In the study of sustainable wellbeing in mountain areas, there are three debates about the relationship between economy, ecology, and society. The first view is that the three are equal and coexistent and should be of equal importance, often setting equal wight to the three subsystems (Su et al., 2017, Kong et al., 2019, Liu et al., 2016). From the perspective of multi-system coupling, it is reasonable to pursue the parallel progress of multiple systems, but the special feature of mountainous areas is that they have assumed the function of national ecological security, and “ecological priority” has become the priority of mountain development. Thus, the second view is that studies to conduct comprehensive evaluation of sustainable wellbeing in mountain areas should give greater weight to ecological (Zhang and Cheng, 2017). However, China's mountainous areas are not only ecological reserves but also poor areas where public services and living conditions need to be improved (Li et al., 2014). Therefore, the third view holds that, after long-term development, the contradiction between the ecological function of mountain areas and people's increasingly growing needs for a better life and the uneven and inadequate development still exists (Tian and Fu, 2018). Under such a contradiction, will the original “ecology first” meaning change? Clearly, three contentions, which cannot be answered definitively by simple data characteristics, need to be answered through multiple interviews. Therefore, a hierarchical analysis based on expert consultation was used to conduct the empowerment study. The expert consultation was conducted in the form of a Questionnaire Star app (https://www.wjx.cn/ ). The consultation objects were industry experts in the majors of economic management and ecological environment, government officials, and the general public, with a total of 38 questionnaires received, and 16 of them passed the consistency test. Input the statistical results into the judgment matrix, and use the YAAHP 10 software to survey the statistical results, calculate the decision of each expert by geometric mean method, and obtain the final weight. The basic procedure of the AHP group decision making method in this study is as follows. In the first step, a hierarchical model was built. In this study, only the economic, ecological and social capital accounts, namely the middle layer, are empowered by the AHP. The specific indicators, i.e., the program level, were not only too numerous but also the specific indicators under each account had equal significance under each subject area, so a common approach to the assignment of specific indicators was to decompose the weights obtained in the intermediate level to its subordinate program level with equal weights. In the second step, the judgment matrix was constructed. A judgment matrix is constructed for the criterion-level indicators, as in formula (6), and a two-by-two comparison of factors at the same level is conducted, and a scale of 1–9 is introduced to quantify it.(7) A=w1/w1w1/w2…w1/wnw2/w1w2/w2…w2/wn…………wn/w1wn/w2…wn/wn In the third step, expert consultation was conducted. Experts were asked to judge the importance of the two factors and the results were included in a matrix. In the fourth step, a consistency check is performed. First, calculate the consistency index of the judgment result CI.(8) CI=(λmax-n)(n-1)Where λmax is the maximum characteristic root of judgment matrix A, and n is the order of the judgment matrix. then find the corresponding average random consistency index RI. Final calculation of consistency ratio CR, CR = CI/RI. It is generally considered that the consistency of the judgment matrix is acceptable when CR > 0.1. In the fifth step, the index weights were determined. The judgment matrix that passed the consistency test was applied to the geometric mean method for statistics, and the weights of the program-level indicators were calculated. In order to accurately and comprehensively reflect the aggregation and correlation among economics, ecology, and society in sustainable wellbing system, it is necessary to construct mathematical models for further investigation. In response, Costanza (2016), an economist of ecological economics, proposed a mixed concept model for the measurement of sustainable wellbeing, which includes factors such as physical wealth, human capital, and environmental capital. Costanza R argued that if one side is very big, its term in the equation will be close to the maximum, but if one side is very small, its term will be a small part, which will reduce and limit the overall level of happiness, that is, the best system is to achieve the overall goal of simultaneous prosperity, high quality, fair sharing, and sustainable life. However, the framework is conceptual, yet has not been applied in practice (Cook and Davidsdottir, 2021). Nevertheless, the systemic view of sustainable wellbeing has provided this research with ideas on exponential aggregation. Combining with existing research findings, the mathematical expression of Coupling Coordination is closest to the mathematical model of sustainable wellbeing, and coupling coordination is not only the most widely applied exponential aggregation method, but also one of the methods to measure the interaction between multiple systems. Therefore, the highly applicable SWI aggregation method constructed by this study is as follows. First, standardize the raw values of each indicator by normalizing the extreme values so that they are distributed between [0,1] in order to eliminate the influence of the magnitude level and direction of the data. Positive indicator standardization:(9) Xij+=(Xij-min{Xj})(max{Xj}-min{Xj}) Negative indicator standardization(10) Xij-=(max{Xj}-Xij)(max{Xj}-min{Xj})Where Xij is the original value of the i-th indicator in year j of a capital account in a county, min(X) and max(X) are the minimum and maximum values of the i-th indicator in a capital account of a county in year j, respectively. Then, the evaluation value of each capital account is calculated. Based on the standardized values, the evaluation value of each capital account is calculated. The equation for the score of the p-th capital account is as follows.(11) f(p)=∑wpijXpij,(p=E,N,S)where wpij represents the weight of each indicator of the three major capital accounts, and p = E, N, and S represent economic capital, ecological capital, and social capital, respectively. Finally, the SWI is calculated. With the idea of coupling coordination, the SWI model is constructed with the following equation.(12) SWI=f(E)×f(N)×f(S)[f(E)+f(N)+f(S)]/33×[α×f(E)+β×f(N)+γ×f(S)]Where f(E), f(N), and f(S) are the evaluation values of the three major capital accounts, respectively. α, β, and γ are parameters to be estimated, α + β + γ = 1, taking values depending on the importance of each capital account. SWI is distributed between [0,1], The maximum SWI can be achieved when all accounts are at their maximum values at the same time, i.e. any one account can be the limiting factor. For the setting of the parameters to be estimated, the assignments will be made according to the special characteristics of the ecological priority of the Qinba Mountain Area, using the method of AHP. The AHP reflects the expert's empirical judgment and overcomes the limitations of the traditional objective empowerment method expressed only in terms of data characteristics, which may lead to the phenomenon that the quantitative results do not match with the perception. Meanwhile, related scholars have adopted this assignment method in their subsequent studies on sustainable wellbeing (Kibria et al., 2022), in order to realize the continuity of the research, this method has been adopted in this study.
