Enhancing the Sustainability of Social Housing Policies through the Social Impact Approach: Innovative Perspectives form a “Paris Affordable Housing Challenge” Project in France

The environmental, economic and social challenges re-launched in the European Union Agendas (e.g., Horizon 2020 and Europe 2020–2030) have recently returned to being highly debated. In particular, policies and interventions in the field of social housing (SH) are still remaining crucial issues for urban regeneration. These interventions are aimed to combine sustainability criteria with architectural, urban and environmental quality. In this context, our goal in this article is to provide an innovative perspective on the topic highlighting the positive returns enabled by the logic of the social impact approach (SIA). A pilot project is proposed to be performed in the VI arrondissement of Paris. Starting from the French regulatory context and the requirements set by the “Paris Affordable Housing Challenge” competition, the levers of social finance for new social demands and the levers of incentives are applied to a real case. The research results show that the application of the emerging principles of social impact investing (SII) in areas difficult to access in the private market had positive returns. The final aim of the article is to outline guidelines that consider the quality, management and generation of the social impact requirements highlighted in the proposal to facilitate the application of the SIA to other interventions and contexts.


Introduction: Objectives, Research Questions and Expected Results
Social housing (SH) is a phenomenon that is currently attracting increasing attention in different European contexts. In fact, at least up to the surveys of the second half of 2019 [1][2][3] and before the spread of the Covid-19 pandemic, SH has returned to be a dynamic field in the construction sector. In Italy legislative reforms on the procurement sector and the three-year public programming of major public works [4][5][6] have fostered this type of intervention. In this context, however, central issues remained unresolved or not fully investigated. Some examples include the following: • The quantification and the nature of the financial resources to be allocated to these intervention programs, as well as the strategies for accessing EU funding from the perspective of environmental sustainability.

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The types of management models to refer to, not only of a public nature.

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The new social emergencies with respect to non-traditional user profiles.

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The identification of priority hierarchies in different political and decision-making contexts, maintenance plans, etc.
In addition to the theme of social emergencies, there are other crucial issues related to the quality, accessibility and maintenance of the building stock erected after World War II. The worsening of these three factors was been intensified by increasing spending review measures and by the crisis that affected global economies as well as the construction and real estate sectors. The international response has been both conservative in nature and open to change and innovation, as outlined by Scanlon et al. (2015) [7] in their analysis of the international framework (12 nations analysed, but not including the Italian context).
Recently, perhaps also in the face of these critical issues, the theme of policies and interventions in the field of social housing has returned to being debated, thanks to some well-known national and international experiments. Their objective sustainability criteria related to the issues of architectural quality and context and the verification of a positive economic return starting from logic derived from the social impact approach.
The theme is closely connected to the urban regeneration processes and to the investment policies, which, following the real estate bubble started in 2008, have witnessed a drastic reduction in profit margins and a contraction in demand in the face of excess offerings [8,9]. The complexity, therefore, also falls on the investment decision models, in which the gap between the two points of view of the promoters of a different nature is evident. On the one hand, are the public subjects who see urban transformation as an opportunity to improve the quality of life for citizens; on the other, are individuals of a private nature who have yet to pursue a positive economic and financial result, in containing the risk.
In the face of this debate and these reflections [9,10], researchers appear to have not yet identified an alternative and effective management model that can respond promptly, with tight deadlines and with the characteristic of "flexibility" for both social emergencies and requests for quality living in design terms.
In terms of a more strictly theoretical research and application tools, social housing has been extensively studied as an important innovation within urban and housing policies: particularly promoted in Europe, social housing is also recording in Italy as a growing interest in new forms of shared living. This contribution, starting from the background of research and experimentation case studies, asks (1) which new tools can provide the recent approach of the social impact assessment, in terms of tools to more effectively assess the sustainability aspects of these operations; (2) on the new demand targets that show new needs; and (3) on partnerships for new mixed management models of these transactions, in which the redistribution of investments is not only linked to the risk component, but also to that of "social responsibility"?
The innovative perspective starts from a case study to test the assumptions and outline the theoretical-practical implications for the following elements: (1) a re-reading of the "traditional" sustainability elements related to SH policies that is not only in terms of "subsidiarity" but also the responsibility of private operators who compete with public entities in the identification of targeted policies (for example, incentive and tax relief policies); (2) the application perspective starts from the design components and puts, at the centre of the reasoning, the project brief phase that becomes one of the elements to build sustainability and management models also from the point of view of conductors/users; and (3) the subject is suitable for the ongoing reasoning in this phase of the Covid-19 emergency.
In this context, we provide an innovative perspective on the topic presenting a project proposal to be performed in one of the less accessible estates of the world, such as Paris. The project was conceived to join the "Paris Affordable Housing Challenge" competition, and the authors chose the VI arrondissement of Paris. Starting from the French regulatory context and the requirements set by the competition, the theme of social housing emerged as an affordable solution. The levers of social finance for a new social demand and the levers of incentives are applied to a current deal for the city. This intervention aimed to combine sustainability criteria with architectural, urban and environmental quality, while trying to evaluate the positive economic returns. The logic of the social impact approach (SIA) allowed us to calculate the social investment not only by considering the economic sphere but also by evaluating the social and environmental impacts. This is a proposal that stops at the preliminary phase (as required by the announcement, Section 3.4), which is currently undergoing a technical-planning and technical-financial study with the testing of Table 1. Research questions, social needs, and reference question (source: Authors' elaboration).

Research Question
Reference Question (Section Dedicated to In-Depth Analysis to Provide Methods and/or Elements to Provide Answers to the Issues Highlighted) (1) How would it be possible for urban contexts (in our case Paris) to meet the requirements related to policies that also look at the circular economy with a sustainable approach, without increasing land use?
With the proposed intervention on the urban environment located in the central area of Paris, an attempt was made to design a scenario that, in the briefing phase, would take into account the link between founding elements of the sustainable approach (also in terms of "urban metabolism" and circular economy) and principles of social impact investing (Section 2, articulated in Sections 2.1 and 2.3) and had, as references, international cases (Section 2.2) and specifically French (Section 2.4). The research hypotheses were analysed and applied in the Parisian case, starting for instance from the case of Amsterdam, for which a brief reference is made at Section 2.3, useful to the reasoning conducted here. The issues mentioned are those related to recent studies: the Amsterdam Circular research evaluated opportunities for the creation of an urban metabolism based on closed cycles. The former industrial district of Buiksloterham is interested in a new typology of development, coordinated by cooperation between different actors, with the common goal of a gradual, organic, sustainable and participatory regeneration.
(2) How can we ensure a fair distribution of social profiles within the city and therefore a mixité sociale (social mix) analysis on some specific areas? Section 2.3 highlights changes in the needs and profiling of users, which are analysed, in particular, from the perspective of the Parisian case (Section 3.3): the new beneficiaries do not belong only to clusters characterized by low income, literacy problems, etc., but also to clusters that present other types of discomfort, loneliness and problems of integration or reconciliation between home and work life.
(3) Can the social impact investing methodology combined with the processes of investment in Social Housing be the engine of new management models? Can it be a lever for urban development interventions and making them scalable to other contexts?
The proposal illustrated in Section 4.3 seeks to identify, in the project briefing phase, mechanisms that can simplify the management and sharing of risks between investors, public promoters and users. Starting from housing rights up to the evolving framework of tax concessions and economic compensations between public bodies, economic managers and lessees, etc. These arguments are declined in the Parisian case in sections Sections 3.3 and 4.2.
To answer these objectives, questions and research gaps and to provide guidelines for an approach that also looks at project management as an indispensable approach in investment strategies and the planning and management of resources in the SH sector, the paper is articulated in four sections. In particular, Section 2 deals with the link between the social impact approach and sustainability in social housing, which has been little debated to date, investigating research issues (Section 2.1) and also focusing on the new approach offered by the application of social impact principles to the SH sector (Section 2.2). The specific issues of sustainability linked to SH, not only referring to the international panorama, are addressed in Section 2.3. The issues presented in Section 2.3 are contextualized in the French case in Section 2.4.
The article then deals with this innovative approach through the lens of the French-and Parisian in particular-context. After presenting and addressing the objectives of the "Paris Affordable Housing Challenge" (Sections 3 and 3.1), its regulatory and procedural contexts (Section 3.2) are outlined, together with the opportunities that this competition offers in terms of experimentation of new and integrated approaches. The methodological and design proposal for the intervention in a selected area of the 6th arrondissement of Paris is then presented in detail in Section 4. In this paragraph, we underline the innovative aspects in terms of the financial mechanisms and in the identification of clients and users, as well as the sustainability and quality aspects included in the design guidelines. At the end of the paper, the results, scalability, research openings and future developments are highlighted (Section 5). Then, guidelines that consider the quality, management and generation of social impacts requirements highlighted in the proposal are finally outlined to facilitate the application of the SIA to other interventions and contexts.

