area using a map; the result of the convergence is represented by a portion of territory small enough for the scope of the investigation [12]. The Spatial Shang arises from the same considerations which have led to the Spatial Delphi, with the added advantages of the Shang method; it is, therefore, applicable whenever the research problem involves issues related to the choice of a geographical location. The application we present here, is related to a protected area in a coastal region: the Costa Teatina National Park, in Abruzzo, Italy. The Spatial Shang has been applied as a tool for the definition of the park's boundaries. After the legal institution in 2001 — through the National Law 93/2001, art. 8 — its delimitation has not been defined yet. This is because of a severe conflict taking place in the area between the groups in favor and against the protected area. The Spatial Shang has been used as a methodology and tool to reach the convergence of opinions of the local stakeholders concerning the park's limits. In the remainder of the paper, after a description of the Shang method (Section 2), we illustrate the Spatial Shang in Section 3, while we present the application on a coastal park in Section 4. In Section 5 we conclude with a brief discussion the results of the application together with the strengths and weaknesses of the method. 2. The Shang method The Delphi method is an iterative process designed to achieve consensus in a group of experts on a particular topic. Originally developed by a research group at the RAND Corporation, the Delphi technique has seen many applications in the course of half a century [1,13,14]. The method consists of a number of iterations, or rounds, during which the administrator who manages the process, also called facilitator, provides participants with statistical summaries of the answers given by all the panel members. There are many versions of this method but the main steps of the classical version [14] can be summarized as follows: a) formation of the panel of experts and construction of the questionnaire; b) submission of the first questionnaire to the panel; c) calculation of a statistical summary of responses (typically the interquartile range containing 50% of the evaluations); d) submission of the second questionnaire. Panel members are asked to provide a second assessment, typically within the limits of the interquartile range, together with comments on their responses. In case of an external evaluation the expert is asked to argue the choice; e) calculation of a new interquartile range and inclusion in the questionnaire of the reasoning and comments, with preparation of specific spaces for any counter-arguments; f) iteration of steps b–e until the desired degree of consensus is achieved or, if consensus could not be achieved, crystallization of the reasons for disagreement. The Delphi can generate a convergence of opinions: starting from a decisional problem, it facilitates the achievement of a common solution, shared as much as possible. The convergence of opinions is considered a structured process, in which individual thoughts on issues under discussion lead to relatively shared conclusions. However, the objective of a Delphi process is not always consensus; according to each specific application,
different goals can be achieved, such as stability in estimations or, even, generation of alternatives [14]. The Shang method has been described for the first time by Ford [5], as an alternative to the traditional Delphi method. Like the Delphi, it consists of a series of questions directed to a panel of experts, with the scope of progressively facilitating a shared solution. The panel implies several interviews of the same persons at different times; both in Delphi and Shang the guarantee of the anonymity among the participants avoids a series of problems typical in a face-to-face group interaction. In face-to-face communication many mechanisms of distortion may occur and, generally, they affect the reached solution. The most important are the following ones: 1. The error of Leadership. When the highest-ranking person in a group (e.g. in military, political, academic or corporate hierarchies) expresses his/her opinion, the others usually tend to follow him/her. 2. The error of Spiral of Silence. Those whose opinions reflect the ideas of the majority are more likely to feel confident in expressing their opinions; on the contrary those whose opinions are in the minority, fear that expressing their views will result in social ostracism, and therefore remain silent. Those perceptions can lead to a spiraling process, in which minority's viewpoints are increasingly withheld and, therefore, underrepresented. 