1. Introduction: redefining sports spaces as places of justice

Sports are often regarded as a field that reflects an individual's athletic talent, efforts and competitive spirit. However, beneath the surface of sports victory lies a deeper issue of justice: Who has the opportunity to enter the sports space for training and competition? Although sports talent and hard training are praised, the prerequisites that make sports participation possible - such as accessible sports Spaces, operable sports equipment and community support - are rarely examined from the perspective of distributional justice. Analysis lacking a perspective of justice can have adverse effects. It will naturalize inequality in sports participation, thus viewing participation in sports as a personal issue rather than a matter of fair distribution of social sports resources [1].

This article holds that public sports infrastructure, including public sports fields, community gyms, swimming pools and recreational Spaces, must be redefined as basic rights of citizens rather than privileges accessible only to a few. To support this viewpoint, this paper constructs a normative theoretical analysis framework based on sports justice, extending the principle of distributive justice to the fields of sports and collective participation. The idea of sports justice holds that the opportunity to participate in sports activities is not a luxury but a necessary condition for the equal development of society. Therefore, it must be protected and distributed in accordance with the principles of fairness, equality and non-exclusion [2].

This argument is divided into three parts. Firstly, this paper utilizes Amartya Sen's competency analysis theory to explain how the lack of sports infrastructure inhibits the cultivation of human basic development capabilities. Secondly, this paper employs Michael Walzer's theory of complex equality to criticize the dominant position of economic forces in determining the distribution of sports opportunities, emphasizing that this violates the autonomy in the field of sports culture. Finally, this paper integrates these analyses into a unified framework for sports justice analysis, which redefines public sports Spaces as an important component of social equal development. The core conclusion of this thesis is that distributive justice not only involves the distribution of wealth or income, but also includes the right to freely and safely participate in sports in public sports Spaces.

2. The ability to move: a fundamental right to freedom

Amartya Sen's competency analysis shifts the analytical focus from social resources and wealth to freedom, focusing on what individuals can actually do and become, thereby changing the traditional theory of justice. In this framework, the criterion for measuring justice is not the distribution of goods, but the expansion of capabilities or the genuine opportunities for people to improve their living standards.

The core competencies listed by Sen include physical health, physical integrity and social participation. These are not abstract concepts but specific conditions for enhancing human well-being. Sports, as an activity that enhances physical health, regulates negative emotions and strengthens social connections, make direct contributions to all three. Participating in sports in a safe stadium not only ensures physical health but also helps to build personal resilience, teamwork skills and a sense of social identity. Adults who use public gyms can improve their cardiovascular health while also expanding their informal social networks. Therefore, sports are not an additional accessory to social development, but a component of human healthy development.

However, equal opportunities to participate in sports have not been fully realized. A person may have the idea and talent to participate in sports, but if there is a lack of safe, inclusive and well-maintained sports infrastructure around them, this ability cannot be achieved. As Sen emphasized, the realization of freedom requires an opportunity structure, including social, economic and spatial conditions, which enable individual agency to be realized. When government departments fail to provide such an opportunity structure, it is not merely a lack of a public service; They will weaken the ability of local residents to develop comprehensively [3].

It can be considered that if a child lives in a community lacking sports services and is unable to exercise due to the lack of space and facilities, their physical health ability will be weakened. If women are excluded from public sports Spaces due to cultural norms or the lack of gender segregation facilities, their ability to participate in society will be restricted. This is not an individual failure but a systemic injustice - the state has failed to ensure equal conditions for achieving capabilities [4].

Therefore, from the perspective of sports justice, public sports infrastructure is not only a necessary expenditure of the government but also a fundamental moral obligation. It is a means to expand individual freedom. Therefore, its distribution must be guided by the principle of fairly enhancing the capabilities of all people.

3. Complex equality and autonomy in the sports field

Amartyasen's framework can help understand why sports are crucial to social justice, while Michael Volzer's complex equality theory provides a theoretical tool for analyzing how resources should be allocated. Wolzer believed that a just society must maintain complex equality. In this society, different social resources, including money, education, political power and honor, etc., must be allocated according to their own logic. No single resource (especially money) can dominate the distribution of others.

In a society dominated by complex ideas of equality, one cannot purchase political positions, bribe judges or buy quality medical services through wealth. Each field of resources has its own operational logic: education is allocated based on individual characteristics and needs, political power is allocated according to democratic principles, and medical services are allocated based on the urgency of treatment [5].

As a social resource, public sports facilities should also follow their own principles, namely fairness, inclusiveness and collective participation. However, in contemporary urban life, the allocation of sports resources is increasingly dominated by market logic. Whether one has the opportunity to access sports facilities, receive high-quality training and compete is not determined by sports talent or ability, but by purchasing power.

This violates the principle of complex equality. When wealth becomes the main way to obtain opportunities to participate in sports, it turns sports from a public good into a commercialized privilege. Children from wealthy families can participate in Tours and receive personalized coaching - these advantages have nothing to do with talent, but are related to wealth [6].

Wolzer warned that such domination would lead to social stratification and erode the equal order of community life. When sports become a field that excludes the majority, it is no longer a place for diverse integration and common participation. On the contrary, it will intensify class division, making the privileged know that their children's success can be achieved through their parents' wealth, while the marginalized internalize failure as a personal defect.

Therefore, public sports infrastructure must be separated from other resources and protected as an independent domain, free from the influence of market forces. Its distribution should not be guided by income or wealth, but by the principles of equal access and social inclusion. Only in this way can sports venues realize their potential as Spaces for the integration of sports, democracy and society [7].

