Conceptualization of policy diffusion

As a process of knowledge production, the study of policy diffusion originated in the United States and is widely applied in political science and public administration as a key theory of policy change [8]. Policy diffusion is defined as the process by which an innovation is communicated among members of a social system, through certain channels over time [9]. Furthermore, it allows an innovation policy to spread to its users [10]. The diffusion of an innovation policy requires two actors: a policy disseminator, who passes on new ideas, policies, and programs to a policy recipient, and the policy recipient themselves [11]. The diffusion of public policy occurs when a government’s decisions are influenced by other governments [12]. Scholarly attention to the phenomenon of policy diffusion adoption over time has increased [13,14]. Numerous concepts with overlapping boundaries have emerged, such as policy convergence, transfer [15], emulation [16], learning [17], and lesson learning [18]. Furthermore, All these involve the mobility or diffusion of policy innovations from government to government and indirectly have the same characteristics. Policy diffusion differs from it by characterizing diffusion as a continuum, encompassing all points within the system [19].

Research history of policy diffusion

Policy diffusion emerged as a field of research in the 1960s, with American scholars initially focusing on policy adoption, exploring why particular states adopt certain policies and not others [20]. Such research in political science also pioneered the use of event history and regression analyses to empirically model policy diffusion across states, which led to the concept of a new diffusion paradigm [20]. Based on Walker’s research, Gray [21] examined the diffusion of multiple policies. In the area of government-incentive behavior, Welch and Thompson [22] proposed that policies with federal incentives diffused faster than those without incentives based on motivation theory. In 1990, some scholars integrated national characteristics with regional diffusion models, proposing the concept of national policy diffusion model transformation. This perspective highlighted the interaction between national and regional traits in the policy diffusion process, offering a new lens for multidimensional studies on policy diffusion [23]. In the same year, numerous studies focused on government implementation of national policies at the grassroots level [24–26]. However, these studies emphasized macro-level factors, such as spatial, temporal, and hierarchical dimensions of policy diffusion, with limited attention to the micro-level actions of local governments in adapting and updating policy texts according to local development needs.

Theoretical characterization of policy diffusion

As a process that facilitates policy exchange [27], the diffusion of policy innovations involves policy transfer. However, policy transfer emphasizes transfers between political systems [15] and is the application of public policies, administrative arrangements, and institutions located in one spatio-temporal context to other such contexts [28]. In terms of spatial diffusion, the diffusion mode describes how policies spread geographically and is characterized by extensibility and migration [29]. Regarding the development process of policy diffusion in terms of time, space, and organizational hierarchy, an S-shaped curve exists in the time dimension, a “proximity effect” in the spatial dimension, and a “leader–follower” effect in the hierarchy dimension. The spatial dimension is characterized by a “proximity effect” and a “leader–follower” cascading effect within regions [30].

However, which forces drive policy diffusion in the spatial-diffusion process? In terms of political forces, central government organizations, national organizations, and policy promoters drive the diffusion of public policies [31]. When variety of innovative policies are adopted and diffusion occurs, policy diffusion mechanisms emerge. In terms of policy diffusion dynamics, two main types of models—internal decision and external influence models [32]—are distinguished by the learning effect of early policy adopters, economic competition among neighboring cities, strong promotion by state governments, and imitation among large cities [33]. These effects are summarized by the terms “learning,” “competition,” “coercion,” and “imitation,” respectively [34]. Learning, competition, coercion, and constructivist theories provide the theoretical basis for policy diffusion [12].

Influencing factors of policy diffusion

Domestic and international policy diffusion studies, have primarily examined external and internal factors. The external environmental factors influencing local governments’ policy adoption are attributable to the policy pressures exerted by higher-level and peer governments [35]. This study categorizes these influences into two modes of policy diffusion: top-down vertical diffusion [36] and horizontal diffusion among peer governments [37]. In China’s pressure-driven system, higher-level authorities typically establish policy targets and performance evaluation criteria, requiring local governments to comply with central directives, mandates, or regulations. This dynamic, referred to as central government policy pressure [38], compels local governments not only to conform but also to implement policies promptly in response to central authority. Additionally, local governments may actively adopt and reproduce policy texts to attract the attention of higher authorities and secure political or economic incentives, thereby promoting policy diffusion [39]. Alongside vertical policy diffusion, horizontal learning effects among local governments play a crucial role. This process involves an interactive mechanism among peer governments. Successful experiences in adopting and implementing sports policies are observed and emulated through meetings, forums, and research exchanges; this enables local governments to adjust and optimize their policies, thereby minimizing the cost and risk of policy innovation [40]. Consequently, both top-down legitimacy pressures and horizontal learning between peer governments significantly influence local governments’ policy adoption [41].