3. The error of Groupthink. It occurs when the pressure to conform within a group, interferes with the group's analysis of a problem and causes poor group decision making. Individual uniqueness and independent thinking are lost in the pursuit of group cohesiveness. When members strive for unanimity their motivation to realistically assess alternative courses of action is affected. A typical advantage of the Shang (with respect to Delphi) is that participants are not anchored to a position from which they are, later, asked to deviate; this is possible since, in the Shang, at each round, a different question is posed (as will be explained later, indeed, the expert is asked to give, at each round, an estimate above or below a value that is always different). As a consequence, the well known problem of abandon of the Delphi — due to the boredom of answering multiple times the same question — is a little reduced. Furthermore, according to Ford, the Shang — while preserving Delphi advantages — avoids problems derived from pressure toward convergence and response commitment [5]. Finally — since the evaluation interval is halved at each iteration — that method is much faster than Delphi. We now describe schematically the main steps of the Shang method. a) Selection of participants. Like in the traditional Delphi, the construction of the panel is a critical phase, the success of the study depending on it. The knowledge and cooperation of the panelists affect the results of the entire procedure. Generally speaking, the participants can be identified through literature searches (persons who have published on the subject under study), recommendations from institutions (e.g. heads of institutions, mayors, politicians) or recommendations from other, already known, experts. b) First round. Once the problem under study has been defined, the first questionnaire has to be set up; experts
Please cite this article as: S. Di Zio, B. Staniscia, A Spatial version of the Shang method, Technol. Forecast. Soc. Change (2013), http:// dx.doi.org/10.1016/j.techfore.2013.09.011
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will be asked to express their opinions about a minimum and a maximum regarding the value to be estimated. The questionnaire has to be equipped with all necessary information and instructions for drawing it up. c) First elaboration. After the collection of all the answered questionnaires, two groups of values can be found: one for the minimum and one for the maximum values. Denoting with n the cardinality of the panel, if all the participants respond to the questionnaire, we have: • m a vector of n elements for the minimums; • M a vector of n elements for the maximums. For each vector a statistical synthesis is calculated, which summarizes in a single value all the n subjective estimates. We denote these indices, respectively, with m0 and M0 and the interval [m0,M0] constitutes the initial range of assessments. From this range a central value is calculated: C0 ¼
M 0 þ m0 2
This number represents the basis for the construction of the second questionnaire. An important decision concerns the choice of the statistical synthesis. Depending on the objective of the study, it is possible to choose among one of the following criteria: 1. m0 = the maximum of m; M0 = the minimum of M; 2. m0 = the arithmetic mean of the vector m; M0 = the arithmetic mean of the vector M; 3. m0 = the median of the vector m; M0 = the median of the vector M; 4. m0 = the minimum of m; M0 = the maximum of M. It is evident that according to the chosen criterion, the interval will be more or less wide (see Fig. 1). For example, if we want to consider the widest range we will choose criterion 4, while if for the purposes of research a small interval is necessary the criterion 1 will be the most suitable one. In practical applications,
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it may happen that the maximum of m is greater than the minimum of M, therefore the option will be among criteria 2, 3 and 4. d) Second round. According to the object of the study a new question is formulated for the panelists. Now each expert has to answer if his/her evaluation is above or below the central value C0. Each participant is invited to compare the central value C0 with what he/she believes more plausible, simply answering “greater than” or “lesser than”. e) Second elaboration. After the second consultation, the majority of the estimates given by the experts can be greater than or lesser than the central value C0. In the first case the new range of assessment is the distance between the central value and M0, namely [C0,M0]. On the contrary, if the majority of the estimates is lesser than the central value, the new range is the distance between m0 and the central value, namely [m0,C0]. At this point a new central value — say C1 — is calculated. Depending on the two cases above, the central value C1 will be given by one of the following two formulas: C1 ¼
M0 þ C 0 2
C1 ¼
C 0 þ m0 2
f) Iterations. Further rounds are performed, calculating new ranges and new central values (…, C2, C3, …, Ck), until a sufficiently narrow range is obtained, and the convergence of opinions is considered reached (step k). Note that, from the second round on, the structure of the question is the same — namely each expert responds with a value either above or below the central one — but the central value is never the same; therefore, the question is different at each round. If the experts do not stiffen on opposite initial positions and behave in a consistent way in subsequent iterations, the
Fig. 1. Scheme of the different criteria for the construction of the first range.
