[author]Cheng Jinhua

[content]

Beyond the distinction between "East and West": The spatial evolution and typification of China's judicial needs

Shi Lei， Assistant Professor at Tongji University Law School

Cheng Jinhua，Distinguished professor at the Koguan School of Law of Shanghai Jiao Tong University and the vice president of the Chinese Academy of Law and Society.

Abstract: In the pursuit of spatial justice, the traditional simple and vague distinction between "things" cannot fully reflect the regional differences in judicial needs, which is not conducive to the rational allocation of judicial resources. It is necessary to deepen the spatial typology of judicial needs from describing the scene to explaining the causes. Empirical research from a geographic perspective shows that the "east-west differentiation" pattern of judicial demand in China is showing a potential weakening trend in spatial evolution. Judicial demand not only has spatial dependence, but also has spatial heterogeneity in its causes. The demand for justice is influenced by multiple factors such as population density, urbanization process, economic development, education level, government governance, and availability of legal services, but their impact is not consistent at the regional level. Based on this, by objectively classifying and comparing within and outside the group, the dominant factors are identified, and China's judicial needs are divided into four new spatial types: social economic education dominant, legal social dominant, government education dominant, and diverse weak dominant. This typological attempt can provide policy references for accurately and dynamically improving the balance of judicial supply and demand in the region.

Keywords: judicial needs; Spatial effect; Influencing factors; Spatial type; legal Geography

1. Problem posing

Reasonably allocating social resources and opportunities between regions and meeting the basic needs of different regional groups are important connotations of spatial justice. The report of the 20th National Congress of the Communist Party of China pointed out that efforts should be made to promote high-quality development, rural revitalization, and regional coordinated development, in order to achieve common prosperity for all the people. This undoubtedly reflects that spatial justice is a major strategic goal pursued by the Party and the state. However, whether narrowing the regional development gap can be implemented and whether the people can fully enjoy the development dividends cannot be achieved without the improvement of the legal system and the fairness of judicial operation. From the perspective of the relationship between the central and local governments, this requires judicial capabilities across the country to be at a relatively high level of basic consistency and achieve equal legal effects. In this sense, in addition to material common prosperity, equal satisfaction of judicial needs also belongs to the realm of spatial justice.

The discourse in both theoretical and practical circles often contains a binary regional view of "East West" regarding the regional perception of judicial needs and resources. From both official and practical perspectives, since 2006, the work reports of the Supreme People's Court have often pointed out that some courts in the eastern region are under great pressure to handle cases, while judicial resources in the western region are relatively scarce. In recent years, there have been some judicial policies that require "cooperation between the east and the west" and "assistance from the east to the west". These contents clearly reflect the inherent empirical assumptions that there are differences in judicial supply and demand between the east and the west or that the east and the west should be treated differently. There are also many similar views in academic research. Fan Yu believed earlier that there were significant differences in the demand and form of grassroots justice between the eastern and western regions of China, and the construction of the small claims litigation system should pay attention to regional differences in order to improve the efficiency of judicial resource allocation. Jiang Bixin made a typical summary of the regional characteristics of judicial supply and demand, that is, "the courts in western China have fewer cases and more people, and the efficiency of handling cases is not a problem, but the quality of cases may be a prominent issue; while the courts in eastern coastal areas of China have more cases and fewer people, and although the quality of cases is relatively high, the efficiency of handling cases is more prominent.

However, the portrayal of judicial needs under the binary view of "things" often stops here. Regarding the specific spatial distribution, not only is the official expression vague, but the academic community is also at a loss. Previous studies have focused on meeting the diverse needs of institutional level groups, rather than explaining regional differences. The difficulty in obtaining local case volume data objectively limits the development of related spatial research. Taking a step back, even if the details are made public, a simple division of things may not truly effectively solve the problem of judicial supply-demand imbalance. On the one hand, this binary classification is only a description of the surface distribution of demand, and the particles are too coarse. If policies are implemented based on this, it is inevitable that the symptoms will be treated without addressing the root cause. Both of them can easily lead people to subconsciously view economic development as the only factor causing regional differences in judicial demand, resulting in policy makers being unable to fully understand the formation mechanism of judicial demand and difficulty in scientifically and reasonably allocating resources from the perspective of pursuing long-term benefits. Therefore, exploring the spatial types of judicial needs should go beyond the distinction between "things" and go deeper from describing the scene to explaining the causes.

