Environmental risk evaluation of overseas mining investment based on game theory and an extension matter element model

Data sources

The data come from the Ministry of Commerce of the People’s Republic of China’s 2019 Guide to Foreign Investment and Cooperation Country, as well as the websites and research literature from the Fraser Institute and the World Bank. The datasets include 14 factors that influence the environmental risk of overseas mining investment in the Philippines are summarized in Tables 1 and 2. The specific reasons that we choose these data in the Philippines are as follows:

The Philippines is a multi-ethnic island nation in Southeast Asia located in the western Pacific Ocean. The country has a total land area of 299,700 km² and a population of 101 million. The Philippines is rich in mineral resources, and the area of known mineralization accounts for 30% of the land area in the country. According to the National Bureau of Geology and Mining in the Philippines, gold, copper, nickel, and chromium reserves rank third, fourth, fifth, and sixth in the world, respectively, in terms of mineral reserves per unit area. Nonferrous metal mining in the Philippines has great potential. To date, 13 types of metal minerals have been discovered, including gold, copper, nickel, aluminium, chromium, silver, lead, and zinc, with total reserves of 7.1 billion tons. Twenty-nine types of nonmetallic minerals have also been discovered with total reserves of 51 billion tons. The Philippines is an important producer and exporter of metallic mineral resources such as copper and nickel^6,33.

The Philippines has been one of the countries most in favour of overseas mining investment in the region near China. Before the mid-1990s, the Philippines was a favoured country for international mining investors; however, in the late 1990s, changes to national policies and social unrest led to a decline in the mining investment environment. Since January 2003, President Arroyo has proposed a reform of the mining development strategy in the Philippines, and the mining investment environment has improved. However, combined with the political, religious and security issues in the Philippines, especially the peoples’ attitude towards foreign investment, the current mining policy environment in the Philippines is not ideal. Therefore, to comprehensively and objectively understand and analyse the mining investment environment in the Philippines, relevant documents were collated and analysed. Following the principles of importance, practicality, scientificity and systematicness in the design of the index system, the accepted classification rules and data released by authoritative agencies such as the World Bank were used for the evaluation basis^{1,2,3,4,5,6,7,8}, which selected 14 factors that have bearing on political policy, economic, financial, sociocultural, and infrastructure risks. The classification standard and valuation of each index are provided in Table 1. According to the classification standard and valuation index objectives, the risks were divided into five levels (i.e., I–V, which reflect high, higher, general, lower, and low risks, respectively). The Philippines’ risk index data are listed in Table 2.

Determination of index weights: analytical hierarchy process

This method integrates quantitative and qualitative evaluations to improve the accuracy of decision making^{32,33,34,35,36,37,38}. The basic principles and steps of the AHP method are as follows:

Step 1: The complex problem is decomposed to make it multi-element in nature.

Step 2: These elements are grouped, and a hierarchical structural model is established.

Step 3: A discrimination matrix is constructed, and any two factors are compared with a 1–9 scaling method to obtain the relative importance of each index at each level, which can be expressed quantitatively.

Step 4: The largest eigenvalue and the corresponding eigenvector of the discrimination matrix are calculated using the mathematical method, where the eigenvectors and weight coefficient values are listed in terms of the importance of the evaluation factors.

Step 5: The consistency of the discrimination matrix is tested based on the consistency index ( CI) calculated as (CI = frac{{{lambda_{max }} – n}}{n – 1}) as well as with the average random consistency index (RI). If the random consistency ratio (CR = frac{CI}{{RI}} < 0.10), then the results of the hierarchy analysis are considered to be consistent, and the resulting weight distribution values are reasonable. If this is not the case, then the weight coefficient values should be redistributed to adjust the values.

Entropy weight theory

In information theory, the importance of studying the degree of dispersion of the whole system is central to the entropy method. The specific steps for these calculations are as follows:

Step 1: Data collection and sorting: The initial evaluation matrix composed of (m) evaluation indexes and (n) evaluation objects is as follows:

Step 2: Data standardization: All index values ( {x_{ij}}) in matrix ( {X_{ij}}) are normalized as follows:

Step 3: Calculation of information entropy: The entropy of each evaluation index can be obtained from

Step 4: Calculation weight: The weight of each evaluation index can be calculated as follows:

where ( {w_j}) is the index weight and ( sumlimits_{j = 1}^n {{w_j} = 1} ). The larger the entropy weight is, the greater the effect of the index on the scheme, in that it contains and transmits more decision information that has a greater influence on the final evaluation decision^{39,40,41,42,43,44}.