Please cite this article as: S. Di Zio, B. Staniscia, A Spatial version of the Shang method, Technol. Forecast. Soc. Change (2013), http:// dx.doi.org/10.1016/j.techfore.2013.09.011
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procedure generally converges. Like in the classical Delphi, there is not a standard rule to define the number of iterations a priori. The amplitude of the ranges certainly leads, in real applications, to operational guidance to understand when the procedure should be stopped. The convergence speed of the Shang is greater than in Delphi, given that at each iteration the range of evaluations is halved. Note that, at each round, the expert is not asked to change his/her previous estimate (like in Delphi), but simply to compare it with a reference value. As explained by Ford [5] this is an advantage with respect to Delphi, because it avoids pressures toward consensus. Finally, it is worth noting that if n is even, then ties are possible, when 50% of experts respond “above” and 50% “below”. This is a stalemate, difficult to overcome, and remains an open question. It suffices to say that Ford himself proposed to go on a coin toss as a possible solution [5]. 3. The Spatial Shang The Spatial Delphi is applicable when the research problem involves issues related to the choice of a geographical location. In literature, a wide range of possible applications are proposed; they range from the problem of choosing an optimal site to place goods or services or to act for a specific intervention, to the problem of selecting the best area for deforestation, the best field for crops, the best location for drainage, the best place for nuclear waste storage, and so on. Forecasting problems can be approached as well since it is possible to ask a group of experts where a future event will be most likely to happen [12]. In Spatial Delphi the opinions are expressed by placing a series of points on a map. Following the Delphi logic, at each round the experts can revise their previous evaluations and, consequently, move their points. The interquartile range of the classical Delphi is replaced by a circle containing 50% of the points and the radius of the circle tends to decrease at each iteration, indicating in the space the convergence of opinions [12]. Here we propose the Spatial Shang; it starts from the same consideration that gave rise to the Spatial Delphi but takes advantage of the additional benefits of the Shang. Many problems involve decisions made on a map. The map can be on paper or on a computer screen and, in the context of shared choices, the space is an important element to be considered. In real application, the method must be considered as a support to the decisions to be made in a spatial context: a decision support that is the result of the convergence of different (spatial) viewpoints. The main steps of the Spatial Shang are the following: a) Selection of participants. Like in the classical Shang, the construction of the panel is the first phase. Let's denote with n the number of participants. b) First round. The first questionnaire must be constructed using a map. The decision problem must be formalized according to a spatial logic. Therefore, the question(s) for the panelists must contain expressions such as “the most appropriate location for …”, “the most appropriate location where …” or “the place where most likely a future event will occur”. The experts are invited to draw 4 points on a map containing the territory under study. Two
points are the extreme positions along the direction North–south and two are the extreme positions along the direction East–west. In other words, given expert i, one point expresses the upper limit, in the direction of latitude, beyond which the expert considers that the phenomenon will not occur or will not be located (in symbol Ni with i = 1, …, n). A second point expresses the lower limit in the direction of latitude (in symbol Si). Similarly, in the direction of longitude two points represent the leftmost limit (Wi) and the rightmost limit (Ei) of the phenomenon. Thus, those points identify four imaginary lines that surround the area with a rectangle, representing the boundaries of the spatial problem. There will be n different rectangles, one for each expert. c) First elaboration. After having collected the results of the first round, there will be four groups of values (points): one for North, one for South, one for East and one for West. In symbol we have1: g) N a vector of n points for the North limits; h) S a vector of n points for the South limits; i) E a vector of n points for the East limits; j) W a vector of n points for the West limits; These vectors define n different rectangles on the map. Like in the classical Shang, a statistical synthesis must be calculated for each vector; it summarizes in a single value all the n subjective estimates. We denote those indices, respectively, with N0, S0, E0 and W0. One of the criteria used for the classical Shang can be applied for the indices (see Fig. 1). Let's now consider that “maximum” is the latitude/ longitude of the farthest point from the center of the map and “minimum” is the latitude/longitude of the closest point to the center of the map. More precisely, for the calculation of N0 and S0 the values of the latitudes of the points contained in the vectors N and S are used, while for the calculation of E0 and W0 the values of the longitude of the points contained in the vectors E and W are employed. These four values define a rectangle of convergence (ABCD in Fig. 2) with the following vertices: A(W0,N0), B(E0,N0), C(E0,S0), D(W0,S0); it represents a statistical synthesis of the n rectangles. From the four indices two central values are calculated, one for the latitude: C 0;LAT ¼
N 0 þ S0 2
and one for the longitude: C 0;LONG ¼
E0 þ W 0 2
which define the center of gravity of the rectangle. The initial geographical area of evaluations is therefore bounded by a rectangle, with area A0 = (|E0 − W0|) ⋅ (|N0 − S0|) and with center of gravity having geographical coordinates G0(C0,LONG,C0,LAT). By drawing a vertical line and a horizontal line passing through this center of gravity, the rectangle ABCD is divided in four sub-rectangles each having a quarter of its area, namely A1 = A01/4 (see Fig. 2). For 1 Note that each point is defined by two values: one for the latitude and one for the longitude.