Conceptual Background of the Social Impact Approach and Research Question
In general, the definitions of social impact adopted at the theoretical level are deliberately large and articulated, and the literature has been recently enriched with many ideas [12][13][14]. In this article, we focus on the innovation of the social impact approach, specifically focusing on the SH sector, considering that it has been applied in pilot cases both abroad and in Italy [15,16].
In these experiences, the urgency of disciplinary and interdisciplinary comparisons emerged, also in light of the increasing diffusion of these new methods of investment and their ethical value, which is an aspect of extreme topicality and strategic nature. It is necessary to scan the classic paradigms of investment assessment and analysis. The multidimensionality of social impact investing can "contribute to the diversification of systemic risk", since "the ( . . . ) underlying value does not depend on the economic situation of the market but rather on the ability of social actors to implement an efficient project" [17] (p. 13).
The scientific community unanimously recognizes that the achievement of social impact (SI) can be fostered and facilitated through social impact investing (SII). SII can be defined as an investment aimed at generating both a positive social impact and a financial return, and it is understood as a promising approach to solve the most urgent social challenges [18].
In addition, SII focuses on achieving positive and sustainable social impacts and financial returns, with a perspective of blended value [19]. However, it is also unanimously recognized that the concepts of SI related to social finance and sustainable finance are not so clear and consolidated.
The interaction between these innovative financing mechanisms and changes in urban transformation processes is of interest. In Western countries, cities are currently trying to re-invent themselves [20]. This has been made possible after the impacts of the economic crisis and urban decline, also due to the phenomena of decentralization and deindustrialization.
The topic of urban regeneration, or better of "generative" interventions (for those who want to innovate these concepts [21]), has led political agendas to consider a multiplicity of problems related to them. In building restoration and retrofit operations, the social dimension is taking a central position [22], especially when integrated into programmes aimed at eliminating social decline, increasing the quality of life of inhabitants, enhancing cultural heritage, protecting and safeguarding the environment and ecosystems, fostering economic development, containing land consumption, etc.
In this regard, the measurement of (social) performance remains an essential requirement for the development of such operations, combined with the pursuit of new social finance mechanisms related to them [23,24]. In general, the measurement of the impact is in its initial phase worldwide, and Italy is no exception.
However, the wealth and variety of experiences of the Italian landscape, and its areas of development, testify to the liveliness of operators in the sector. At the heart of the reasoning lies the identification and testing of fiscal, administrative and innovative partnership mechanisms, together with the emergence of approaches able to measure the impact generated in relation to other phenomena [17,25].
In the experiences of SH attempting to pursue SI, another common theme (which also inspired the proposal for the case of Paris) emerges, i.e., the theme of sustainable social impact understood as active and collaborative well-being. This is one of the objectives to be achieved in interventions and processes in which people organize themselves to improve an aspect of their living condition, putting in place collaborative and sustainable solutions to achieve their purpose.
In the phase of construction of the process of partnership and commissioning, as well as in the moment of the design brief and then of realization, this interaction mainly lies in thinking and making Sustainability 2020, 12, 9903 5 of 27 the concept of "efficiency and everyday life" viable, as well as in being able to respond to certain strategic needs of everyday life by reducing waste and optimizing the time and resources available. Quoting Ferri and Pedercini, "this trend, now widespread, sees people active in the construction of their housing context in the broad sense: examples include social streets, buying groups, community gardens or carpooling. The groups that are formed around these objectives are able to manage services and spaces, to guard the territory and to exchange knowledge" [26] (p. 1). According to the scientific community [26][27][28], the SI grafted on the SH segment highlights some common "necessary" traits, which are available in exemplary case-studies, including the following: • The activity and identity of user groups and their predisposition to the practice of union; • The genius loci and the strong roots in the place; • The importance of the network and social networks; • Spontaneous professionalism, namely a high degree of professional organization applied to everyday life; • Alternative finance models, etc.
Have national and international experiences been able to answer these questions? The following section investigates certain cases and contexts.

Applications
In particular, five European countries (Austria, Denmark, France, the Netherlands and Sweden) have maintained their traditional role of countries highly committed towards SH, while at the same time they have experienced some changes in the traditional processes, particularly regarding financing mechanisms and investment arrangements. However, the 2007 financial crisis [7,29] generally induced a reduction of available resources, together with a slowdown in investment operations concerning both the new housing stock and the redevelopment of the existing one. Despite this context, interesting innovations can be nonetheless found in the type of providers involved (e.g., cooperatives, methods and tools for inclusion policies of residents) as well as in the more careful design of the housing units (e.g., size and physical characteristics) and of common spaces (e.g., the distribution of common parts in relation to the specific needs of identified users).
If we look at the priority policies set by the European community (at least up to February 2020) in the political axes 'Cohesion" and 'Convergence' [30], it is possible to find the following desired goals: • Improvement in the construction sector-including the interventions with a clear social objective; • Enhancement of competitiveness; • Encouragement of innovation practices and increase of employment levels [31,32].
However, according to the EU, SH is not a fundamental area for the construction sector [32] (p. 85): in fact, although it falls within the economic services deemed of general interest, it is not a universal service and, therefore, is not a direct EU competence (see the principles of subsidiarity and additionally formalized by art. 87 and 88 of the EU Treaties). The 2020 Lisbon Strategy stipulates, in addition to the role of regional governance on this theme, the primary importance of housing policies, in the framework of urban regeneration and fight against social hardship [33,34]. Further elements to be mentioned to frame SH policies are the fragmentation and inconsistency of the way these policies are financed. These may include direct allocations of resources as well as indirect allocations, shadow policies and also partial and specific fiscal measures, such as tax incentives or bonuses on energy efficiency and on the use of renewable energy in existing or new buildings (up to 4% of PON/POR funds-European Union Regulation n • 539/2010).
Overall, this would seem a fundamentally positive picture; however, the truth is that among the variety of criticalities [35] affecting the achievement of effective SH policies, the lack of funds as well asat least in some cases-the lack of transparency of governance still represent substantial and persistent critical factors. Poor transparency in governance has frequently caused the interruption of public tender Bureaucracy and cumbersome procedures perceived as 'hostile' and uncertain by both public and private operators have frequently led these subjects to renounce incentives and additional resources.
In fact, corrective actions should include the use of IT in the management of processes and of standardized systems in the evaluation and certification of proposals. The sustainability of these processes also lies in better control of the implementation process of the SH programs through more flexible solutions, reliable results, transparency, timeliness and quality of interventions.
In Italy, the discussion on the reform of the Public Works (OO PP) is ongoing and the new reforms promoted by the Codice degli Appalti have long be debated [36]. The SH sector is certainly influenced by these issues: in particular, a question that is emerging in this context is whether public-private partnerships (also performed according to new models [2,8,9,37,38]) may constitute a partial solution to the above mentioned problems.
New answers have emerged from recent experiences that, while seeking a sustainability of process, implementation and costs, have combined the aims of SH with the principles of social impact, which is taking on international relevance [39]. Overall, the aim of SH is to promote the formation of a respectable housing and social context within which it is possible not only to access the benefits from adequate housing but also to access services and experience a new interpretation of living, in the home as well as in the neighbourhood.
With reference to Italy, this model has spread in the mid-2000s through the Social Housing Foundation and the program promoted by FIA (Fondo Investimenti per l'Abitare), for example. In 2016 the endowment of the program was 2 billion and 28 million euros: this amount included 1 billion undersigned by Cassa Depositi e Prestiti, 140 million by Ministero delle Infrastrutture e dei Trasporti and 888 million by banking and insurance groups and private welfare funds [40].