Regarding internal factors, local governments’ policy diffusion often depends on factors such as economic capacity, governance quality, urban structure, and population size [2,42]. This is because local government officials’ promotion prospects are often tied to economic performance [43]. Economic development not only dictates local governments’ fiscal capacity but also implies an ability to allocate resources such as funding effectively to ensure policy implementation [44]. This grants them greater flexibility in policy adoption and innovation. Population size directly reflects the complexity and scope of policy implementation at the local level. The success of sports facilities and public sports policies often depends on the locality’s population size and characteristics; when investing in sports infrastructure, local governments must consider these aspects to meet residents’ needs [45].

In policy diffusion, sports organizations act as direct agents of policy by organizing, promoting, and advocating, thereby aiding policy implementation at the grassroots level and providing valuable feedback for policy optimization [46]. Sports organizations can foster community identity through activities, enhancing trust and collaboration between residents and local governments [47]. They play an important role in connecting governments and communities, promoting social integration [48]. As living standards rise, residents’ demands for health and recreational activities increase, directly prompting local governments to prioritize investments and attention to sports policies. Public demand sports has a dual effect on policy diffusion: on the one hand, strong demand motivates local governments to adopt and promote related policies [49]; on the other hand, it provides a foundation for local governments to reproduce policy texts in ways that align with local needs [50].

Scholars have increasingly recognized that policy diffusion is not only a transmission process but also a dynamic one in which local governments innovate and reproduce policies based on specific needs. Particularly in sports policy, local governments face diverse regional economic, social, and cultural contexts; this promps them to refine or modify central policies in the adoption process to reflect the effects of local endowments [51]. Based on the literature, we identify identifies six secondary indicators: economic level, population size, sports organizations, public sports demand, central government policy pressure, and learning effect. The current scholarship provides a theoretical basis and framework for selecting factors that influence policy diffusion. However it does not systematically explain how these factors guide local governments’ decisions around passive compliance or active innovation in the context of sports policy text reproduction. This study aims to expand upon policy diffusion theory by addressing this gap, offering a more nuanced understanding of local governments’ behavior in the diffusion process.

Policy adoption and policy reproduction

Policy adoption is commonly used to analyze local governments’ behavior in implementing policies issued by the central government within the formal institutional framework. Existing studies have primarily examined how a government’s policy choices are influenced by higher-level or peer governments from the perspective of policy diffusion [40]. After the central government releases a policy, various local governments not only adopt it but also engage in innovative policymaking, updating, and refining policy text content [52]. However, most studies have viewed policy adoption as a passive process and overlooked the proactive adjustments or autonomous innovations in policy content made by local governments in policy content during adoption. Additionally, comprehensive studies of the sports sector are lacking, especially in terms of a systematic theoretical framework to explain which factors most significantly influence provincial governments’ policy text reproduction behaviors. This study considers the reproduction of public sports policy texts as a critical innovation within policy diffusion theory. It addresses gaps in the study of sports policy diffusion and offers a deeper understanding of local governments’ decision-making behaviors.

Grey correlation analysis method

The grey correlation analysis method is a tool for evaluating and describing the relationships between factors. It is especially useful in systems with limited or uncertain data, as it reveals the degree of association among variables [53]. It also identifies and ranks the influence of various factors on a target variable, indicating which factors are most closely related to the target [54]. This method focuses on the association between factors rather than absolute values, which allows to assess relative influence even with incomplete data. By contrast, regression analysis typically requires a complete dataset and assumes a normal distribution, emphasizing causal relationships but facing limitations in handling complex dynamic interactions [55]. Although qualitative research can provide understanding, it struggles with quantifying factor impacts across large samples, potentially leading to imprecision. The grey correlation analysis method calculates the similarity between reference and comparison sequences to quantify their association [56]. Therefore, it is the most suitable method for this study.