It is generally believed that judicial needs are directly linked to court litigation, mainly reflected in the number of people choosing litigation as a means of dispute resolution. Therefore, the theoretical focus is on explaining the fundamental question of why people choose litigation. In this regard, the fields of legal sociology and legal economics have formed a relatively abundant accumulation of knowledge. However, human society cannot exist independently without space, and traditional research pursues universal rule explanations from the social state dimension, but rarely considers geographical dimensions and spatial effects, which is insufficient to answer the significant regional differences in China's vast territory. On the one hand, according to the first law of geography, everything is interconnected, and the closer the distance, the closer the connection. Although the theory guided by universal interpretation can reveal certain factors that affect judicial needs from a global perspective and infer that regional differences are caused by them, it only treats "regions" as independent "individuals" and ignores the potential impact of the characteristics and relationships of geographic space on litigation activities. On the other hand, as a potential second law of geography, spatial heterogeneity means that the variance of geographic variables is statistically uncontrollable. In other words, the factors influencing judicial demand and their effectiveness may not be consistent in different regions of the same country. Therefore, at least in the issue of judicial needs, spatial effects cannot be answered by mainstream theories in the current interdisciplinary field of law and social sciences, and they are also unidentifiable by commonly used regression analysis methods. The inclusion of spatial dimensions will help develop a more complete theoretical analysis framework and empirical strategies based on the integration of existing theoretical foundations.

In summary, the core issue of this article is how to summarize and explain the changing characteristics of China's judicial demand from a geographic spatial perspective. This article will explore the spatial evolution pattern of China's judicial demand based on the latest collected provincial panel data, using spatial statistical methods such as Moran's Index I and spatiotemporal geographically weighted regression. It will comprehensively examine the influencing factors and their effect differences, and finally use K-means clustering analysis to identify spatial types based on specific dominant factors, in order to provide reasonable and effective experience references for the relevant judicial reform of "improving quality and efficiency".

2. Theoretical analysis

2.1 Definition of judicial needs

Strictly speaking, judicial demand is a relatively specific concept with different meanings in different social and political contexts. This is because justice and demand themselves have multiple connotations. In modern Western countries with a decentralized political structure, justice is equivalent to trial, which is a specialized activity in which the state applies laws to resolve disputes. Judicial organs exercise judicial power, forming a balance between administrative and legislative powers. In contrast, China's institutional practice has actually expanded the scope of judicial concepts. Influenced by the tradition of politics and law, there are roughly two main judicial views formed in official texts: the "dual judicial view" of trial and prosecution, and the "grand judicial view" that is not limited to trial and prosecution. In addition, the judicial work of Chinese courts is not limited to litigation cases, but also includes activities beyond handling non litigation cases, enforcing effective judgments, issuing judicial recommendations, educating citizens on legal knowledge, and participating in grassroots governance. However, if we set aside political factors, the judicial activities of judges listening to both sides and mediating judgments have always been the foundation of the concept of "justice" in ancient and modern times, both domestically and internationally. Therefore, the legal community generally narrows down the concept and specifically refers to judicial activities to analyze the court and judge system. This article also holds this understanding.

There are differences in the size of 'justice', and the 'needs' of justice are more internal and external. In the perspective of reductionism, justice is a tangible public good, with "adapting or satisfying social needs as the basic or even the only dimension". Accepting cases and resolving disputes is a service or commodity provided by the court, and the parties to the dispute are the direct "consumers". In this sense, their needs can be expressed as a clear desire to be willing and able to purchase judicial services when disputes arise, also known as superficial judicial needs. The objective implementation of the judicial function is the satisfaction of needs, regardless of motives. At the same time, the condition of "willingness and ability" indicates that judicial needs are a unity of subjective identification and objective ability. Consumers not only subjectively believe that court trials are more fair and effective than other dispute resolution methods such as forbearance, reconciliation, and mediation, but also need sufficient financial and energy resources to bear litigation costs. Therefore, the demand for justice also contains good expectations from society for the performance of court work, such as requiring judicial accessibility, fairness, efficiency, approachability, authority, etc. Although there is a complex interactive relationship between court performance and public litigation decisions from a micro perspective, making litigation decisions itself implies prior recognition of court performance, and the relationship between the two is balanced to a certain extent at the macro level. Therefore, the number of lawsuits can be regarded as the minimum standard for measuring superficial needs.

