Assessing tourism sustainability through stochastic multi-criteria acceptability analysis: insights from the Italian regional context Open Access

Tourism is among the most dynamic sectors of contemporary economies. It drives growth, cultural exchange, and territorial development. Yet its rapid expansion has generated environmental and socio-cultural pressures, raising concerns about long-term sustainability. The notion of sustainable tourism − seeking to reconcile competitiveness with environmental protection and social well-being − has therefore become central to academic debate and policy agendas (Ko, 2005; Simo-Kengne, 2022). International bodies such as the United Nations World Tourism Organization (UNWTO) and the European Commission stress the need for reliable measurement frameworks to guide evidence-based decision-making. Yet challenges persist in operationalising indicators and aggregation. Key issues include fragmented data, the dominance of economic metrics over environmental and social ones, and the absence of consensus on aggregation methods. These tensions mirror broader debates on indicators. While they foster comparability and benchmarking, measurement can easily become an end in itself, obscuring the social processes that underpin sustainability (Miller and Torres-Delgado, 2023). Measuring tourism sustainability thus remains a contested issue, requiring approaches that are both conceptually rigorous and methodologically flexible. At the regional level, these issues intensify, as sustainable tourism is multidimensional and place-specific, demanding frameworks that capture local traits while ensuring comparability (Fernández and Rivero, 2009). Italy offers a pertinent case. As a leading tourist destination, it experiences both the benefits of tourism-driven growth and the risks of overtourism, environmental degradation, and socio-cultural tensions. The Italian context also illustrates that sustainability in tourism is not confined to ecotourism but represents a transversal goal that should permeate all forms of tourism and regional development strategies.

Scholars have proposed several approaches to address these challenges. Synthetic indicators are commonly used to integrate heterogeneous information into a single, comprehensive measure, enabling more straightforward interpretation and benchmarking. Yet the degree of compensation between indicators remains debated, as compensatory and non-compensatory approaches carry different policy implications. Hybrid methods combining these logics have been developed to produce more robust measures of tourism sustainability. This plurality reflects broader debates in sustainability assessment: while synthetic indicators are useful communicative tools, they must be carefully designed to avoid misleading conclusions (Mikulić et al., 2015). Alongside these, multi-criteria decision-making (MCDM) methods (see, for example, Kitsios and Grigoroudis, 2020), and particularly stochastic multi-attribute acceptability analysis (SMAA, Lahdelma et al., 1998), offer promising ways to address uncertainty and the subjectivity of weighting systems. By exploring the entire space of possible weights, SMAA reduces the arbitrariness of pre-defined schemes and allows for probabilistic rankings of regions (Greco et al., 2018). Unlike traditional synthetic indicators, SMAA does not assign a single score but generates distributions of rankings, highlighting the robustness of outcomes under alternative weightings. Applications to Italian regions confirm its ability to produce nuanced rankings and reveal patterns beyond traditional north–south divides. These advances reflect a conceptual shift in sustainability measurement, where uncertainty, subjectivity, and pluralism of stakeholder values are integral. SMAA thus represents both a methodological innovation and a theoretical alignment with contemporary debates on sustainability assessment.

Within this context, the present study addresses a clear research gap. While previous works have developed dashboards and synthetic indices of sustainable tourism, the integration of advanced MCDM methodologies such as SMAA in this domain remains underexplored. Moreover, sustainability indicators should be examined not only as monitoring tools but also as instruments that shape stakeholder perceptions and inform governance. This paper aims to fill this gap by developing and testing an indicator of tourism sustainability for Italian regions, explicitly designed to integrate economic, social, and environmental dimensions while accounting for uncertainty in the weighting of indicators. Accordingly, the research is guided by two questions:

This study has two goals: first, to develop a methodological framework for weighting and aggregating sustainability indicators in the Italian regional context; and second, to apply it empirically to generate a regional ranking and discuss policy implications. Its contribution is threefold. Conceptually, it advances debates on sustainable tourism measurement (e.g. Grassini et al., 2023; Giambona et al., 2024) by integrating indicator-based and decision-analytic approaches. Methodologically, it applies SMAA to tourism sustainability, offering a transparent and replicable solution to the weighting problem. Empirically, it provides a systematic assessment of Italian regions, yielding insights directly relevant to policymakers, destination managers, and scholars (Alaimo and Finocchiaro, 2022; Cesarini et al., 2025). The paper is organised as follows. Section 2 reviews the literature and state of the art. Section 3 outlines the proposed framework, including indicator selection and the SMAA application. Sections 4 and 5 present and interpret the empirical results. Section 6 concludes with limitations and avenues for future research.

Sustainable tourism has become central in academic and policy debates, as destinations seek to balance economic gains with environmental protection and socio-cultural well-being. Early studies stressed that a single dimension cannot capture sustainability, since tourism generates economic value alongside ecological pressures and cultural transformations (Garibaldi and Pozzi, 2018; Kristjánsdóttir et al., 2018). Grounded in sustainable development principles, sustainability in tourism is generally framed around three dimensions − environmental, economic, and socio-cultural − sometimes complemented by governance aspects. A balanced view requires indicators that reflect community engagement, fair distribution of benefits, and protection of ecosystems and heritage, which are essential for policies that foster resilient tourism systems (Dwyer, 2023).

The first significant wave of research translated conceptual frameworks into indicator-based systems, widely applied at the territorial scale, especially in the Mediterranean. These frameworks organised indicators around themes such as economic benefits, seasonality, residents' perceptions, accessibility, climate change, water management, and cultural heritage. Most converged on the three sustainability dimensions, with some adding governance to reflect institutional capacity. Bibliometric analyses confirm the rapid growth of research on tourism indicators, highlighting both methodological diversity and unresolved issues (e.g. Ruhanen et al., 2015; Streimikiene et al., 2021). Participatory processes such as consultations, workshops, and expert panels have become central to selecting indicators that reflect local priorities. The Organisation for Economic Co-operation and Development (OECD) framework for Spain formalised this participatory logic, proposing 21 core indicators and 47 metrics covering prosperity, seasonality, water, accessibility, climate action, and local perceptions (OECD, 2024).

As indicator frameworks matured, the need for aggregation led to the development of synthetic indices. These models are generally classified as compensatory or non-compensatory, depending on whether strong performance in one dimension can offset weaknesses in another (Greco et al., 2019). The notion of compensability is central to synthetic indicators, as it defines how much strength in one dimension can counterbalance weakness in another. Fully compensatory models, such as arithmetic means, allow complete trade-offs among dimensions, whereas non-compensatory ones penalise imbalances and emphasise coherence. The degree of compensability thus reflects a normative choice about the substitutability of sustainability dimensions within the index. Early systems relied on weighted aggregation based on expert consensus, statistical analysis, or multi-criteria techniques. Later, multilevel aggregation was proposed to synthesise results stepwise, first within dimensions and then across the system. Key contributions include the Goal Programming Synthetic Indicator and the Vectorial Dynamic Composite Indicator, which applied goal programming and dynamic integration to support policy benchmarking and territorial comparisons (Blancas et al., 2010). Subsequent designs, such as the Mazziotta–Pareto Index, penalised imbalances across dimensions to encourage balanced outcomes (Mazziotta and Pareto, 2016; Antolini et al., 2024). Weighting remains a crucial step, as different schemes embody distinct methodological and normative assumptions. Equal weighting ensures transparency but ignores indicator relevance; expert-based methods reflect context but risk bias; statistical approaches, such as principal component analysis, produce data-driven weights but complicate interpretation; and frequency- or probability-based schemes highlight indicator salience or rarity (OECD/European Union/EC-JRC, 2008; Greco et al., 2019). The appropriate method depends on data availability, indicator properties, and stakeholder preferences (Alaimo, 2022). Hybrid models now aim to reconcile these trade-offs—for example, Punzo et al. (2022) proposed multi-modelling frameworks combining weighting, aggregation, and scenario analysis to improve robustness. Despite these advances, synthetic indices still face enduring limitations. The debate on these aspects echoes long-standing methodological discussions in the field of synthetic indicators (e.g. Maggino, 2017; Alaimo, 2023). Indicator selection is often constrained by data availability. At the same time, weighting is not merely technical but also normative, as it embodies value judgements about indicator relevance and compensability, linking statistical synthesis to broader sustainability priorities.