What is Sustainability in Social Housing? Emerging Issues in the International Context
As anticipated in the introduction, the aim of the paper is to identify a framework that highlights the levers of sustainability in the planning of SH interventions, adopting approaches and tools for strategic evaluation specific to SII. In this sense, to propose guidelines still experimented with at a preliminary stage in an area of the city of Paris, it is appropriate to return to certain aspects and issues discussed in the past and, in part, left unresolved.
The construction boom throughout the EU was mainly a post-war phenomenon, and this applies to SH too. In fact, the boom was rooted in the deficiencies that accumulated during the conflict [41] and was, of course, supported by the allocation of resources and programming closely linked to the socio-economic and administrative-regulatory framework of each country. After strong investments in SH occurred in the 1970s and 1980s, certain factors led to a clear change in housing policies: different relationships between supply and demand, changes in the priorities of government agendas, obsolescence of social housing, decreasing investments and increasing social hardship linked not only to low income or "traditional" types of social discomfort.
In Europe and Italy, contemporary SH policies derive from operations and reasoning that originated in the 1970s. Italy differs from the European framework for its different relationship between houses in property (accessible more to "traditional families") and houses for rent; following a pattern almost unique in Europe for its great extent. The second type of house appears to be at a clear disadvantage compared to the first type. However, European models remain a reference. In the 1970s and 1980s, policies to reduce assistance and direct subsidiarity were launched to contain public spending [42], even in those States with a strong tradition of social rented housing.
In addition, new operators and investors have entered the SH segment. They are not only of public nature: in fact, they may be real estate investment companies, non-profit real estate funds for social purposes, banking foundations, ethical funds, etc. The aim is to contain public budgets, whereas the underlying idea is that a more private and liberal approach can be more efficient and unrelated to subsidiarity.
On the European scene, a line has been drawn between governments that have continued to support the public role in the planning of social housing as an important element in urban redevelopment operations and governments that have gradually delegated these "public social missions" to private investors.
As far as Italy is concerned, in recent years, there have been deep legislative changes in the rental property market. The market has been progressively liberalized and new rules have been introduced to help low-income households, either through direct benefits or through tax concessions for property owners. The key focuses appear to be the following: • New housing applications (public or private, arising from university students and disadvantaged social groups); • A specific structure of the housing market leased in sub-markets: on the one hand, housing leased to the business communities and student population; on the other hand, the free and controlled rents segment; • The existence of a national social fund, based on the triangulation between request, need, and efficiency; • Tenant income levels and solvency bands; • Changes in the trend of returns from investment in rental properties.
Currently, we also see debates that address the issues of rethinking the cities of the future in a perspective of sustainability, multicentricity and social equity, with a specific sensitivity to the connections between Economia Circolare (EC) and Metabolismo Urbano Circolare (MUC) [43][44][45][46][47].
In the redesign, the contemporary city becomes strategic-as for example in Dutch contexts: the identification of "malleable areas". According to the definition of Secchi (1984) [48], these areas are available for recovery and regeneration actions without further soil consumption. Such areas can be the ideal landing place to test new SH models, which can potentially generate highly positive environmental, space, economic and quality of life impacts. Recent scientific literature highlights that a similar approach must be unequivocally multidisciplinary and systemic [49][50][51][52][53].
In the simulation proposed in Section 4, we attempt to reason with the knowledge that the area being analysed does not represent a standard area for the application of the MUC approach. In fact, traditionally it has been applied to ex-industrial districts, hardly in central areas. Our reasoning starts from the observation that now that the central areas are emptying for the dematerialization of work (as well as for current health emergencies), and the depreciation of the areas must be re-interpreted as an opportunity for the development of social housing interventions with energy containment features, the correction of social inequalities and the innovation of management models of an entrepreneurial and mixed public-private nature.

Applications in French Context
With reference to the French context-which is the object of the proposed case-study-the logements sociaux are generally addressed and managed by bodies linked to the State and public institutions. These authorities are identified as bailleurs sociaux. The 1989 Act on the Amélioration des Rapports Locatifs and the Code de la Construction et de l'Habitation defines bailleurs sociaux as owners of real estate leased to individuals with modest incomes [54]. They act in the service of the general interest, helping the State and communities to respond to social problems related to living, the management of public space and the increase of the mixité sociale.
In these cases, social owners receive grants and tax aid, such as interest-free loans (PTZ prêt à taux zéro) and PSLA (prêt social de location-accession) loans, which enable them to benefit from a 5.5% reduction in the TVA (taxe sur la valeur ajoutée) and a 15-year exemption from the TFPB (taxe foncière sur les propriétés bâties). They can also receive a PC (prêt conventionné) loan or a 5.5 % reduction in the TVA on purchases or construction works of major residences with an urban renewal agreement signed with the ANRU (Agence Nationale pour la Rénovation Urbaine) [55]. Figure 1 summarises the construction process mechanisms that usually take place when the above-mentioned actors are involved. management of public space and the increase of the mixité sociale.
In these cases, social owners receive grants and tax aid, such as interest-free loans (PTZ prê t à taux zé ro) and PSLA (prê t social de location-accession) loans, which enable them to benefit from a 5.5% reduction in the TVA (taxe sur la valeur ajouté e) and a 15-year exemption from the TFPB (taxe fonciè re sur les proprié té s bâ ties). They can also receive a PC (prê t conventionné ) loan or a 5.5 % reduction in the TVA on purchases or construction works of major residences with an urban renewal agreement signed with the ANRU (Agence Nationale pour la Ré novation Urbaine) [55]. Figure 1 summarises the construction process mechanisms that usually take place when the above-mentioned actors are involved. However, in the current trend, the State tends to increasingly involve the private sector to compensate for the lack of logements sociaux. In fact, this dynamic can be effective to combine profitability, tax relief and support to families in difficulty. A concrete example is the development of an interesting model by a company operating in the real estate field. In 2001, the PERL company developed the Usufruit Locatif Social (ULS) model, which allows private investors, local communities and social owners to interact in the production of new or existing housing, with moderate rents where demand is higher [56].
In conclusion, guidelines for responsible capitalism appear to have emerged recently; in this perspective, it will be necessary for the State to encourage investors operating in the field of investments with social or environmental impact to review their financial profitability criteria to encourage the generation of common welfare.
The choice of which evaluation tools and models to apply to validate the "social" sustainability of these interventions is an extreme debate. Some tools proposed include Value Based Management, the Market Added Value-MAV and the Total Shareholder Return-TSR [57].
In the case of Paris, for the evaluation phase on the convenience to invest and the construction of the financial statements for the different stakeholders involved, the preference to adopt the SROI, recently adopted in the SII processes, has emerged as one of the most effective profitability indicators However, in the current trend, the State tends to increasingly involve the private sector to compensate for the lack of logements sociaux. In fact, this dynamic can be effective to combine profitability, tax relief and support to families in difficulty. A concrete example is the development of an interesting model by a company operating in the real estate field. In 2001, the PERL company developed the Usufruit Locatif Social (ULS) model, which allows private investors, local communities and social owners to interact in the production of new or existing housing, with moderate rents where demand is higher [56].
In conclusion, guidelines for responsible capitalism appear to have emerged recently; in this perspective, it will be necessary for the State to encourage investors operating in the field of investments with social or environmental impact to review their financial profitability criteria to encourage the generation of common welfare.
The choice of which evaluation tools and models to apply to validate the "social" sustainability of these interventions is an extreme debate. Some tools proposed include Value Based Management, the Market Added Value-MAV and the Total Shareholder Return-TSR [57].
In the case of Paris, for the evaluation phase on the convenience to invest and the construction of the financial statements for the different stakeholders involved, the preference to adopt the SROI, recently adopted in the SII processes, has emerged as one of the most effective profitability indicators [58]. We refer to further insights through the observation lens of the case "Paris Affordable Housing Challenge", illustrated in Sections 3 and 4.

Aims of the Study
Taking into consideration the premises outlined in paragraph 2, we present a suggestion for an alternative sustainable process that meets the future requests for Social Housing that Paris will have to cope with by 2025.
As indicated in Section 2.1, in addition to providing loans through the Caisse des dépôts et consignations (CDC), the French government has the task of defining housing needs in a centralized form by approving the projects and determining the total amount of subsidies for social housing. In addition, Article 55 of Law No 2000-1208 of 13 December 2000 on solidarity and urban renewal (see Act SRU 2000 [59]) prescribes that densely populated municipalities must have at least 20% of logements locatifs sociaux on the main residences. By "densely populated", this means over 1500 inhabitants in Ile-de-France and more than 3500 inhabitants in the other regions, included in an urban agglomeration of more than 50,000 inhabitants with at least one municipality of more than 15,000 inhabitants [59].
The SRU 2000 was subsequently amended by Law no. 2013-61 of 18 January 2013 on the mobilization of public land in favour of housing and strengthening of obligations to produce social housing (Duflot Law) [60]: this percentage will be replaced by the obligation to respect 25% of logements locatifs sociaux on the main residences. These measures have been adopted in order to increase the mixité sociale and to contrast the social and spatial segregation caused by the concentration in few specific poles.
In the capital city, the logements sociaux active on 1 January 2018 were 245,210 and represented 21.1% of the main residences [61]. The official figures as of 1 January 2019 are not known yet, but in view of the programs of logements sociaux funded in 2018 (5087 logements), should reach 250,297 (21.5% of the main residences). By adding the number of logements sociaux under construction or under renovation to the previous figure, the percentage would approximately reach 23.6% [61]. However, it is important to note that 50% concentrate in only three arrondissements, i.e., XIII, XIX, and XX [61].
Consequently, to reach the amount required by the 2013 Duflot Law [60], it would be necessary for the city to acquire 16,270 properties, thus reaching 25% by 2025. Analysing the data published by the Atelier Parisienne d'Urbanisme (APUR) in 2019 [61], from 2001 to 2018, 47% of the new acquisitions of logements sociaux were new construction (48,524 units). Therefore, this would mean building about 7647 new sociaux logements for the city of Paris.
Here, we report an alternative approach (and the related project proposals) that arises from the reasoning performed for participation in the Paris Affordable Housing Challenge competition (Section 3). To answer these questions, we require certain premises on the case study operational and regulatory framework. These are presented below.