Combination weighting model based on game theory

This approach differs from the traditional simple linear combination weighting method. The central idea of this approach is to “coordinate conflicts and maximize benefits” by comprehensively considering the relationship between the indexes, balancing the subjective and objective weights, and optimising the index weight values. The basic algorithm is as follows:

Construction of the basic weight vector set

Assuming that ( H) weight values are obtained using the ( H) weighting method, the basic weight vector set of the ( H) method is

Any linear combination of ( H) weight vectors is

where ( {a_k}) is the linear combination coefficient, and ( w) is the comprehensive index weight value of the ( H) weight set.

Optimal combination weight

To find the balance between the different weights, the optimal effect weight vector ( W) was obtained. In the calculation process, it is converted into an optimisation of the weight coefficient ( {a_k}) to minimise the deviation between ( w) and ( {w_k}), as follows:

From the differential properties of the matrix, the first-order derivative condition for the optimisation of Eq. (7) becomes

By solving Eq. (8), the combination coefficients ( left[ {{a_1},{a_2}, cdots ,{a_H}} right]) can be obtained and normalised according to ( a_k^* = {a_k}/sumlimits_{k = 1}^H {a_k} ). The final combination index weight is ( W = sumlimits_{k = 1}^H {a_k^*W_k^T} ,k = 1,2, cdots ,H) ^31,32.

Workflow of extension matter element theory

The theoretical basis of extenics involves the matter element and extension set theories, and its logical cell is the matter element. As such, extenics introduces the concept of the matter element that organically combines quality and quantity. It is a triple group composed of things, features, and quantity values for things, which are depicted as R = (things, features, quantity values). The matter element concept correctly describes the relationship between quality and quantity, and it can be more appropriate to describe the change process of objective things. Different objects can have the same characteristic element and are represented by the matter element with the same characteristics. For convenience, many matter elements with the same characteristics are expressed in a simple way.

Determination of the classical and joint domains

Equation (9) is a matter element body with the same characteristics of a matter element with the same characteristics ( {R_{ij}}), in which ( {N_j}) is the ( j) evaluation category, ( {C_i}) is the ( i) evaluation index, and ({V_{ij}} = left( {{a_{ij}},{b_{ij}}} right)left( {i = 1,2, cdots ,n;j = 1,2, cdots ,m} right)) is the range of quantity values ( {N_j}) for the index ( {C_i}), which is the classical domain of the data range taken by each category for the corresponding evaluation index.

where ( P) is the whole of the category, ( {V_{iP}}) is the range of quantity values taken of ( P) for ( {C_i}), and ( {R_P}) is the ( P) joint domain.

Determination of the matter element to be evaluated

For ( q) to be evaluated and using the matter element to express the detected data or analysis results, the matter element ( {R_q}) to be evaluated can be expressed as

where ( q) is some thing and ( {v_i}) is the quantity value ( q) for ( {C_i}), which are the specific data obtained by the monitoring of the things that are to be evaluated.

Determination and calculation of the degree of relation

Determination of the degree of relation for the thing to be evaluated in each category is expressed as follows:

where ( rho left( {{v_i},{V_{ij}}} right) = rho left( {{v_i},left( {{a_{ij}},{b_{ij}}} right)} right) = left| {{v_i} – frac{{{a_{ij}} + {b_{ij}}}}{2}} right|-frac{{{b_{ij}} – {a_{ij}}}}{2}).

The calculation of the thing ( q) to be evaluated for the degree of relation ( j) is expressed as

Determination of the level

Determination of the level is expressed as follows:

If ( {K_{j0}} = max left{ {K{}_jleft( q right)} right},j in left( {1,2, cdots ,m} right)), ( q) belongs to level ( {j_0}).

In the extension set, the concept of a relational function is established. Any element in ( U) can be quantitatively described by the relational function value, which can belong to the positive, negative, or zero domains (i.e., belongs to the elements in the same domain). It is also possible to separate different levels from the size of the relational function valu^27,28,29,30.

Source: Ecology - nature.com