In addition, there are often various motives behind people's adoption of judicial measures, which vary from person to person and belong to deep judicial needs. According to the degree of relevance to the case, these motivations can generally be divided into two categories: in case and out of case. Internal motivation refers to the desire of the parties involved in a dispute to end the dispute, obtain the rights or compensation they deserve, and address the matter at hand. The extrinsic motive is to "instrumentalize" or "weaponize" the litigation. For these people, litigation is just a means to achieve other goals, such as using the judiciary to suppress business competitors for economic or political purposes, forcing others to reach some kind of compromise, affecting others' reputation, or simply for moral and emotional needs, wanting to "seek justice" and "vent their anger" through the judiciary. Deep level needs are only the intrinsic drivers of superficial needs, with strong individuality, and the satisfaction of superficial needs is the prerequisite for achievement, so they are not easily discovered.

Based on the above analysis, this article's definition of judicial needs will focus on the core functions and external manifestations of judicial needs, which is both in line with general understanding and practical. In short, the judicial demand referred to in this article refers to the clear desire of social entities to seek and have the ability to afford court judgment services when disputes arise. At the same time, referring to existing literature, the volume of court litigation cases can serve as an appropriate proxy variable for judicial demand in empirical research.

Finally, it should be noted that this article mainly interprets judicial needs from a social or civil perspective. It cannot be denied that judicial needs may vary in their generation logic due to differences in the nature of the case and the participating parties. For example, the demand in criminal matters focuses on the national need to combat criminal behavior, the demand in administrative matters focuses on the individual need to resist government administrative violations, and the demand in civil matters focuses on the social need for equal subjects to resolve disputes. Among them, the identification of social oriented needs has stronger theoretical and practical significance. Firstly, theoretically, the demand for civil justice has strong social initiative. Compared to criminal and administrative demands, it is not constrained by internal political structures and can more effectively demonstrate the "state society" interactive relationship in terms of supply and demand. Moreover, from the perspective of theoretical explanatory power, both crime and administrative violations belong to broad social conflicts. Therefore, in terms of understanding the formation of conflicts, there is a certain commonality between the formation mechanism of civil judicial needs and the other two. Explaining the former is also helpful in understanding the latter. Secondly, this orientation can better reflect the real situation. According to the first instance case volume data of the China Legal Yearbook, civil cases were the main component of judicial demand from 1997 to 2020, accounting for over 84%, far higher than criminal and administrative cases.

2.2. The spatial effect on judicial demand

This article conceptually regards space as a physical geographical space. According to the basic understanding of modern geography, the simplest understanding of geographic space is a surface area. From a vertical perspective, a surface area with a range size is a "site" where natural things exist and social things and their relationships arise in human life and production activities. The things and their relationships within these geographic spaces constitute the geographic elements or attributes within the space at the group level. From a horizontal perspective, a surface area can also be divided into multiple continuous areas of different sizes. The distance and relative position between these areas affect the flow and interdependence of human beings themselves, as well as the transmission, reception, and interaction of social things such as knowledge, habits, culture, economy, and politics created by humans, resulting in various patterns of human social phenomena on the surface. In this sense, geographic space has basic characteristics such as distance, relative position, accessibility, agglomeration, and scale. Among them, distance is the most fundamental. It can not only measure and describe the length of regional boundaries, the relative position of regions, and the degree of correlation between different regions, but also have an impact on human behavior. For example, people gather together to reduce communication and survival costs caused by distance. Under the concept of geographic space mentioned above, the spatial effects in geographic analysis refer to the basic characteristics of the geographic space in which a certain social object is studied, the different positions of the object and other related objects in space, and the resulting spatial relationships that affect the changes in the object. In short, the spatial effect of this article aims to reveal the shaping and adjusting effects of geographic space and its relationships on human social affairs and their relationships.

This effect can be divided into two basic aspects: spatial dependence and spatial heterogeneity. The former is reflected in the first law of geography, which states that the closer things are, the higher their spatial correlation, also known as the proximity effect; The latter refers to the differences in the distribution and relationship structure of the same thing or geographical element within a spatial unit due to the influence of the size and shape of the spatial unit, resulting in inconsistent performance results of things. In practical terms, spatial heterogeneity emphasizes the spatial differences in the development process of things, or the instability of the causal mechanisms, which helps to draw more reliable conclusions in parameter estimation, while spatial dependence pays more attention to the spatial similarity of the characteristics and formation processes of neighboring things, which is conducive to identifying valuable spatial distribution patterns.