The Social Housing Policies in France and in Paris
The French social stock has approximately 5 million logements [62]. A total of 84% of these belong to HLM (Habitations à Loyer Modéré), of public nature, unified in the OPH agency (Office Public de l'Habitat), for a total of 241 bodies. Other reference bodies for social housing policies are those of a private nature, such as ESH, (Entreprises sociales pour l'habitat), which includes 209 bodies, or cooperative entities, such as COOP'HLM (Sociétés coopératives Hlm), composed of 38 members [63] (p. 9).
The remaining 16% is managed by the EPL (Entreprise publique locale), the state, local authorities, public establishments and other authorized actors. The HLM stock, consisting of 4.6 million housing units (of which 4.4 million are currently occupied), hosts 10 million people [63] (p. 9). To these, approximately 300,000 co-housing units must be added. This classification determines the calculation of the rent, as the rent must fall within a range that varies according to the category.
Access to HLM housing is bound by certain criteria, such as French citizenship or permanent and regular residence in France. Different income thresholds are set according to the number of people who make up the household, the type of funding assigned and the geographical area [64]. Contrary to what one might think, these income thresholds are not very high. In fact, 60% of the population could potentially be eligible [55]. In Paris, for example, housing financed between 2001 and 2018 fell into three distinct types of financial aid: PLAI (Prêt Locatif Aidé d'Intégration), reserved for people in situations of great precariousness; PLUS (Prêt Locatif à Usage Social) that correspond to traditional HLMs and are the most numerous (80%); PLS (Prêt Locatif Social), attributed to households with too high incomes to be able to access ordinary HLM leases, but too low to enter the private park [61,65,66]. The monthly rent per square meter varies according to the type of financial aid (Table 2). Table 2. Monthly fee per sqm for each category of financial aid [63].
A single person, indeed, will not have to earn more than €2130 per month to apply for a logement PLUS [67]. The time frame between the financing of a programme and its offering for rent may vary from a few months to several years, depending on the duration of the yards. On average, there is three to four years between one programme and another. A total of 80,104 of the 104,484 social housing funded from 2001 to 2018 (77%), were delivered at the end of 2017 [65].
The number of applications for social housing in Paris has increased significantly (+44% compared to 139,985 in 2012) in comparison to previous years: 249,671 families renewed or filed a first application in 2018 at the Paris city services or at another instructor service in Île-de-France. The analysis of this request shows that 135,169 requests came from families residing in Paris (12% of Parisian families). The large number of applicants is the result of the socio-economic situation of households wishing to stay in Paris and the particularly high price of housing [65], as shown in Figure 2.

PLUS
(Prêt Locatif à Usage Social) that correspond to traditional HLMs and are the most numerous (80%); PLS (Prêt Locatif Social), attributed to households with too high incomes to be able to access ordinary HLM leases, but too low to enter the private park [61,65,66]. The monthly rent per square meter varies according to the type of financial aid ( Table 2).  6.09 €/m 2 6.84 €/m 2 13.34 €/m 2 .

PLS (Prêt Locatif Social)
A single person, indeed, will not have to earn more than €2130 per month to apply for a logement PLUS [67]. The time frame between the financing of a programme and its offering for rent may vary from a few months to several years, depending on the duration of the yards. On average, there is three to four years between one programme and another. A total of 80,104 of the 104,484 social housing funded from 2001 to 2018 (77%), were delivered at the end of 2017 [65].
The number of applications for social housing in Paris has increased significantly (+44% compared to 139,985 in 2012) in comparison to previous years: 249,671 families renewed or filed a first application in 2018 at the Paris city services or at another instructor service in Île-de-France. The analysis of this request shows that 135,169 requests came from families residing in Paris (12% of Parisian families). The large number of applicants is the result of the socio-economic situation of households wishing to stay in Paris and the particularly high price of housing [65], as shown in Figure  2.  As of December 31, 2018, 67% of the families registered as housing seekers in Paris had an income level below the PLAI limits, which corresponds to a reference income of €30,050 for a family of four. Only 11% of families registered as housing applicants had higher resources than the PLUS maximum, with a reference income of €54,628 for a family of four [61].
In addition, the "Borloo Populaire", a tool introduced by law No 2006-872 of 13 July 2006, on a national commitment to housing [66] (which proposes a tax deduction whether there is a contract with a minimum duration of at least nine years stipulated to households that have an income threshold lower than the PLAI maximum) further encouraged investments on this market. This tool has been improved and replaced several times up to the current versions. For new buildings, we refer to the Pinel tool, a provision of the code général des impôts introduced by the 2015 financial law [68]. For existing buildings, we refer to the Louer abordable device, called the Cosse Law [69], named after the ministre du Logement Emmanuelle Cosse, who brought it to parliament in 2017 with the financial law [70]. Later, it was extended until 31 December 2022 due to article no. 23 of the 2020 financial law [54].
After 1979, agreements were signed between the owner and the state, to have a property fall into the social housing category. The owner becomes a social owner as the one who manages and regulates logements sociaux. We are referring to the APL convention (Aide Personnalisée au Logement), an agreement that allows taking advantage of the State's aid to both property owners (during the construction phases) and renters [61]. The board of directors of the HLM body determines rental fees annually. An increase of rental fees is performed for families who raised their income during the lease [64].

Mechanisms and Incentives: the Levers of Social Finance for a New Social Demand in France
To have an overall view of the mechanisms governing the new proposal of Social Housing it is necessary to consider that the development of a sustainable project intervention develops on three dimensions: social, economic, and physical. The sustainability of the work is linked, first, to the search for high standards of architectural and urban quality, but also of services for the community. It is important to provide common areas dedicated to the socialization and leisure of tenants.
The project also includes economic sustainability, which is determined by the containment of maintenance and management costs and new management models, generated by a new device that can simplify the administration of the asset.
As mentioned above at Section 3.2, in France, the bodies linked to the State and the public bodies are the ones that usually manage the logements sociaux, with the role of bailleurs sociaux [71]. In 2001, PERL developed the Usufruit Locatif Social (USL) model: the model is based on the decomposition of the right of ownership of an asset between the legitimate owner (bare owner) and the person who enjoys this good and reaps its fruits (usufructor) [72] (see Figure 3).
For existing buildings, we refer to the Louer abordable device, called the Cosse Law [69], named after the ministre du Logement Emmanuelle Cosse, who brought it to parliament in 2017 with the financial law [70]. Later, it was extended until 31 December 2022 due to article no. 23 of the 2020 financial law [54].
After 1979, agreements were signed between the owner and the state, to have a property fall into the social housing category. The owner becomes a social owner as the one who manages and regulates logements sociaux. We are referring to the APL convention (Aide Personnalisé e au Logement), an agreement that allows taking advantage of the State's aid to both property owners (during the construction phases) and renters [61]. The board of directors of the HLM body determines rental fees annually. An increase of rental fees is performed for families who raised their income during the lease [64].