Step 1: Construct the Reference Sequence and Comparison Sequence. We set the reference sequence of the system as X₀, with the formula as follows:

This is a time series, where t represents a specific year, and each x₀ (t) indicates the value of the reference variable at time t. The m sequences to be compared with the reference sequence are set as X_i, with the formula as follows:

where m represents the number of comparison sequences (i.e., the number of influencing factors), and x_i (t) is the observed value of the i comparison sequence at time t.

Step 2: Calculate the Difference Sequence. Define the difference sequence as Δ_i(t), with the formula as follows:

Using the above formula, we obtain m difference sequences Δ_i(t), where t = 1,2,…,n.

Step 3: Determine the Maximum and Minimum Difference Values. To ensure comparability on a unified scale in the following steps, we calculate the maximum and minimum values of the difference sequences as follows:

The formula identifies the maximum and minimum difference values across all sequences i and time points t.

Step 4: Calculate the grey correlation coefficient, which indicates the similarity between the reference sequence X₀ and each comparison sequence X_i at each time point, using the following formula:

The parameter ρ is the distinguishing coefficient, which typically takes values in the range [0,1] [57].

In recent years, numerous scholars have applied the grey correlation analysis method to fields such as sports tourism, the sports industry, and the digital economy [44,58,59], demonstrating its utility. However, in the study of sports policy diffusion, this method has not yet been widely adopted. Current research in sports policy tends to rely on qualitative analysis or traditional quantitative methods, which often struggle to capture the complex interactions between factors in policy diffusion processes. This study employs the grey correlation analysis method [57] to explore the correlation between provincial policy text reproduction and the factors influencing public sports policy diffusion. It offers a new perspective for quantitatively assessing complex dynamic relationships.

Design of data indicators

Policy diffusion research has focused on the process whereby one entity adopts an innovative policy introduced by another. Consequently, the factors influencing the diffusion of China’s public sports policies should reflect the elements that affect local governments’ policy adoption. This study employs a two-tier indicator system to represent the policy diffusion process on various levels (see Table 1).

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Table 1. Factors influencing the proliferation of the main public policies in the field of sports.

https://doi.org/10.1371/journal.pone.0320651.t001

We derive the primary indicators in this research—policy subjects, policy objects, and policy environment—are derived from established policy science frameworks. Policy subjects are individuals, groups, or organizations directly or indirectly involved in policy formulation, execution, evaluation, and monitoring [5]. As the subjects of provincial governments directly shape policy reproduction, this research identifies provincial governments as the primary policy actors [60]. Policy objects are the entities affected by policies and play a key role in policy acceptance, implementation, and feedback [61]. Within policy diffusion, policy objects need to be covered by the policy and should actively engage and respond positively to its implementation. The policy environment encompasses all factors that influence the policy’s development, existence, and progression [62]. In China’s pressure-driven system, both higher-level and peer governments influence provincial governments’ policy behaviors, facilitating or hindering broader policy diffusion.

We develop the secondary indicators of this study are developed based on the primary indicators, which include economic level, population size, sports organizations, public sports demand, central government policy pressure, and learning effect.

The study designates economic level (annual GDP) and population size (end-of-year population total) as secondary indicators under the primary indicator of “policy actor”. GDP, representing overall economic strength, provides a comprehensive reflection of the local government’s economic status and policy implementation capacity, more so than other economic indicators such as per capita income or fiscal expenditure, it thus offers a macro-level perspective [63]. Population size reflects the scope of public service demand and the extent of resource allocation pressures on local governments. Using year-end population totals enables tracking dynamic changes over time, thus showing the pressures faced by local governments in terms of resource distribution, infrastructure, and policy execution [64].