Judicial demand is a manifestation of human social activity, without exception, it has spatial dependence. As the saying goes, the soil nurtures the people. Different customs vary from a hundred miles, and different customs vary from a thousand miles. Due to frequent population movements and close socio-economic interactions in neighboring areas, cross domain disputes and related litigation are often more common between them than between distant regions, making it more likely for similar types of judicial needs to arise in neighboring areas. For example, with the continuous promotion of regional integration in the Yangtze River Delta, there are increasingly more cross regional dispute cases between Shanghai, Jiangsu, Zhejiang, and Anhui, which are geographically closely related. According to reports, in 2021, the number of civil and commercial cases involving Jiangsu, Zhejiang, and Shanghai enterprises concluded by Anhui courts alone reached more than 15000, and showed an increasing trend. In addition, regions that are closer in distance often have similar natural endowments, economic conditions, cultural customs, etc., and are more likely to face similar social problems and public litigation awareness. Therefore, there is a tendency for judicial needs to converge. A study on the spatial configuration of people's courts pointed out that there are significant differences in population density, terrain and rivers, and economic development among the eastern, central, and western regions, which also have different demands for people's courts. Therefore, the number and jurisdiction of people's courts should be dynamically adjusted in each of the three regions. Regardless of whether it is accurate or not, this common pattern of empirical division at least reflects its inherent logic: the closer the spatial distance, the more likely the relevant regions are to exhibit a gathering trend and proximity effect in terms of judicial demand.

Moreover, the formation of judicial demand also exhibits spatial heterogeneity. This judgment can be theoretically supported by legal geography. As an extension of the spatial shift of human geography and social theory in legal research, the fundamental position of legal geography is that legal activities require scenarios. For example, there are differences in legal protection between urban and rural areas, significant differences in legal demands between rich and poor regions, and the actual performance of judicial actions with homogeneity at the normative level in specific spatial environments often varies greatly. This indicates that the social attributes and structures formed based on geographic space vary due to differences in physical characteristics such as location, size, and form, so the influencing factors and mechanisms of legal behavior also have spatial differences. Essentially, this is not a viewpoint unique to modern legal geography. As early as the Enlightenment period in the 18th century, French philosopher Montesquieu pointed out in "The Spirit of Law" that the geographical environment has a decisive impact on the formation of a country's political system and laws. Therefore, as something closely related to legal phenomena, it is reasonable to assume that the formation mechanism of judicial demand has spatial heterogeneity.

The hypothesis of spatial heterogeneity is not mutually exclusive with the theoretical assumptions about the factors influencing judicial demand in traditional research. When there are multiple regions, the former can be considered as a supplement or correction to the latter. The existing explanatory theories generally assume that the relationship between judicial demand and its influencing factors is consistent and fixed across all regions. On the contrary, the assumption of spatial heterogeneity suggests that this relationship varies with the location and distance between regions. A certain factor may have a strong positive correlation with judicial demand in one region, while in another region it may have a weak positive correlation, negative correlation, or no correlation. Only by combining spatial heterogeneity with existing explanatory theories can we truly understand the reasons for regional differences. Therefore, traditional theoretical achievements can still serve as the theoretical analysis basis for this article, but ultimately need to be tested and explained in each region and the larger spatial scope they constitute. The following will outline the possible factors and their effects that may affect judicial demand.

2.3 The main influencing factors and their roles in judicial demand

As defined by the aforementioned concepts, "conflict litigation" constitutes the basic logic of the generation of judicial demand, that is, judicial demand is based on contradictions and conflicts as the core premise, and the intervention of judicial power as the condition for its occurrence. In other words, judicial demand is equivalent to the product of the number of disputes and the willingness to sue. Therefore, in theory, factors that create disputes or affect litigation willingness can explain judicial needs. These factors can generally be divided into two categories: one is bottom-up, grassroots led factors, and the other is top-down, state driven factors.

Grassroots dominant factors are a type of spontaneous formation within the grassroots level of society, which can directly, horizontally, and diffusely influence the behavior of individuals in conflict generation and litigation choices by changing their way of survival and shaping social relationships, including population density, urbanization process, economic development, education level, etc. The following elaborates on these specific factors and their ways of action.

Firstly, disputes arise in the process of interpersonal relationships, and the population of a country or region determines the potential dispute base of society. The growth and aggregation of population have led to an expansion of interpersonal communication, resulting in an increase in the number of disputes, and more disputes will be resolved through judicial means. Therefore, population factors, especially population density, will undoubtedly have the most basic and direct driving effect on judicial demand.