Please cite this article as: S. Di Zio, B. Staniscia, A Spatial version of the Shang method, Technol. Forecast. Soc. Change (2013), http:// dx.doi.org/10.1016/j.techfore.2013.09.011
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simplicity, we call these sub-rectangles with NE (the north-east one), NW (the north-west one), SW (the south-west one) and SE (the south-east one). d) Second round. The center of gravity G0 — together with the horizontal and vertical lines passing through it — is drawn on the map that is then submitted to the panel for the second consultation. Sub-rectangles are not shown to the panelists; they are only used internally, during the elaboration phases. Each expert is asked to choose one of the four sub-areas defined by the two lines, to indicate where he/she feels the true value falls with respect to the center of gravity. This is analogous to the question posed in the classical Shang that is “above or below the central value”. Note that the answer is very easy and fast to be given. e) Second elaboration. In this step, the objective is to choose one of the four sub-rectangles as new rectangle of convergence, together with its center of gravity and its sub-rectangles. After the second consultation, the number of preferences of each sub-areas is counted and this is equivalent to having “votes” for each sub-rectangle. If one of the four sub-rectangles receives the majority of votes, it becomes the new rectangle of convergence which — once calculated a new center of gravity G1 — will be divided in four sub-rectangles. Each sub-rectangle has a sixteenth of the area of the initial rectangle ABCD, namely A2 = A01/ 16. On the contrary, if two or more sub-rectangles receive the same (maximum) number of preferences, there is a problem of stalemate. One possible solution is to consult once again those experts who chose the sub-areas with maximum number of preferences, and ask them to locate a point on the map, representing her/his evaluation, somewhere in the selected sub-area. The point represents the opinion of the expert about the spatial problem under investigation; therefore, following Di Zio and Pacinelli [12], we can define it as opinion-point. The choice will fall on the sub-area (and, then, the sub-rectangle) which contains the farthest points from the center of gravity. That sub-area can be found by calculating the sum of distances from each point and the center of gravity.2 This procedure can solve any situation of tie while, as seen before, in classical Shang it is still an open problem. In this particular situation, it is useful to ask the experts reasoning of their choices. As known [1,11,14], reasoning is an essential aspect of the original Delphi process and in our case the reasons (together with the sum of distances) can provide valuable hints in choosing a sub-area. More generally, reasons constitute valuable material for the purposes of ongoing research. Let's take an example. If the sub-rectangle NW is chosen — because the sub-area NW received the majority of preferences or because the points are the furthest away from the 2 If the points in a sub-area are very close to the center of gravity, it means that the preferences of those experts are not far from those located in the other three sub-areas. It is like saying that there is not much difference between the chosen area and the others. If, on the contrary, the points are very far from the center of gravity, this means that the estimates of the panelists are far from the remaining rectangles; that sub-area is much more important than the other three. Therefore, if two sub-areas receive the same number of points, the one whose points are farther from the center will be chosen. We can state that the sum of the distances of the points from the center represents a weight of importance of the sub-area.
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Fig. 2. Representation of the result of the first elaboration.
center — the new center of gravity G1 has the following coordinates: C 1;LONG ¼
C 0;LONG þ W 0 N0 þ C 0;LAT ; C 1;LAT ¼ : 2 2
The new center of gravity G1 and its vertical and horizontal lines are drawn on the map, and submitted to the panel for the third consultation. Note that sub-rectangles are used only during the elaborations, while the experts see only the center of gravity with both the horizontal and the vertical lines, delimiting the four sub-areas. In general, from this moment the sub-areas have different sizes but their union always covers the whole study area. f) Iterations. Further rounds are performed, selecting new sub-rectangles and new centers of gravity, until a sufficiently small portion of territory is delimited. If we denote with k the iterations (with k = 0 the iteration in which the first rectangle is obtained), at each iteration the area of each sub-rectangle, say Ak, is reduced by a factor of 1/4k, namely k
Ak ¼ A0 1=4 : This means that the process of convergence is very fast. The procedure can be stopped after a certain predetermined number of rounds or when the area of the rectangle reaches a given value. One can, for example, establish that the rectangle should have an area below than a certain percentage (say P) of the area of the initial rectangle. In symbols the stopping criterion could be: when Ak ≤ P ⋅ A0. Like in the classical version, in subsequent rounds of the Spatial Shang the question is always different, because while the structure of the question is the same, the central value is never the same. In the Spatial Shang, the procedure does not require a change of opinion — right as in the classical Shang — and there is no pressure toward convergence. If an expert has an estimate in mind from the beginning of the procedure, he/she can keep that value throughout the duration of the survey, and simply compare it with the central value (each time different) that is proposed from time to time. This is one of the advantages of Shang with respect to Delphi and, similarly, of Spatial Shang with respect to Spatial Delphi. In Spatial
Please cite this article as: S. Di Zio, B. Staniscia, A Spatial version of the Shang method, Technol. Forecast. Soc. Change (2013), http:// dx.doi.org/10.1016/j.techfore.2013.09.011