Mechanisms and Incentives: the Levers of Social Finance for a New Social Demand in France
To have an overall view of the mechanisms governing the new proposal of Social Housing it is necessary to consider that the development of a sustainable project intervention develops on three dimensions: social, economic, and physical. The sustainability of the work is linked, first, to the search for high standards of architectural and urban quality, but also of services for the community. It is important to provide common areas dedicated to the socialization and leisure of tenants.
The project also includes economic sustainability, which is determined by the containment of maintenance and management costs and new management models, generated by a new device that can simplify the administration of the asset.
As mentioned above at Section 3.2, in France, the bodies linked to the State and the public bodies are the ones that usually manage the logements sociaux, with the role of bailleurs sociaux [71]. In 2001, PERL developed the Usufruit Locatif Social (USL) model: the model is based on the decomposition of the right of ownership of an asset between the legitimate owner (bare owner) and the person who enjoys this good and reaps its fruits (usufructor) [72] (see Figure 3).
This mechanism was then formally framed in 2006 by Article L253-1 of the Code de la construction et de l'habitation as of 13 March 2020 [68]. The purpose of this scheme is to encourage the development of mixité sociale while allowing investors to acquire considerable amounts of real estate, at reduced costs, and tax exempt [56].  This mechanism was then formally framed in 2006 by Article L253-1 of the Code de la construction et de l'habitation as of 13 March 2020 [68]. The purpose of this scheme is to encourage the development of mixité sociale while allowing investors to acquire considerable amounts of real estate, at reduced costs, and tax exempt [56].
The investor will acquire, therefore, only the property of an asset, with a discount of 30%-40% and will transfer the purchase of the usufruct to a social lessor for a minimum duration of at least fifteen years [68]. The latter will be responsible for managing a pool of social housing, selecting the occupants and collecting the rents, without having to invest large sums to make new housing available. The social property owner, moreover, thanks to the obligation that the future inhabitant will have to engage with a contract initially of nine years and then renewable every three years, will have the security to receive a monthly sum in a constant way. This security is also guaranteed by mechanisms, such as Garantie Visale, a free service offered by Action Logement that ensure the balance of each fee when the tenant is not able to [73]. In addition, tenants are often recipients of aid from the Caisse d'allocations familiales (CAF), which can partially cover the costs of the rent depending on the family's economic condition [74].
Investors, although having to forego the rent return, will avoid the financial risks associated with the private rental market and, in addition, recover full ownership of the asset at the end of the contract. These mechanisms must be linked to a new social demand: in 2016, France counted 29.2 million households. Overall, the number of households has progressively increased (+4.9 million compared to 1999); however, the number of members of each one has increasingly decreased: households are now formed, on average, by 2.2 people, compared to 2.4 in 1999 [75] (p. 28).
We are witnessing an increasingly widespread vulnerability of family structures that tend to fragment. Of households, 36% consist of one person, one third consist of two people (26%), just under one third consist of a couple with one or more children (26%) and only 10% consist of a single person with one or more children [63] (p. 9). (see Figure 4). Single parent families and large families are more present in the realm of logements sociaux than in the whole population (21% and 10%, respectively, for single parent families and 11% and 6% for families with three or more children) [63] (p. 9).
have the security to receive a monthly sum in a constant way. This security is also guaranteed by mechanisms, such as Garantie Visale, a free service offered by Action Logement that ensure the balance of each fee when the tenant is not able to [73]. In addition, tenants are often recipients of aid from the Caisse d'allocations familiales (CAF), which can partially cover the costs of the rent depending on the family's economic condition [74].
Investors, although having to forego the rent return, will avoid the financial risks associated with the private rental market and, in addition, recover full ownership of the asset at the end of the contract. These mechanisms must be linked to a new social demand: in 2016, France counted 29.2 million households. Overall, the number of households has progressively increased (+4.9 million compared to 1999); however, the number of members of each one has increasingly decreased: households are now formed, on average, by 2.2 people, compared to 2.4 in 1999 [75] (p.28).
We are witnessing an increasingly widespread vulnerability of family structures that tend to fragment. Of households, 36% consist of one person, one third consist of two people (26%), just under one third consist of a couple with one or more children (26%) and only 10% consist of a single person with one or more children [63] (p.9). (see Figure 4). Single parent families and large families are more present in the realm of logements sociaux than in the whole population (21% and 10%, respectively, for single parent families and 11% and 6% for families with three or more children) [63] (p.9). In addition, the population is gradually ageing, due to the increase in the number of households consisting of a childless couple (25% in 2016, compared with 23% in 1990), and more elderly people are living alone: 27% of men and 62% of women aged 80 or over [75] (p. 24).
Thus, due to these demographic changes, the new beneficiaries will be single-nuclear families, single-parent families and young couples, but also families with elderly people who are not selfsufficient or with a member with a form of disability, families with large numbers of dependent children and the unemployed. As for living standards, the poverty threshold was approximately 1026 € per month in 2016. The standard of living of tenants of logements sociaux was about 40% lower than that of owners (it was 31.8% in 2012), and the poverty rate was much higher (see Figure 5). In addition, the population is gradually ageing, due to the increase in the number of households consisting of a childless couple (25% in 2016, compared with 23% in 1990), and more elderly people are living alone: 27% of men and 62% of women aged 80 or over [75] (p. 24).
Thus, due to these demographic changes, the new beneficiaries will be single-nuclear families, single-parent families and young couples, but also families with elderly people who are not self-sufficient or with a member with a form of disability, families with large numbers of dependent children and the unemployed. As for living standards, the poverty threshold was approximately 1026 € per month in 2016. The standard of living of tenants of logements sociaux was about 40% lower than that of owners (it was 31.8% in 2012), and the poverty rate was much higher (see Figure 5). In the SH domain, households at risk of poverty account for 34% against 14% of all households [63] (p. 11).

Focus on the Paris Affordable Housing Challenge Competition
The alternative approach proposed in this section comes from the participation of the Authors in the Paris Affordable Housing Challenge competition. This competition is part of a series of challenges In the SH domain, households at risk of poverty account for 34% against 14% of all households [63] (p. 11).

Focus on the Paris Affordable Housing Challenge Competition
The alternative approach proposed in this section comes from the participation of the Authors in the Paris Affordable Housing Challenge competition. This competition is part of a series of challenges (Global Housing Availability Challenge) aimed at identifying innovative solutions to the housing problem in the world. In the case of the Paris Affordable Housing Challenge, the focus is on the city of Paris.
As already indicated in Section 3.1, Paris, like many metropolises in the world, is facing a huge problem of housing accessibility. It appears among the ten most expensive cities to live in, which means that the sale prices of the apartments are naturally higher than in other regions in France: it is about 10,773 €/sqm for the city of Paris against 3636 €/sqm of the national average (about three times higher) [76].
One of the factors that drives house prices up is the massive request for rental properties. The tendency to rent in the short-term is increasing, due to the growing number of tourists [77]. Consequently, the owners prefer this type of lease as it allows them a higher profitability compared to a long-term lease. Compared to an offer reduction and constantly high requests, the almost impossibility to find an affordable accommodation to live in in the Ville Lumière is evident. On this basis, the Paris Affordable Housing Challenge competition was launched. It requires participants to design a solution capable of responding to the city's housing problem.
The project area of the competition is not defined; therefore, the projects must be versatile and scalable to adapt to different places in the city. Participants will have to consider the variety of housing solution sizes able to conform to different users (large families, single-parent families, couples, etc.) and their different needs [78]. Social housing was proposed as the first solution to the competition requests. As illustrated in Section 3.1, the city should acquire 7647 new social housing by 2025, to achieve the goals imposed by the Duflot I law [60].
Increase in the number of its social housing to reach the legal threshold before the deadline set; 2.
Improvement of the social housing distribution in the territory; 3.
Production of family housing more suited to the demand; 4.
Diversification of the rental offer for each individual property in order to guarantee mixité sociale.
However, to date, only four arrondissements have a percentage higher than 25%. In contrast, there are ten arrondissements, mostly placed in the central areas, not even reaching 10% (see Figure 6). Sustainability 2020, 12, x FOR PEER REVIEW 14 of 28 The reasoning starts from generating interventions and with the social impact approach (Section 2.2) as a possible link between the growing need for new buildings for social architecture and the fight against urban sprawl. Why not densify the already dense Haussmanian fabric in favour of social integration? If urban density has been fought for years because of its unhygienic and unhealthy  The reasoning starts from generating interventions and with the social impact approach (Section 2.2) as a possible link between the growing need for new buildings for social architecture and the fight against urban sprawl. Why not densify the already dense Haussmanian fabric in favour of social integration? If urban density has been fought for years because of its unhygienic and unhealthy nature, now, it appears as the only solution we have. This is not only to safeguard our natural heritage, but also to promote social equity. Quoting Jane Jacobs " . . . it will be through a variety of primary uses, an architectural heterogeneity, made of buildings of different height, shape and age of origin, and an urban density that we can guarantee the survival of our reality" [80].
In Paris, the approval of the law ALUR [81] brought to the parliament by Cécile Duflot as a legislative translation of proposal 22 of the presidential program of François Hollande aims to promote access for all to a logement "worthy and affordable". This law aims to fight against "unworthy living and degraded co-ownership" to improve the understanding and effectiveness of public policies related to housing and modernize urban planning documents. A strategy proposed to achieve the goal is to remove the soil occupancy coefficients (COS) [82] on parcels where the density rules prevented the realisation of the totality of the areas established by the local town planning plan (PLU). In addition, the law provides the transfer of PLU expertise from the municipality to the intercommunalité on the project and implementation of local urbanisation plans (PLU), which become plans locaux d'urbanisme intercommunaux PLUI [82].
Another incentive is that the city must respect the mixité sociale constraint that, following the ordinance No. 2013-889 of 3 October 2013 on the development of the construction of the logements, provides the possibility of building further levels to allow the property to align with the neighbouring ones, derogating from the rules imposed by the PLU [83]. However, the ALUR Act deals with a complex scenario in which most properties have apartments with different owners. The law mitigates this complexity mainly through two changes.
First, due to Article 61 of Law No. 2014-366 of 24 March 2014 [81], to authorize the raising of a property with more than one owner it will no longer be necessary that the decision is made unanimously, but it will be sufficient that 2/3 agree. Secondly, the law gives co-owners of the last floor the priority to purchase the newly created apartments. If the co-owners refuse to use it, the additional storey rights may be assigned to third parties [82], in accordance with the dynamics described above in the paragraph (Section 2.1). In the case of an initiative of the co-owners of the last floor, the question might be treated as a private affair [82].
Thus, new possibilities are opening up for the construction of 7647 new logements sociaux in the central districts of the city.