Secondly, the urbanization process in modern society promotes the transformation of social interaction patterns. On the one hand, a large number of laborers are gathering in cities, and the relationship between life and production is becoming increasingly complex, leading to more conflicts and disputes. On the other hand, the traditional "acquaintance society" has shifted towards a "stranger society". The bonds of kinship and morality that maintain interpersonal relationships have broken, and people have begun to view interpersonal relationships with a rational and equal mindset. The way of getting along has also transitioned from collectivism to individual liberalism. At this point, the parties involved in the dispute are more inclined to use formal litigation channels to resolve the dispute due to the lack of strong emotional constraints and third-party intervention mechanisms. Therefore, urbanization may have a positive driving effect on the demand for justice.

Thirdly, the impact of economic development on judicial demand consists of two aspects. Economic development not only affects the degree of regulatory uncertainty, but also adjusts the relative benefits of litigation, thereby affecting judicial demand. Specifically, in the process of modern economic development, the traditional production mode dominated by agriculture is transforming into a modern production mode dominated by industry. The emerging production modes and relationships not only generate more disputes, but also bring new social problems. However, in the early stages of this process, the existing social norms were difficult to solve these new problems, and the uncertainty of norms increased. The demand for the public to seek court resolution of new disputes and establish new norms increased. As the economic development enters a mature stage, the applicable norms are gradually established, and the rationalization and complexity of the law reduce the judicial needs of dispute parties to solve real "legal problems". Judicial activities show a trend of "routine management", and the positive impact of economic development on judicial needs gradually weakens. In addition, economic development can increase social wealth and improve individual living standards, thereby changing the relative costs and benefits of litigation and influencing individual litigation choices and needs. On the one hand, the parties involved in the dispute are more capable of bearing the litigation costs and tend to prefer judicial resolution; On the other hand, as the average wealth of society continues to grow, the opportunity cost of litigation increases, the litigation value of small disputes decreases, and the demand for justice may correspondingly decrease. In general, both positive and negative correlations may occur in the relationship between economic development and judicial needs.

Fourthly, the legal awareness and legal ability of the public are closely related to their level of education. Especially in China, legal and moral education is a fundamental component of the national education system. The higher the education level of a group, the clearer their understanding of the rule of law, higher judicial recognition, stronger awareness of rights protection, and more inclined to seek judicial intervention when encountering disputes. At the same time, the highly educated group not only has more legal knowledge compared to the low educated group, but also leads in learning and understanding legal rules and procedures, as well as handling complex information. For this group of people, they are more likely to have an advantage in litigation, resulting in lower litigation costs and higher willingness to sue. But in addition to having a promoting effect, educational factors may also play a inhibitory role. The cultivation of legal awareness not only includes the concept of rights, but also the concept of law-abiding and obligation. Therefore, the overall education level of society may promote more compliance with rules, reduce conflicts, and lower the demand for justice. Therefore, both positive and negative effects of education on judicial needs may exist.

Relatively speaking, state driven factors refer to a type of factor created and imposed by the state on society, which indirectly, vertically, and selectively intervenes in the behavior of individuals in conflict and litigation choices through means such as command and authorization to regulate social relations, such as government governance.

Among them, the governance role of the government in maintaining social order and stability cannot be ignored. The current social governance work often advocates learning from the "Fengqiao experience" and resolving conflicts at the grassroots level. This essentially requires the government to enhance its management initiative, strengthen the collection of information on grassroots social life, cooperate with courts, social organizations, and industry organizations, intervene in a timely manner when conflicts arise, solve livelihood problems from the source in a diverse and effective manner, resolve social conflicts, and reduce litigation cases. In this sense, the improvement of government governance capacity has a restraining effect on judicial demand. Government governance capacity is a comprehensive concept that includes structural elements, but the exertion of capacity must rely on the fundamental element of resources. The larger the size of the government, the more abundant the reserve of human resources. Therefore, the size of the government will serve as a proxy variable for its governance capacity, perhaps negatively correlated with judicial demand.

In addition, unified laws must demonstrate their true effectiveness through judicial practice. In this sense, the lawyer profession is deeply involved in daily legal practice, and the availability of legal services largely represents the level of legalization in reality. Specifically, the professionalism and complexity of law often force parties to disputes to seek advice from lawyers, in order to rationally judge the pros and cons of litigation, decide whether there is a need to go to court, and avoid unnecessary litigation. But sometimes, especially when the legal profession is saturated and highly competitive, a significant increase in the availability of legal services can also increase judicial demand. This is because lawyers may give clients higher and inappropriate litigation expectations in order to obtain the source of the case. Therefore, this article believes that the availability of legal services may be positively or negatively correlated with judicial demand in theory.