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Shang, at each consultation, the experts have the same whole initial area to make their choices. At each round, there is only a shift of the center of gravity (and of the relative two lines) and each expert contributes to this movement. Convergence is not requested in this method and, in general, is not the main objective of the techniques that fall within the Delphi family. However, the researcher can use the calculation of the areas of subsequent sub-rectangles as a measure of convergence. Table 1 summarizes the main steps of the Spatial Shang method and compares it to the classical Shang. 4. A Spatial Shang application to localize the boundary of a coastal park In the year 2001, through the Italian National Law L. 93/2001, art. 8, the Costa Teatina National Park was established in central Italy. It involves eight municipalities along the Adriatic coast, from Ortona to San Salvo and has a length exceeding 60 km. It is a coastal park — not a marine one — thus protection concerns the coast and its natural (animal and plant) species [15]. Already in 1985, the Abruzzo Region had considered those areas worthy of protection through the Regional Landscape Plan (Piano Regionale Paesistico, L. 431/85). Later on, the Italian Ministry of the Environment considered that area as meriting preservation for its environmental, landscape and cultural values. In a working document [16] that territory was described as “winning and varied, with the alternation of sandy and gravelly beaches, cliffs, rivers' mouths, areas rich in spontaneous vegetation and cultivated lands (mainly olives), dunes and forest trees”. The above mentioned Law established the park but did not define its boundaries. That is why a very heated debate has been developed since then about that issue. Which portions of the territories of the eight municipalities should be included within the park boundaries? What are the criteria the definition should be based on? What are the procedures to be adopted? In 2001 the orientation was towards a top-down approach: the Italian Ministry of Environment had the task to define the park's boundaries in agreement with the Abruzzo Region, where the park is
located. In 2007 the Abruzzo Region issued a special law (L.R. 5/2007) to protect that territory. The Region created a “System of Protected Areas of the Costa Teatina”, including six natural reserves. Since the park's boundaries had not been defined yet, the Ministry transferred to the Abruzzo Region the task to solve the problem, in agreement with the local authorities. An agreement was not reached, that is why the process of definition is still in act. In recent years a bottom-up approach has been preferred: the decisional process should include local stakeholders, including local public authorities, local communities, enterprises, NGOs and associations. The Abruzzo Region started a formal consultation procedure but, so far, has not obtained the consensus about the park's boundaries. Given the situation, our task was to provide a tool to support the local stakeholders in the decisional process. Our aim was to provide a scientific methodology that could guarantee the convergence of opinions among the stakeholders. The spatial problem we posed to them concerned the definition of the park's boundaries or, at least, a territorial buffer small enough to define the boundaries. We've involved representatives of all the stakeholders, able to give voice to a plurality of opinions and interests. 62 were the stakeholders involved in the process, representing the whole community from different perspectives. Among them there were representatives of the local public bodies (mayors, city and provincial councilors), of national institutions (MPs), of political parties, of the church (parish priests and representatives of the bishop's court), of the trade unions (general secretaries of the provincial bodies), of entrepreneurs and producers' associations (in the agriculture, handicraft, commerce, tourist sectors), of entrepreneurs operating in the environmental field and in the third sector, of the citizens' associations and NGOs, of the environmental and cultural associations, of the local media, of the local development agencies, of schools and universities. The selection of the stakeholders was based on three main criteria: (i) deep knowledge of the territory and awareness of the on-going conflict; (ii) capacity to represent a clear and transparent position in the conflict; (iii) capacity to give voice to the general interest of the specific category they represent.
Table 1 Comparison of Shang and Spatial Shang. SHANG
Spatial SHANG
1. Formation of the panel (n experts) and construction of the first questionnaire. 1. Formation of the panel, construction of the questionnaire and preparation of the maps together with explanatory documents of the area of interest. 2. Submission of the first questionnaire. Panelist must give 2 values: 2. Submission of the first questionnaire/map. Panelists have to indicate 4 one minimum and one maximum. Two vectors of values are obtained. points on the map: two extreme locations along the direction north–south and two extreme locations along the direction east–west. Four vectors of points are collected. 3. Calculation of two synthetic values (m0 and M0), which summarize the 3. Calculations of four synthetic values (N0, S0, E0 and W0), which summarize maximums and the minimums estimated. Calculation of the first central the four vectors containing each n subjective estimates. Calculation of the value: C0 = (M0 + m0)/2 first center of gravity: G0. This produces four sub-rectangles. 4. Submission of the second questionnaire. Panel members are asked to 4. Submission of the second questionnaire, consisting in the initial map with provide an assessment above or below the central value C0. the center of gravity and the horizontal and vertical lines passing through it. Panel members are asked to choose one of the four sub-areas. 5. According to the results of the second consultation a second range is 5. According to the results of the second consultation a sub-rectangle is calculated ([C0,M0] or [m0,C0]). The second central value C1 = (M0 + C0)/2 chosen. Its center of gravity — G1 — is then calculated. By using this point the or C1 = (C0 + m0)/2 derives from this range. Panelists have to give a new initial area is divided in four new sub-areas, generally having different sizes. Panelists have to choose one of these sub-areas. assessment, above or below this central value. 6. Steps 4 and 5 are iterated until the range will be sufficiently small. 6. Steps 4 and 5 are iterated until the rectangle will be sufficiently small.