Introduction to the Case
In the light of the premises set out in Section 3, we propose the application of an investment process that considers the principles of sustainability and social impact. The paper's objective is to provide a set of tools that allow the diffusion of the proposed prototype within a much wider spectrum than that of the arrondissement in which it is located. In other words, the model has been designed in such a way as to be reproducible in different urban contexts, regarding the economic and social profile of the inhabitants and the shape of the area. The scalability of the intervention is given by the verticality of the SH system that provides supervision of the municipality in all the passages.
It is the responsibility of the latter to ensure the correctness of the allocation procedure and management of the future product through specific legislature that regulates the terms in which the lease takes place. Tenants are protected, for example, if the annual enquête ressources shows that the maximum permitted income is exceeded [84] and also dwelling.
In addition, the possibility of creating a real network of sustainable housing is given by the applicability of the process (see Figure 7) to interventions of a variable scale. This means that the participation of small or large private investors will be encouraged. designed in such a way as to be reproducible in different urban contexts, regarding the economic and social profile of the inhabitants and the shape of the area. The scalability of the intervention is given by the verticality of the SH system that provides supervision of the municipality in all the passages.
It is the responsibility of the latter to ensure the correctness of the allocation procedure and management of the future product through specific legislature that regulates the terms in which the lease takes place. Tenants are protected, for example, if the annual enquête ressources shows that the maximum permitted income is exceeded [84] and also dwelling.
In addition, the possibility of creating a real network of sustainable housing is given by the applicability of the process (see Figure 7) to interventions of a variable scale. This means that the participation of small or large private investors will be encouraged. We have to understand the deepening of a specific case as an opportunity for the practical application of what has been learned following the analysis of the legislative landscape, the current policies and similar cases. To assess the increased investment risk in a complex regulatory framework such as Paris intramuros, the search for the project site fell into the 6th arrondissement where the market data show the least favourable conditions for this kind of procedure.
The 6th arrondissement presents, in fact, the most expensive selling and rental prices per sqm of the city, with values of €12,360/sqm and €43.52/sqm, respectively [66] (pp. [12][13]. In addition, We have to understand the deepening of a specific case as an opportunity for the practical application of what has been learned following the analysis of the legislative landscape, the current policies and similar cases. To assess the increased investment risk in a complex regulatory framework such as Paris intramuros, the search for the project site fell into the 6th arrondissement where the market data show the least favourable conditions for this kind of procedure.
The 6th arrondissement presents, in fact, the most expensive selling and rental prices per sqm of the city, with values of €12,360/sqm and €43.52/sqm, respectively [66] (pp. [12][13]. In addition, according to data provided by INSEE, Institut national de la statistique et des études économiques, the percentage of inhabitants receiving social benefits and of people on low incomes is low compared to the city average [83]. Precisely, the parcel is located at 14 Rue D'Assas, a few blocks from the Jardin de Luxembourg and the Saint Sulpice church. It consists of two parts, one overlooking the road, giving access to the inner court, and a second part, placed inside the court. The area that to be raised is this last one (Figure 8). Inside the courtyard, the buildings have a heterogeneous nature, both in terms of height and from a stylistic point of view.
However, the reason for choosing this parcel is not only an architectural one but also due to the mixité sociale. The parcel has a large flat roof perfect for hosting additional storeys. This parcel can be representative of a phenomenon that is emerging in urban models today: being one of the urban multipolarities. Today, starting from the idea that the concentric urban model of urban rent exists, the concept of centre-suburbs has entered a crisis, making room for one of multipolarity/multicentrality [85]. The experiment on the parcel is to rethink the common, residual or underused spaces to combine private social housing with new collective services, aiming to increase social impact through enhanced quality of life levels. This is also in light of the challenge "Paris in 15 min" recently launched by the mayor Anne Hildago [86], which aims to pursue an urban revolution based on urban proximity and areas within the city that should be capable of fulfilling six social functions: living, working, supplying, caring, learning and enjoying.
In the block, there are several offices, coworking spaces and meeting rooms. The selected area hosts, in particular, the headquarters of the Maison Magis, a Jesuit community that has been located in Rue D'Assas since 2018. It is a space of more than 1000 m 2 spread over three floors and divided into a pastoral centre, a multipurpose room and a coworking space. A single stairwell and an external lift, added later, connect the three floors. From Monday to Friday dozens and dozens of visitors frequent the spaces of the Maison Magis. In fact, access to the area is free, an element that gives the court liveliness.
The new volume will reach a height of 25 m, i.e., the height of the two neighbouring buildings, both residential. In fact, with the new building we want to exploit the constraint for the city of respect However, the reason for choosing this parcel is not only an architectural one but also due to the mixité sociale. The parcel has a large flat roof perfect for hosting additional storeys. This parcel can be representative of a phenomenon that is emerging in urban models today: being one of the urban multipolarities. Today, starting from the idea that the concentric urban model of urban rent exists, the concept of centre-suburbs has entered a crisis, making room for one of multipolarity/multi-centrality [85].
The experiment on the parcel is to rethink the common, residual or underused spaces to combine private social housing with new collective services, aiming to increase social impact through enhanced quality of life levels. This is also in light of the challenge "Paris in 15 min" recently launched by the mayor Anne Hildago [86], which aims to pursue an urban revolution based on urban proximity and areas within the city that should be capable of fulfilling six social functions: living, working, supplying, caring, learning and enjoying.
In the block, there are several offices, coworking spaces and meeting rooms. The selected area hosts, in particular, the headquarters of the Maison Magis, a Jesuit community that has been located in Rue D'Assas since 2018. It is a space of more than 1000 m 2 spread over three floors and divided into a pastoral centre, a multipurpose room and a coworking space. A single stairwell and an external lift, added later, connect the three floors. From Monday to Friday dozens and dozens of visitors frequent the spaces of the Maison Magis. In fact, access to the area is free, an element that gives the court liveliness.
The new volume will reach a height of 25 m, i.e., the height of the two neighbouring buildings, both residential. In fact, with the new building we want to exploit the constraint for the city of respect for the mixité sociale, imposed by the ordinance No. 2013-889 of 3 October 2013 [87], through which it is possible to build further levels to allow the building to align with neighbouring ones (Figure 9). Sustainability 2020, 12, x FOR PEER REVIEW 17 of 28 for the mixité sociale, imposed by the ordinance No. 2013-889 of 3 October 2013 [87], through which it is possible to build further levels to allow the building to align with neighbouring ones (Figure 9).

Mechanisms and Incentives: the Levers of Social Finance for a New Social Demand in the VI Arrondissement of Paris
As indicated in the previous chapter, the quality of the context emerges among the dimensions that must be considered to achieve the goal of sustainability. This term includes a high quality of architectural intervention and a coherent insertion in the urban fabric, while considering the existing urban and landscape constraints.
As previously mentioned, the project lot is located in a particularly sensitive area. The city of Paris has many constraints linked to the protection of urban forms and architectural heritage, of which the VI arrondissement is no exception. The block examined is part of the Périmètre de protection de Monuments Historiques and is marked for "its heritage, cultural or landscape interest" [88]. The building on which the interventions are proposed does not fall within the protected buildings or in a plot with protected buildings inside.
However, to be able to obtain an easy feedback on the feasibility, reference could be made to the case study of 11 logements sociaux of the Chartier-Corbasson Architectes in the Marais. In this case, it was not a simple elevation, but, rather, a real intervention on the existing levels. In doing so, the creation of seven PLUS and four PLAI logements, in a district with a high density of buildings protected for their capital interest, has created a new urban front [89].
That intervention does not conform to the surrounding buildings and is clearly distinguishable from the stylistic point of view. For this reason, it was chosen as a reference project for the development of our case study (Section 4.3). In this case, we also opt for a strong stylistic break, while preserving the volumes prescribed. However, it would not be the only case where a stylistic break