In summary, this article assumes from a geographical perspective that spatial effects exist on the judicial needs and their causes that target court trials. To test this hypothesis and derive meaningful spatial types from it, subsequent empirical analysis will focus on three specific sub questions: firstly, what are the spatial distribution characteristics of China's judicial demand and whether it has spatial dependence? Secondly, does the influence of state driven and grassroots led factors have spatial heterogeneity? Thirdly, what types of judicial demand space can be reconstructed based on the explanatory analysis results obtained from answering the aforementioned questions, in order to more effectively help solve the spatial imbalance problem of judicial supply and demand?

3. Data sources, variable settings, and identification strategies

3.1 Data source

The litigation case volume data used in this article mainly comes from the provincial yearbooks of 31 provinces, autonomous regions, and municipalities directly under the central government in China from 1997 to 2020. Unlike the formatted data of provincial statistical yearbooks, provincial yearbooks are generally compiled and published in text form by professional institutions of the local chronicles compilation committees of each province, autonomous region, and city. The chapters such as "Court" or "Trial" in the yearbook generally record the litigation case volume data provided by the court. Therefore, we have conducted a thorough and rigorous manual sorting of relevant textual materials in all provincial yearbooks. At the same time, all other materials containing case volume data should be collected as much as possible, including work reports of higher people's courts in various provinces, regions, and cities, judicial statistical data publicly available on the websites of higher people's courts, provincial statistical yearbooks, and local chronicles. After extracting data from it, the provincial yearbook data was verified, corrected, and supplemented to ensure the authenticity and completeness of the data. Based on this, linear interpolation was used to fill in a small amount of missing data during the research period, resulting in 744 structured case volume data.

The data sources for the remaining variables are quite diverse. Specifically, the per capita real GDP, number of permanent residents per square kilometer, urbanization rate, and per capita years of education are calculated from relevant data in the annual "China Statistical Yearbook", "Compilation of Statistical Data for the Sixty Years of New China", and the National Administrative Division Query Platform of the Ministry of Civil Affairs; The number of employees in government agencies comes from the "China Labor Statistics Yearbook"; The number of practicing lawyers is compiled from data from the "China Lawyer Yearbook" and provincial statistical yearbooks. Therefore, this article constructs a balanced panel data of provincial-level judicial demand in China from 1997 to 2020. The descriptive statistics of data and variables are shown in Table 1.

Table 1 Descriptive statistical results of each variable

3.2 Variable settings

As mentioned earlier, the volume of litigation cases is a suitable proxy variable for judicial demand. Therefore, this article chooses the volume of cases concluded per square kilometer as the specific dependent variable to measure judicial demand. It should be noted that the first instance procedure is the first litigation procedure initiated by the court for a certain dispute, so it is equivalent to the first direct expression of judicial needs. In addition, although theoretically the number of cases received is more accurate, there are currently difficulties in applying data. The statistical caliber of the number of cases received is not consistent, and there are differences in whether to include the number of old cases from the previous year in yearbooks from different years or provinces. In contrast, the indicator of settlement volume remains consistent across all yearbooks, including both new and old cases. The key is that under China's strict trial limit system, the number of cases closed in the first instance is almost equal to the number of cases received, so it can also better reflect judicial needs. Finally, to achieve regional horizontal comparison, variables are expressed in relative numbers. Regarding the measurement of explanatory factors, the variable settings are as follows. Firstly, the number of permanent residents per square kilometer represents population density. Second, the urbanization rate, that is, the percentage of urban registered residence population in the regional population, represents the process of urbanization. Thirdly, dividing the actual GDP of 1995 as the base year by the number of permanent residents, the per capita real GDP is obtained to represent the level of economic development. Fourthly, the per capita years of education is an indicator for measuring the level of education. The calculation method is to multiply the number of people in each education stage by the corresponding years of education, add them up, and divide by the number of permanent residents over 6 years old. Fifth, the employment ratio of government agencies, which refers to the percentage of employment in government agencies to the total employment, is used to measure the government's governance capacity from the perspective of government size. Sixth, the accessibility of legal services is measured by the number of full-time lawyers per 10000 permanent residents.

3.3 Identification strategy

In terms of analysis methods and identification strategies, this article first uses Moran's index I to explore spatial autocorrelation problems, in order to discover spatial dependence and proximity effects; Secondly, using a spatiotemporal geographically weighted regression model, incorporating spatial scale factors, comparing its explanatory power with general linear regression models, revealing spatial heterogeneity and its methodological significance, and obtaining more effective parameter estimates; Finally, based on the parameter estimation results of explanatory factors in various regions, the K-means clustering analysis method was used to identify several spatial types and interpret them according to the dominant factors. The specific research methods are explained as follows.