Please cite this article as: S. Di Zio, B. Staniscia, A Spatial version of the Shang method, Technol. Forecast. Soc. Change (2013), http:// dx.doi.org/10.1016/j.techfore.2013.09.011
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To this group of stakeholders we applied the Spatial Shang methodology. Considering that the problem of the boundaries of the park is reduced to the definition of a line at a certain distance from the shoreline (more or less parallel to the coastline), the Spatial Shang is reduced from two to one spatial dimension in this application. In other words, given that the Adriatic coast extends from North to South, the analysis was conducted only in the direction of the longitude (East–west). 4.1. First round Using a map of the coast containing the eight municipalities involved in the park's area, we asked the stakeholders to indicate two values, representing the minimum and maximum distance of the park boundaries from the coastline. Therefore, for each respondent we collected two values in the direction of longitude, representing the left maximum limit (Wi) and the right minimum limit (Ei) of the park (i = 1, …, 62). In addition to the map on which drawing the points, we also provided supporting maps such as a map of the road network and a satellite image, in order to support the respondents in the evaluations. 4.2. First elaboration After the first questionnaire, we obtained two groups of points on the map, one group for East (representing the minimum evaluations) and one for West (representing the maximum evaluations). According to our notation we have a vector E containing 62 points for the East limits and a vector W containing 62 points for the West limits. For each point, we calculated the distance from the coast, therefore obtaining two distributions, respectively of the minimum and maximum distances from the coastline (see Table 2). Given the resolution of the map used for the survey, we approximated the values of the distances to values of 0.5 Km. The mean of the minimums is 2.0 and the mean of the maximums is 3.1. By looking at the variability of the two distributions, we can have a measure of the convergence of opinions after the first consultation. There was a greater consensus regarding the minimum values (st. dev. 4.7) with respect to the maximum values of the limit of the park (st. dev. 12.8). Table 2 Frequencies of responses of the first round. Distance (km)
Frequencies for E (minimum)
Frequencies for W (maximum)
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
1 15 10 6 9 4 3 3 3 3 5 62
0 4 6 7 6 5 5 5 1 3 20 62
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Note that, the smallest value for the maximum (0.5 km) is lower than the highest value of the minimum (5 km). In other words, the group of evaluations for the minimum and the maximum are overlapping. Probably, this can be read as a reflection of strong contrasts and disagreements involving the establishment of the park. As a synthesis of the two vectors of values we used the arithmetic mean of the distances, therefore according to our notation we have E0 = 2.0 and W0 = 3.1. These two values define two lines, parallel to the coastline, which delimit a first large area of convergence, having a width of 1100 m (see Fig. 3). Its central value is
C0 ¼
E0 þ W 0 ¼ 2:55 2
The eight municipalities interested by the coastal park are now crossed by an imaginary line at 2.55 km from the coastline (Fig. 3).
4.3. Second round and elaboration The stakeholders were asked whether the limit of the park should be fixed at a distance that is higher or lower than 2.55 km from the coastline. At the second consultation only 35 stakeholders responded to the questionnaire, so there was a large drop-out rate, also in this case due to the sharp conflicts which are still in progress on this issue. The 65.7% of the respondents set a limit that is above 2.55 km while 34.3% set a limit that is below that distance. Thus, according to the panel of respondents, the limit should be placed at a distance higher than 2.55 km from the shoreline. The new area of convergence is therefore a buffer of 550 m, included between 2.55 and 3.10 km from the coastline (see Fig. 3). The new central value within this range is:
C1 ¼
W 0 þ C 0 3:10 þ 2:55 ¼ 2:82: ¼ 2 2
Since the convergence area of 550 m is very little compared to the maximum area expressed by some stakeholders during the first consultation, we decided to conclude the consultation after the second round. In conclusion we can affirm that, according to the panel of stakeholders, the limit of the coastal park should be at about 2.8 km from the coastline or, more generally, in a buffer of 550 m between 2.55 km and 3.10 km from the coastline. These results do not represent the final solution to the strong on-going conflict in this territory, but a support to the mitigation of those conflicts. The buffer of 550 m is the result of the iterative consultation of the stakeholders; it can, therefore, be used as a decision support for the choice on where to set the limit of the park. Furthermore, the survey generated a debate in the area, among the main players of the conflicts; this is, anyhow, a positive fact for the solution of the problem.