Mechanisms and Incentives: the Levers of Social Finance for a New Social Demand in the VI Arrondissement of Paris
As indicated in the previous chapter, the quality of the context emerges among the dimensions that must be considered to achieve the goal of sustainability. This term includes a high quality of architectural intervention and a coherent insertion in the urban fabric, while considering the existing urban and landscape constraints.
As previously mentioned, the project lot is located in a particularly sensitive area. The city of Paris has many constraints linked to the protection of urban forms and architectural heritage, of which the VI arrondissement is no exception. The block examined is part of the Périmètre de protection de Monuments Historiques and is marked for "its heritage, cultural or landscape interest" [88]. The building on which the interventions are proposed does not fall within the protected buildings or in a plot with protected buildings inside.
However, to be able to obtain an easy feedback on the feasibility, reference could be made to the case study of 11 logements sociaux of the Chartier-Corbasson Architectes in the Marais. In this case, it was not a simple elevation, but, rather, a real intervention on the existing levels. In doing so, the creation of seven PLUS and four PLAI logements, in a district with a high density of buildings protected for their capital interest, has created a new urban front [89].
That intervention does not conform to the surrounding buildings and is clearly distinguishable from the stylistic point of view. For this reason, it was chosen as a reference project for the development of our case study (Section 4.3). In this case, we also opt for a strong stylistic break, while preserving the volumes prescribed. However, it would not be the only case where a stylistic break and the use of high-tech materials were used to conform the new buildings to the environmental constraints required by Plan Climat [90] for the city of Paris. The multiple objectives pursued by the municipality are to contain energy consumption and to achieve 100% of renewable energy, through the application of appropriate measures. In an area of great urban transformations, such as the Rive Gauche, real symbolic buildings are built with the aim of giving a new face to the capital. This is the case, for example, of ICF La Sablière from the Bernard Buhler agency in the 13th arrondissement. The project overlooks the Seine and is immediately recognizable thanks to numerous light effects that bring to the project an aspect of constant change. The high-tech windows provide a peculiarity to all the eighty-seven apartments and allow the building to halve its energy consumption.
Although it may seem a viable intervention only in the peripheral areas of the city, there are case studies carried out even in the most central, well-known and tourist areas of Paris. The agency Vous Êtes Ici Architectes, in 2014, realized 11 logements collectifs in the area of the Quartier Latin with the aim of de-densifying the block and donating spatiality and air to the pedestrian street. The entire project met the needs of the Plan Climat and reduces the ecological footprint of the building, with efficient and contemporary architecture [91].
The social housing definition is linked to a set of residential units and services that encourage the creation of a decent housing and social environment. Together with the evolution of the demand, there has been a change in the concept of homelessness. Primary social needs, such as lack of housing have now been added to other themes, such as loneliness or the lack of integration of individuals. The quality of a social housing intervention is also linked to the development of human relations. For this to happen, special attention must be paid to the relationship between public and private spaces.
The search for collaborative and sustainable solutions, with a strong value of social impact investing, offers the possibility of producing efficient properties for the development of a neighbourhood and a community. The cohesion of public and private spaces is becoming increasingly important for a satisfactory quality of life, which is why, throughout Europe, a gradual offer of housing services is being proposed rather than simple housing [92].
Citing well-known concepts by Hannah Arendt, public spaces are created through human interaction, communication and cooperation within shared spaces where it becomes possible to live with others rather than just oneself [93].

A proposal for Guidelines: Interventions, Management and Social Impacts
The project proposal seeks to provide answers to the questions raised in Section 3.1. The new volume proposes to exploit, in part, the already existing distribution system in the building below. The stairwell should be improved and redesigned with the addition of a new elevator. In this way, the inflow to the coworking spaces will not be increased, which, on the contrary, will maintain the external distribution system.
Then, the distribution system will allow the organization of the spaces in apartments, private leisure areas and common areas according to a grid. Common areas will be dedicated to recreational activities, sports or meeting rooms/workspaces. In this way, distribution will play an active role and encourage the participation of tenants in the social life of the community. The corridors will no longer simply be distributive elements but will sometimes become real spaces for meetings and activities ( Figure 10).
This project aims to minimize the public/private border to allow spaces, often considered as secondary, to increase relations between the inhabitants. It is also important to specify that it has been possible to mitigate the expected operating costs, in particular, those related to heating, through design choices. The common areas are tripartite: closed heated areas, closed areas not heated and open areas. In this way, the heated areas, devoted to group activities, are reduced, also reducing the costs of ordinary and extraordinary maintenance of the heating systems ( Figure 10).
The project proposes the construction of twenty-one apartments that could potentially accommodate forty-eight people. Despite having only four different sizes (i.e., 15, 20, 30, and 35 sqm), each house is modelled based on potential use. The project proposes the construction of twenty-one apartments that could potentially accommodate forty-eight people. Despite having only four different sizes (i.e., 15, 20, 30, and 35 sqm), each house is modelled based on potential use.
These elements will then be enclosed inside an envelope modelled starting from the imitation of typical Parisian roofs. This was made permeable by the choice of metal profiles spaced a few centimetres apart. At the compositional level, we want to underline the opening of the project, by a visual perspective, to the courtyard and to the neighbouring buildings. This choice ensures protection from intrusion problems, while at the same time allowing the passage of air and light. The 180° twist allows differentiating the degree of shielding, which is very low in the correspondence of windows and terraces.
However, what are the reasons that drive the owners to decide to build on the roof of their property? There are many possible answers and among these the economic and environmental advantages stand out, mainly relying on an approach that encourages models of living that contribute to the reduction of waste [92].
By 2025, all private residential buildings with a primary energy consumption of more than 330 kW/h of primary energy per meter and per year shall be subject to energy efficiency measures [93]. As a result, the decision to raise the ceiling may make it possible to cover part or all of the energy renewal costs.
More than 60% of co-owners are over 40 years old. The properties of the 1960s, or older ones, generally need retrofit interventions that can be realized thanks to elevation works and the owners often take the opportunity to restore the underlying building. It will be necessary to create a uniformity between the old and the new, through the renovation of the facade in some cases, or with retrofits able to improve the energy efficiency in others. In addition, it will be possible to carry out work on internal common parts, such as the stairwell or the elevator. The latter can be replaced with a more modern one when it cannot meet the quality and performance requirements of the new building ( Figure 11). These elements will then be enclosed inside an envelope modelled starting from the imitation of typical Parisian roofs. This was made permeable by the choice of metal profiles spaced a few centimetres apart. At the compositional level, we want to underline the opening of the project, by a visual perspective, to the courtyard and to the neighbouring buildings. This choice ensures protection from intrusion problems, while at the same time allowing the passage of air and light. The 180 • twist allows differentiating the degree of shielding, which is very low in the correspondence of windows and terraces.
However, what are the reasons that drive the owners to decide to build on the roof of their property? There are many possible answers and among these the economic and environmental advantages stand out, mainly relying on an approach that encourages models of living that contribute to the reduction of waste [92].
By 2025, all private residential buildings with a primary energy consumption of more than 330 kW/h of primary energy per meter and per year shall be subject to energy efficiency measures [93]. As a result, the decision to raise the ceiling may make it possible to cover part or all of the energy renewal costs.
More than 60% of co-owners are over 40 years old. The properties of the 1960s, or older ones, generally need retrofit interventions that can be realized thanks to elevation works and the owners often take the opportunity to restore the underlying building. It will be necessary to create a uniformity between the old and the new, through the renovation of the facade in some cases, or with retrofits able to improve the energy efficiency in others. In addition, it will be possible to carry out work on internal common parts, such as the stairwell or the elevator. The latter can be replaced with a more modern one when it cannot meet the quality and performance requirements of the new building ( Figure 11). In this way, the building will increase its real estate value and its lifetime will increase. However, for the more "fragile" co-owners, investing in such a large-scale intervention may not be of much interest. In this respect, all low-income co-owners will be eligible for government aid and subsidies, such as the Crédit d'impôt pour la transition énergétique, which allows the deduction from income tax of up to 30% of expenditure incurred for certain energy improvement works [94]. It entails a cap considering the family situation and the persons liable for taxation [95]. From 2020, this funding will be replaced by Maprimerénov' and will be paid by the ANAH (Agence Nationale de l'Habitat) in the form of a bonus [96].
There is also the possibility of obtaining a 10% or 5.5% reduction in TVA (Taxe sur la Valeur Ajoutée) compared to 20% for renovation works within the private domain [97]. Another option is a partial or total exemption from the Taxe Foncière sur les Propriétés Bâties (TFPB) for buildings completed before 1 January 1989 that require energy renovation costs. To qualify for this five-year exemption, the amount of expenditure incurred must be more than €10,000 for the year preceding the application of the exemption, or € 15,000 during the three years preceding the application of the exemption [98].
Finally, if the owners or co-owners do not want to manage the project personally or cannot meet the costs related to the efficiency works, there is the possibility of giving the rights to build to third parties. The latter will be responsible for financing energy renovation and managing the new elevations.
However, the benefits will not only be of economic nature and not only related to the "security" of the investment. The social dynamics triggered will make the project fall into the category of social impact investing, which assumes that investors or special purpose companies balance the risk components and waiver of part of the return with social responsibility and ethical capacity in addition to ordinary business. As already mentioned in Section 2.2, this is an investment with a strong social In this way, the building will increase its real estate value and its lifetime will increase. However, for the more "fragile" co-owners, investing in such a large-scale intervention may not be of much interest. In this respect, all low-income co-owners will be eligible for government aid and subsidies, such as the Crédit d'impôt pour la transition énergétique, which allows the deduction from income tax of up to 30% of expenditure incurred for certain energy improvement works [94]. It entails a cap considering the family situation and the persons liable for taxation [95]. From 2020, this funding will be replaced by Maprimerénov' and will be paid by the ANAH (Agence Nationale de l'Habitat) in the form of a bonus [96].
There is also the possibility of obtaining a 10% or 5.5% reduction in TVA (Taxe sur la Valeur Ajoutée) compared to 20% for renovation works within the private domain [97]. Another option is a partial or total exemption from the Taxe Foncière sur les Propriétés Bâties (TFPB) for buildings completed before 1 January 1989 that require energy renovation costs. To qualify for this five-year exemption, the amount of expenditure incurred must be more than €10,000 for the year preceding the application of the exemption, or € 15,000 during the three years preceding the application of the exemption [98].
Finally, if the owners or co-owners do not want to manage the project personally or cannot meet the costs related to the efficiency works, there is the possibility of giving the rights to build to third parties. The latter will be responsible for financing energy renovation and managing the new elevations.
However, the benefits will not only be of economic nature and not only related to the "security" of the investment. The social dynamics triggered will make the project fall into the category of social impact investing, which assumes that investors or special purpose companies balance the risk components and waiver of part of the return with social responsibility and ethical capacity in addition to ordinary business. As already mentioned in Section 2.2, this is an investment with a strong social connotation, in most cases of a positive character. The economic benefits will therefore coexist with the civic and social responsibility benefits of all parties involved, including the entrepreneurial and not just the public ones.
The tenants already installed in the property, who will enjoy the new benefits brought by the mixité sociale, will also feel this well-being. The multiplicity of problems to which the intervention seeks to respond will give rise to an integrated design in which the centre is the well-being of the community, the subsidiarity and the pluralism.
The issue of measuring and evaluating these interventions is by no means ancillary: in addition to the preliminary proposal illustrated here, project investigations of the preliminary proposal are underway and tests are being conducted using the SROI social profitability indicator: to date there are yet no published results of an executive design simulation.