3.3.1 Moran's index I.

Moran's I is a common measure of global spatial autocorrelation. Spatial autocorrelation refers to the correlation between regions in certain attribute values (variable values representing certain natural or human social phenomena in space), and the degree of correlation is characterized by a "far small near large" relationship due to distance. In other words, the attribute values of a certain region have spatial autocorrelation, that is, there are spatial dependencies and proximity effects; On the contrary, there is no spatial dependency. The spatial autocorrelation test is usually a prerequisite for conducting statistical analysis of spatial heterogeneity. In terms of specific testing, the Moran's index I ranges from -1 to 1. When the index is greater than 0, it indicates that there is a spatial positive correlation between judicial demand, and regions with consistent demand levels show a clustering trend; When the index is less than 0, there is a spatial negative correlation between judicial demand, indicating that regions with opposite levels of demand tend to cluster, or regions with consistent levels tend to disperse; When the index is equal to 0, there is no spatial autocorrelation in judicial demand, and there is no need to use spatial statistical models. The calculation formula for this index is as follows.

In the formula(1), xi and xj represent the judicial demand of the i-th and j-th regional units, n represents the total number of regional units, and S2 represent the mean and variance of the judicial demand of all regional units, respectively. Wij is a spatial weight matrix conceptualized based on adjacent edge corner spatial relationships.

3.3.2 Spatiotemporal geographically weighted regression.

The General Least Squares (OLS) method, as a traditional statistical model for studying correlations, holds the assumption of spatial independence and assumes that variable relationships remain consistent in the global space. Therefore, it cannot identify local characteristic differences caused by geographical location differences, and the effectiveness of parameter estimation results is limited. Regarding this, geographically weighted regression improved the OLS model by taking into account spatial heterogeneity and allowing parameter estimation of variable relationships to form independent results based on spatial characteristics. However, in addition to spatial heterogeneity, judicial demand may also be influenced by complex temporal changes, and the formation of litigation cases may be impacted by external events at specific times, such as legal system reforms. Therefore, Geographically and Temporarily Weighted Regression (GTWR) increases the consideration of temporal heterogeneity and incorporates the temporal instability of parameter estimation into the classical Geographically Weighted Regression model, which can more effectively and accurately reveal the spatiotemporal dynamic characteristics of the factors influencing judicial demand coefficients and help to derive better explanatory theories. The formula is expressed as follows...

In the formula(2), i represents regional units in different time and space, and Yi refers to the judicial needs of regional units in different time and space; (ui, vi, ti) is the spatiotemporal coordinate of the i-th regional unit; UI, VI, and TI respectively represent the longitude, latitude, and time of the center of gravity of a specific unit; Xik is the observation value of the k-th explanatory variable on the regional unit (ui, vi, ti); β k (ui, vi, ti) is the explanatory variable coefficient; β 0 (ui, vi, ti) is a constant term; ε i is the error term of an independent random distribution.

3.3.3 K-means clustering analysis.

The demand for justice is influenced by multiple repetitive and complex factors, and simply dividing it based on economic and geographical characteristics cannot fully reflect the actual spatial differences in the influencing mechanism, while manual classification is subjective and speculative. Therefore, this article uses the K-means clustering algorithm to objectively generate spatial clustering structures and explore their dominant factors, achieving more accurate spatial typing from an explanatory perspective. This model uses an iterative method to find k clusters, minimizing the sum of squared distances between each data point in the cluster and the center of the class. The algorithm steps can be summarized as follows: first, determine the number of k clusters to be searched for, randomly select k data points from the dataset as initial class centers, classify the remaining data into corresponding clusters according to the nearest distance principle, calculate the mean of all objects in each cluster, and use it as the new class center for reclassification. Then, adjust the class center and classification repeatedly using the same method until the results converge. The formula is expressed as follows.

In the formula(3) , J (C, μ) is the sum of squared distances from each data point to its corresponding class center; Cj is the jth cluster; Xi is the data point of the jth cluster; The class center of the jth cluster; K is the number of clusters.