Please cite this article as: S. Di Zio, B. Staniscia, A Spatial version of the Shang method, Technol. Forecast. Soc. Change (2013), http:// dx.doi.org/10.1016/j.techfore.2013.09.011
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Fig. 3. Diagram of the application.
5. Concluding remarks In this paper we have shown that, as much as in the Spatial Delphi [12], it is possible to reproduce the Shang method in a spatial context by using a map. We should, however, consider our method as an initial prototype since several questions are still open. First, the choice of the criterion for the construction of the rectangle in the first elaboration (minimum, maximum, arithmetic mean or median). Second, the rectangle could be replaced by another regular or irregular geometric figure, that may take account of the spatial constraints on the given territory. Other open questions concern the map used for the survey and its scale, as well as which kind of supporting maps are the most appropriate. We also believe that an evolution of this methodology, through the use of a Web GIS technology, could be a real-time version, in analogy to the Gordon's Real-Time Delphi [17,11]. Concerning the application, we are aware that this is only a preliminary experiment, and the applicative potentialities should be more in-depth analyzed; nonetheless our early results are encouraging. We can summarize as follows the main aspects emerged in this paper: • In real applications the method should be considered as a Spatial Decision Support System [18]. In our case study, for instance, the 550 m buffer is the result of the consultation of the stakeholders and can be used as a support for the decision on where setting the boundaries of the coastal park. • The stakeholders appreciated the fact that answering the questionnaire was very simple and intuitive: simply choosing one area on a map. • Because of the ease in giving responses, the total time of the application, including the elaborations, was very short, namely three weeks. • The Spatial Shang should be used only when the decision problem can be traced back to the location of a place on the territory. Otherwise, the method cannot be applied.
• While in classical Shang the stalemate is still an open question, here for the Spatial Shang we proposed a solution by using the opinion-points. • For an actual definition of the park's boundaries, it is clear that it is necessary to consider a boundary with a variable distance from the coast. The choice of a line equidistant from the coastline is only a first research hypothesis. Concretely, the Spatial Shang can be applied in each of the eight municipalities of the park (with local stakeholders), in order to obtain the boundary that best suits local diversity, and takes account of the constraints and specificities characterizing the different areas of the coast. • Strengths of the method. The proposed method has the advantage of being easily accessible and understandable, even for a non-specialized audience. The presentation of the map in a paper or on-line format gave the chance also to the older stakeholders to participate. Therefore, the method can be used both with a panel of experts and with a panel of general stakeholders. The experiment generated a debate in the area that, per se, was positive for the decisional process. While a well known weakness of the Delphi and Delphi derivative methods is the time that they take, we have seen that the simplicity of the responses in the Spatial Shang reduced enormously this problem. Moreover, like other Delphi methods, the Spatial Shang avoids the problems of face-to-face group interaction. As explained by Ford [5], the Shang method has some important advantages with respect to Delphi. In particular, Shang avoids “pressure toward consensus and individual commitment to an initial response” [5]. Similarly, we believe that the same benefits are worth for our Spatial Shang with respect to the Spatial Delphi. • Weaknesses of the method. The selection of the stakeholders was decided by the authors of this paper. It was based on the direct knowledge of the problem, of the territory, of the local stakeholders, after several years of research. Even if not biased by prejudices, the authors made a subjective assessment of who were the important stakeholders, crucial for the problem's solution. There is not objective counterproof that the results would have been the same choosing different
Please cite this article as: S. Di Zio, B. Staniscia, A Spatial version of the Shang method, Technol. Forecast. Soc. Change (2013), http:// dx.doi.org/10.1016/j.techfore.2013.09.011
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representatives of the stakeholders. The risk that a silent minority (or majority) has been ignored because of its silence, cannot be ruled out. In literature there are various criticisms of the Delphi method that can be directed also to our method, like the fact that Delphi does not produce more accurate answers than other methods [19]. Even if this is still an open issue, it must be said that there are many papers that have refuted this criticism (see for example [20]). Finally, like other methods of the Delphi family, the drop out of participants during the process is an inevitable disadvantage. Acknowledgments The research leading to these results has received funding from the European Community's Seventh Framework Programme FP7/2007–2013 under grant agreement n° 244251. The authors would like to thank Angelo Staniscia for the valuable support he provided in all the phases of the research and the 62 stakeholders for their willingness to participate to the Spatial Shang. References [1] N.C. Dalkey, O. Helmer, An experimental application of Delphi method to the use of experts, Manage. Sci. 9 (1963) 458–467. [2] M. Turoff, The design of a policy Delphi, Technol. Forecast Soc. Change 2 (2) (1970) 149–171. [3] O. Helmer, Cross-impact gaming, Futures 4 (2) (1972) 149–167. [4] M.H. De Groot, Reaching a consensus, J. Am. Stat. Assoc. 69 (345) (1974) 118–121. [5] D.A. Ford, Shang inquiry as an alternative to Delphi: some experimental findings, Technol. Forecast Soc. Change 7 (1975) 139–164. [6] A. Delbecq, A. Van de Ven, D. Gustafson, Group Techniques for Program Planning: A Guide to Nominal Group and Delphi, Scott Foresman, Chicago, 1975. [7] W. Rauch, The decision Delphi, Technol. Forecast Soc. Change 15 (3) (1979) 159–169. [8] F. Régnier, Un Outil de Décision pour l'Entreprise, Cpe Bull. 27 (1986) 89–100. [9] F. Régnier, Du Principe de la Pratique de l'Abaque de Régnier, Institut de Métrologie qualitative, Nancy, 1987.