Conclusions and Future Steps
With regard to the research and experimentation questions highlighted in the Introduction, (which we briefly recall: 1. How would it be possible for urban contexts (in our case Paris) to meet the requirements related to policies that also look at the circular economy with a sustainable approach, without increasing land use? 2. How can we ensure a fair distribution of social profiles within the city? 3. Can the social impact investing methodology be a lever for urban development interventions and can make them scalable to other contexts?), clarifications on the preliminary final results of the experience conducted and reasoning of perspective and scalability in other contexts of the proposed approach are necessary.
First of all, our research has shown that the application of the emerging principles of SII to a very peculiar case (i.e., located in an area difficult to access in the private market,) can show positive effects on multiple sides. Overall, the pilot project attempted to pursue mixité sociale in a central area where access to housing is typically prohibitive for people with fragile socio-economic conditions. More specifically, the pilot project proposed an experimental model capable of answering the demand for logements sociaux in the central areas of Paris, increasing the social mix and responding to the needs of a new, constantly evolving real estate demand. This objective-with a more social nature-is also achieved with the "requirements" of economic and environmental sustainability according to the social impact approach.
The location of the parcel, in an absolutely central and valuable area, could seem in contrast with the feasibility parameters and with the Parisian programming policies. The synergy between the SI approach and the inspiring principles of the Plan Climat have constituted a fundamental reference to verify its feasibility as logements collectifs. The main idea to operating in the project with a "gentle" addition of storeys (decreasing the ecological footprint), with retrofit elements for the common parts and the containment not only of rental costs, but also of the costs of collective maintenance and management by single households. Starting from 2020, it is possible to envisage in the Parisian context a system of incentives and tax exemption that are being tackled in other European contexts. With regard to the energy requalification front and despite the current limits to the classic condominium types (for Italy the bonus and incentive plan for the energy sector, Sismabonus, invoice tax discounts, etc.), the mechanism of transfer of construction rights to third parties in cases of addition of storeys on historical assets is of interest-and to be further explored in other contexts.
For the Italian context, the tax exemption mechanisms that could be included among those linked to the incentives of the energy sector seem interesting for private operators, while for the public entities, an interesting element is to operate also on areas with high market values, on which they can to trigger innovative negotiation mechanisms with private operators. The public administrations can function as a catalyst of urban regeneration, as shown for instance by the Tax Increment Financing (TIF), which, in some countries, subsidizes community improvement projects [99].
The project is part of an urban transformation process capable of providing a solution adaptable on a European scale, always placing the emphasis on the quality of the intervention, which must be integrated into the quality of the context and the memory of places [73]. The intervention is particularly ambitious as it operates within a particularly closed private market and integrates innovative financing and programming mechanisms into property management processes.
In particular, through the experimentation of innovative rental processes and the involvement of mixed management companies with new entrepreneurial figures, the proposed experimental model would allow private investors, local communities and social owners to interact in the production of new or existing homes. The simulation of this model was carried out on a small sample of inhabitants and in reference to a model of social enterprise and social entrepreneurship, which are already a reality in certain European contexts [100,101]. For this to be spreadable, it will be necessary for private investors to be encouraged to review their financial profitability criteria, in order to make social impact investing a reality capable of responding to the most urgent social challenges.
In this sense, the recent experiments of mixed evaluation models [8] could support both the decision-making process, test the financial levers (SROI) and indicate impacts and benefits not only for the investor but also for all stakeholders, according to the theories of the Stakeholder Approach and Corporate Social Citizenship.
The research presented here could not be considered exhaustive regarding the complexity of the aspects of public housing: aspects not sufficiently addressed in the proposal include, for example, those relating to the programming of maintenance costs and the management costs of shared services as well as the legal aspects related to mixed management entities.
The COVID 19 emergency phase has further highlighted how the negative effects in economic, social and psychological terms increased the critical issues already present for the most fragile categories [73]. The proposed approach, in this sense, can be a model to be inspired by, with the aim of investing resources in welfare but with public programming mechanisms in collaboration with private operators, which operate as socially responsible entities and companies that are economically responsible [102] toward the social and environmental challenges of the cities of the future.
In conclusion, in Table 3, we highlight the relationship between the research questions that guided the dissertation and some of the open questions and topics that need further research developments. These will be the subject of further research thanks to the progress of decision-making and design related to the Parisian area. The three open topics are: 1.
The definition of mechanisms that analyses the circular economic relationship and the reduction of land consumption in densely populated central urban areas; 2.
In-depth study on the birth and accompaniment of mechanisms of "construction" of mixité sociale; 3.
In a more advanced phase of the project proposal build tools to verify the effectiveness and scalability of social impact investing combined with investment processes in social housing, so as to constitute a lever for new management models. Table 3.
Research question and open question: The future development (source: Authors' elaboration).

Research Question Open Question (Need to be Further Developed or not Resolved)
(1) How would it be possible for urban contexts (in our case Paris) to meet the requirements related to policies that also look at the circular economy with a sustainable approach, without increasing land use?
Some issues are dealt with in theory by extrapolating emerging and experimented themes on the case study: there still remain criticalities on the characteristics of the case study, which is that of the central location, one of the most attractive market areas in Paris (pre-Covid).
(2) How can we ensure a fair distribution of social profiles within the city and therefore a mixitè analysis on some specific areas?
The theme has been extensively explored trying to deal with social, urban and economic aspects. Further research is needed to develop a legislative instrument that could regulate the proposed new system. New fields of study should be investigated to mature the guidelines that are currently only hypothesized for actors, funding, profiles interested, etc.
(3) Can the social impact investing methodology combined with the processes of investment in social housing be the engine of new management models? Can be a lever for urban development interventions and making them scalable to other contexts?
The mechanisms behind the constitution of public-private partnerships are still to be explored, according to different models: (1) consortia, (2) temporary associations of purpose, (3) social enterprises, etc.

Author Contributions:
The article is the result of the contribution of all the authors, but C.C. designed the overall structure. In particular, the introduction and Sections 1 and 2 were designed by C.C.; Section 3 was designed by C.C.; B.L.P. and C.Q.R.; Sections 4.1 and 4.2, by S.M., B.L.P. and C.Q.R.; Section 4.3, by C.C., B.L.P. and C.Q.R.; and Section 5, by C.C., S.M., B.L.P. and C.Q.R. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.