4. Principles of sports justice theory and criticism of elite politics

Based on existing research, this paper proposes a unified normative analysis framework: sports justice. This framework holds that the use of public sports infrastructure is a civil right, based on the principles of equal access, non-domination, and capacity enhancement,and it formed a critique of elitist politics [8].

4.1. Theoretical principles of sports justice

The first is the principle of equal access, which means that regardless of an individual's social and economic status, wealth or ability, they all have the right to obtain basic public sports space. This does not mean that all places have the same facilities, but rather that they should be configured based on demand and population density to ensure that no community is systematically deprived. The second principle is non-dominance, that is, no single social resource, especially economic conditions, can determine whether people participate in sports or deprive others of the opportunity to participate. Public infrastructure must remain free or low-cost, and its mechanism design and governance must resist commercialization and exclusive practices. The third principle is the capacity enhancement principle, which means that the design of sports infrastructure is not merely aimed at improving the level of the elite, but at expanding the capabilities of all citizens, including ensuring physical health, having emotional resilience, a sense of social belonging, and the ability to express oneself. This requires inclusive design and universal accessibility so as to serve the ordinary citizens of the local community. These principles logically conform to the norms of the established theory of justice. If feasibility is at the core of justice and sports resources must be separated from market domination, then sports justice will become a necessary extension that follows [9].

4.2. Criticism of elite politics by sports justice

Elitist sports believe that success is achieved through talent and individual effort. However, as sociologists have long debated, elite management is often a rationalization hoax that conceals structural advantages.

In fact, sports opportunities are stratified from the very beginning. If a child is born into a family with economic resources, he has a great chance to obtain professional sports coaches, sports equipment and sports participation networks. These conditions are not earned by the individual but bestowed by the family. In fact, behind many athletes lies an intangible support system, including parents with economic advantages, schools providing specialized sports education, and communities with public sports Spaces.

Sports justice demands that we dispel the myth of elitism and recognize that individual sports achievements are actually the social products of collective efforts. The government must invest in sports Spaces and basic conditions that allow everyone to participate, not just a few privileged classes.

This does not mean denying the role of individual efforts or talents, but rather insisting on fair competition requires ensuring a fair starting point. Justice does not require that the outcomes of all people be equal, but rather that the opportunities to develop individual abilities be equal [10].

5. The four-dimensional theoretical framework of sports justice

Sports justice is not a single moral claim; it encompasses a series of interrelated dimensions of justice. To fully understand its core structure, this paper proposes a four-dimensional theoretical framework, which includes distributive justice, identifying justice, spatial justice and proxy justice. Together, they form an overall framework that can assess the fairness of public sports infrastructure.As shown in Table 1, the realization of sports justice needs to be carried out from different aspects.

Distributative justice requires that ordinary citizens also truly possess the material basis for engaging in sports activities. This does not mean an equal amount of financial input, but rather reasonable investment based on demand, ensuring that ordinary communities are not deprived of sports facilities either. It also demands the resistance to the market logic dominated by capital and the privilege of turning sports into a form of wealth.

Recognize justice and avoid cultural exclusion. If certain groups such as women, the disabled and ethnic minorities are marginalized by the mainstream of society, then the wide promotion of equality is not enough. Basic sports facilities must attach importance to gender equality and universal accessibility, and recognize the important rights of ordinary citizens to exercise. Justice not only requires presence, but also visibility and respect.

Spatial justice regards space as a social product shaped by power. The unfairness of sports space is manifested in uneven geographical distribution and temporal exclusion. A society needs to integrate sports Spaces equally into all communities, ensuring fair mobility. The equal rights of sports are inseparable from the rights of cities.

Proxy justice emphasizes self-actualization within the collective. Sports are a means of public action and democratic experimentation. Top-down management and the ineffectiveness of neoliberalism have suppressed the initiative at the grassroots level. True sports justice supports the autonomous management of sports Spaces by communities, which can formulate rules suitable for community residents and define the forms and order of sports in the community.

These dimensions are interdependent with each other. Sports Spaces may be well-funded and widely distributed, but if they are inaccessible at night, do not welcome women, and are controlled by external forces, then they cannot be considered fair sports venues. On the contrary, only when all four dimensions, namely fair allocation of funds, inclusiveness, fair spatial design and community self-management, are consistent can sports realize its potential to build an equal society.

This framework goes beyond the single perspective of sports. It positions public sports as a constituent practice of citizens, in which freedom is not abstract but concrete and shared by all ordinary citizens. Therefore, sports justice is not on the periphery of social justice, but one of the most vivid manifestations of it [11].

6. Conclusion: sports are a condition for social equality

Sports are often regarded as a field of entertainment and leisure. But as this article discusses, freely exercising and doing sports in the community is a basic human need. When public sports infrastructure funds are insufficiently allocated and dominated by privatization, this is not only a policy failure but also a moral failure of justice.

By regarding participation in sports as a fundamental right of citizens, it can be in line with the core requirements of distribuential justice, namely fairness, inclusiveness and the expansion of human freedom. The concept of sports justice provides a normative basis for the reallocation of public Spaces and the allocation of social resources, and recognizes that sports are a condition for the construction of equality in modern society.

In a society where inequality is increasingly intensifying, the rich can live in closed communities with private gyms, while the poor are crowded on unsafe streets. At this time, public sports venues become a symbol of equality. Here, the system of social injustice is abandoned. Freedom of movement is not only a fundamental right but also a vivid and realistic experience.