4. Empirical results

4.1 Spatial evolution characteristics and spatial autocorrelation analysis

This article divides the sample into five categories based on the quintiles of one case per square kilometer, including high value area, second highest value area, median area, second lowest value area, and low value area. At the same time, for the sake of simplicity, relevant data from 1997, 2008, and 2020 are selected according to the time division criteria for display. Thus, Table 2 reveals the dynamic spatial distribution characteristics of the evolution of China's judicial demand from "gathering in the east" to "spreading in the central and western regions". Specifically, from 1997 to 2008, eastern provinces and cities such as Shanghai, Beijing, Tianjin, Jiangsu, Shandong, and Zhejiang were located in high-value or sub high value areas for a long time, and the demand for justice was at a relatively high level nationwide, with a clear trend of clustering in the east. Among them, Shanghai has the highest value, increasing from 17.878 cases/square kilometer to 37.206 cases/square kilometer, with an increase of 108.111%. In contrast, the central and western regions such as Hubei, Hunan, and Sichuan have experienced a certain degree of decline during this period, with the number of cases concluded in the first instance decreasing from 1.783 cases/square kilometer, 1.512 cases/square kilometer, and 0.626 cases/square kilometer to 0.888 cases/square kilometer, 0.777 cases/square kilometer, and 0.525 cases/square kilometer, respectively. By 2020, most of the high-value areas for judicial demand were still concentrated in the eastern coastal areas, with Shanghai ranking first at 90.367 cases per square kilometer. The two provinces with the highest demand outside of municipalities were Jiangsu and Guangdong, reaching 8.708 cases per square kilometer and 7.552 cases per square kilometer, respectively, an increase of 60.398% and 189.127% compared to 5.429 cases per square kilometer and 2.612 cases per square kilometer in 2008. At the same time, there is a trend of expansion towards the central and western regions in high-value and sub high value areas. Guizhou, Chongqing, Jiangxi, Henan, Shaanxi, Anhui, Guangxi, Ningxia, and Hunan not only fall into these two categories, but also grow rapidly, with growth rates exceeding 200% compared to 2008, higher than almost all eastern regions. Although Qinghai, Xizang, Xinjiang and other places have been in low-lying areas for a long time, it is undeniable that during this period, the judicial demand in the central and western regions has a potential trend to catch up with the eastern region, and the gap between the east and the west has narrowed as a whole.

Table 2: Spatial Distribution of Judicial Demand in China in 1997, 2008, and 2020

Note: The numerical range indicates the number of cases concluded per square kilometer; The provincial regions within the cell are sorted in descending order of the number of cases concluded per square kilometer; The high-value areas with more than 10 cases per square kilometer include Shanghai in 1997 (17.878 cases per square kilometer), Shanghai in 2008 (37.206 cases per square kilometer), Shanghai in 2020 (90.367 cases per square kilometer), Beijing in 2008 (14.932 cases per square kilometer), Beijing in 2020 (27.479 cases per square kilometer), and Tianjin in 2020 (18.192 cases per square kilometer)..

In terms of testing spatial dependence, ArcGIS 10.4 software was used to measure the annual global Moran's index I of judicial demand from 1997 to 2020. Table 3 shows that during the study period, the global Moran's index I was greater than 0 and had statistical significance at the 5% level. The index showed a fluctuating downward trend within the range of 0.102-0.221, with an overall decline starting from 2002, a slight increase in 2008, and a slow downward trend in 2013. However, these results still consistently indicate that China's judicial demand has spatial dependence and long-term spatial positive correlation, with high and low judicial demand areas forming clusters in adjacent areas.

In summary, from a descriptive perspective, China's judicial demand does exhibit a relatively clear "differentiation between the East and the West" feature, but in recent years, this feature has shown a tendency to weaken or transform. At the same time, the results of the spatial autocorrelation test basically negate the hypothesis of spatial independence, so it is necessary to use statistical methods based on spatial heterogeneity to analyze the relevant influencing factors.

Table 3: Global Moran Index of Judicial Demand in China from 1997 to 2020

Note: *, * *, * * * represent significance levels of 10%, 5%, and 1%, respectively.

4.2 Analysis of spatial heterogeneity of influencing factors

Table 4 presents the regression analysis results of the factors influencing judicial demand using the traditional OLS model and GTWR model. To ensure comparability of the regression coefficients, all variables have been standardized. From this, it can be seen that the variance inflation factor (VIF) of each variable is less than 5, indicating that there is no serious multicollinearity problem and the variable selection is reasonable. In terms of model adaptation, the GTWR model has an 8% higher explanatory power than the OLS model in adjusted R2, and can explain 98.7% of changes in judicial demand. Moreover, the former's Akaike Information Criterion (AICc) is 1294.289 lower than the latter, at -939.91, indicating a significant decrease in the amount of undisclosed information. Therefore, the GTWR model outperforms the traditional OLS model in spatial heterogeneity analysis, with a higher degree of fitting to the spatial evolution of judicial demand and better explanatory power.