Sports organizations (annual number of sports organizations) and public sports demand (ratio of urban population to total year-end population) are included as secondary indicators under the policy targets. The number of sports organizations is an important indicator of community engagement [65]. A high number signifies a robust network linking local governments and grassroots society. Urban population ratio reflects changes in geographic population distribution and indicates potential demand intensity for sports facilities and activities, with higher urbanization indicating stronger public demand for sports services. Population size provides a basis for policy coverage; however, public sports demand is a driving force influencing policy adaptation and reproduction, representing both the breadth and depth of policy diffusion.

“Central government policy pressure” represents the influence exerted by the central government on provincial governments to ensure compliance with higher-level requirements and objectives. It is measured by the volume of policies issued by the central government and the 31 provincial governments. Simply calculating the adoption ratio may lead to imbalance as the central government releases fewer policies each year, whereas provincial governments adopt and issue them in large quantities. Therefore, we introduce an adjustment factor is introduced to account for the frequency of policy issuance, balancing central policy output and provincial policy adoption, resulting in a more accurate measure of the central government’s policy pressure. The calculation formula for central government policy pressure is as follows:

The central government issued 10 policies, which were adopted 172 times by provincial governments, while the total number of policies issued by provincial governments was 249. The parameter α is set to 0.5 by default, striking a balance by neither over-sensitizing the model to differences nor excessively smoothing it. This setting allows for an objectively reflecting on the relationships between different policies. Using −α reduces the influence of high provincial policy counts on central government policy pressure, ensuring that the significance of the latter is not diminished owing to an increase in the denominator.

Cross-regional policy diffusion research has recognized the learning effect as a major driving force. By analyzing and observing policy effects in neighboring or similarly developed areas, regions can better align their policies with local needs and circumstances. The formula for calculating the learning effect is as follows:

Data sources and calculation procedures

This study uses the total number of reproduced public sports policy texts in China’s 31 provinces from 2016–2021 as a benchmark, including both policies adopted from central government initiatives and independently developed innovations. Covering all provinces, autonomous regions, municipalities, and special administrative regions, this scope ensures diverse sample representation across economic levels, enhancing the study’s relevance. The period from 2016 to 2021 marks a pivotal transition in Chinese sports policy, from focusing on public health to enhancing international athletic competitiveness, aligning with the dual goals set in the Healthy China 2030 Planning Outline. Following the 2021 Tokyo Olympics, this timeframe reflects not only the impact of these strategies but also the intensified domestic policy innovation; it thus provides a valuable window for observing the sustained effects of these sports policies.

In the grey correlation analysis method, the primary sequence (reference sequence) represents the main metric in the study, typically reflecting an overarching phenomenon to provide a baseline for comparison. The auxiliary sequences (comparative sequences) are related indicators that influence the primary sequence. This study designates the extent of reproduced public sports policies in 31 provinces from 2016 to 2021 (total policies issued by provincial governments) as the reference sequence. It sets each year’s secondary indicators, which capture factors influencing the diffusion of public sports policies, as comparative sequences.

The data for the reference sequence in this study are sourced from the 2024 Sports Policy Directory published by the General Administration of Sport of China, accessible at https://www.sport.gov.cn/gdnps/files/c28052072/28156549.pdf, as well as from the official portals of the 31 provincial governments (linked through the national government website: https://www.gov.cn) and of provincial sports departments (accessible at https://www.sport.gov.cn).

For the comparative sequences, data on economic level, population size, and public sports demand are derived from the China Statistical Yearbook (https://www.stats.gov.cn/sj/ndsj/), while information on sports organizations is available from the General Administration of Sport of China (https://www.sport.gov.cn). Data for central government policy pressure and learning effect are sourced from both the national government portal (https://www.gov.cn) and the provincial government and sports department websites.

The analysis steps are as follows: First, we establish the reference and comparative sequences functions are established. Second, we perform data normalization by calculating the mean of each data group and dividing each original value by this mean; therefore, we achieve a uniform scale across indicators and eliminating unit discrepancies. Third, we calculate the absolute differences between the reference and comparative sequences at each time point are calculated. Fourth, we process these differences through the grey correlation coefficient formula to derive correlation values. Finally, we determine the overall correlation degrees are determined from these values, This allows us to calculate each influencing factor’s final correlation degree [66].