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[10] F. Régnier, Annoncer la couleur, Institut de Métrologie Qualitative, Nancy, 1989. [11] T.J. Gordon, A. Pease, RT Delphi: an efficient, “round-less” almost real time Delphi method, Technol. Forecast Soc. Change 73 (2006) 321–333. [12] S. Di Zio, A. Pacinelli, Opinion convergence in location: a Spatial version of the Delphi method, Technol. Forecast Soc. Change 78 (9) (2011) 1565–1578. [13] T.J. Gordon, O. Helmer, "Report on a Long Range Forecasting Study,", Rand Paper P-2982, Rand Corporation, Santa Monica, California, September 1964. [14] H.A. Linstone, M. Turoff, The Delphi Method: Techniques and Applications, Addison-Wesley Publ. Co., Reading, Massachusetts, 1975. [15] A. Montanari, B. Staniscia, Global changes, coastal areas and conflicts: experiences from Italy, in: A. Khan, Q. Le Xuan, E. Corijn, F. Canters (Eds.), Environmental Conflicts in Coastal Urban Areas. Towards a Strategic Assessment Framework for Sustainable Development, Casa Editrice Università La Sapienza, Rome, 2013, pp. 100–133. [16] Ministero dell'Ambiente, Progetto di istituzione del Parco Nazionale della Costa Teatina, working paper, Rome, 1998. [17] T.J. Gordon, The real-time Delphi method, in: J.C. Glenn, T.J. Gordon (Eds.), Futures Research Methodology Version 3.0, The Millennium ProjectAmerican Council for the United Nations University, 2009. [18] M.D. Crossland, B.E. Wynne, W.C. Perkins, Spatial decision support systems: an overview of technology and a test of efficacy, Decis. Support. Syst. 14 (1995) 219–235. [19] F. Woudenberg, An evaluation of Delphi, Technol. Forecast Soc. Change 40 (1991) 131–150. [20] G. Rowe, G. Wright, Expert opinions in forecasting: the role of the delphi technique, in: J.S. Armstrong (Ed.), Principles of Forecasting, Springer, New York, 2001. Simone Di Zio is Researcher in Social Statistics at the University G. d'Annunzio Chieti-Pescara (Italy). He is member of the World Future Society and of the Italian Statistical Society. He participated in the SELMA Project (Spatial Deconcentration of Economic Land Use and quality of Life in Metropolitan Areas) financed by the European Commission within the framework of the 5° European Union Research Programme. He has published 25 articles. His scientific activities deal with Spatial Statistics and IRT models. He is expert in GIS (Geographic Information Systems) and fractal geometry. Barbara Staniscia is member of the coordination and research team of the EU-FP7 funded project SECOA, at the Sapienza University of Rome. She is Scientific Secretary of the IGU Commission “Global change and human mobility”. She has been member of the research teams of the EU funded projects MIRE, ESPON 1.1.4, SELMA, EQUAL II-Celine, PLACE and TIGER. She has developed researches concerning urban dynamics and local development, spatial effects of EU policies, tourism and migration, environmental conflicts, rural development and geography of taste.
Please cite this article as: S. Di Zio, B. Staniscia, A Spatial version of the Shang method, Technol. Forecast. Soc. Change (2013), http:// dx.doi.org/10.1016/j.techfore.2013.09.011