To address these challenges, MCDM methods have gained increasing attention. Traditional indicator frameworks require fixed weights, often based on expert judgement or statistical rules, which impose rigid assumptions and rarely reflect diverse stakeholder priorities. Most aggregation schemes also rely on compensatory logics, allowing strong performance in one area (e.g. economic growth) to offset weaknesses in others (e.g. environment). As a result, rankings can be sensitive to methodological choices, undermining policy credibility. Consequently, synthetic indices often yield rankings that are contested, opaque, and of limited use for governance in complex, multi-actor contexts. MCDM approaches explicitly model multiple criteria and embrace uncertainty in sustainability evaluations. Unlike traditional indices, MCDM does not collapse multidimensional data into a single deterministic score. Instead, it provides a structured framework for comparing alternatives across criteria, making trade-offs visible and analytically tractable. Within this family of methods, SMAA offers clear advantages. Instead of imposing predetermined weights, it explores the whole space of feasible ones, generating probabilistic rankings of alternatives. This approach is particularly suitable for Italian regions, where tourism systems are diverse and often characterised by conflicting objectives. By accommodating this diversity and highlighting robustness across value systems, SMAA provides a stronger basis for decision-making. Regions differ in their economic reliance on tourism, ecological vulnerability, cultural assets, and governance capacity. A method that accommodates this diversity and highlights robustness across divergent value systems provides a stronger basis for decision-making. By applying SMAA, this study advances sustainable tourism evaluation, ensuring that findings are credible, transparent, and relevant for policymakers who balance economic, environmental, and socio-cultural goals in complex territorial settings.

Building on the debates concerning compensability and weighting outlined above, this study proposes a Tourism Sustainability Index based on MCDM. Traditional synthetic indicators often rely on rigid weights and compensatory rules, and are not particularly robust under uncertainty. As no approach is free from drawbacks, MCDM is valuable because it models multiple criteria and acknowledges diverse stakeholder priorities. Within this family, we adopt SMAA, which manages weighting uncertainty and enables probabilistic exploration of rankings. Its strength lies in covering the entire space of feasible weights rather than fixing them in advance. In practice, non-negative weight vectors are randomly drawn under a uniform probability distribution. For each configuration, a synthetic score and ranking of alternatives is obtained. The outcome is not a single ordering but a set of rank acceptability indices (RAIs), which measure the probability that each alternative occupies a given rank. This directly assesses ranking robustness, helping policymakers identify both likely leaders and the conditions under which regions may shift position. Full details on indicator treatment, polarity alignment, normalisation, and the stochastic sampling design are provided in the Supplementary Material (Section A.1–A.2), which also reports the algorithmic settings used to ensure reproducibility. It is worth stressing that SMAA does not provide a unique synthetic score or index for each alternative, unlike traditional synthetic indicators. Instead, it produces a distribution of rankings across the whole weighting space. The results, therefore, highlight the robustness of alternatives' positions rather than fixing them to a single deterministic measure. In this sense, SMAA should be understood less as an index-construction method and more as a probabilistic ranking framework that supports transparent and pluralistic decision-making.

Conceptually, this feature is crucial in tourism sustainability, where the weight given to economic, environmental, and socio-cultural dimensions legitimately varies among stakeholders. Scholars may stress cultural or ecological resilience, while policymakers prioritise jobs or competitiveness. A single weighting vector reflects only one view, limiting representativeness. SMAA instead spans the full spectrum of preferences, offering a transparent and pluralistic assessment (Saisana et al., 2005). This shift has been described as moving from subjective objectivity” − the illusion of neutrality in fixed weights − to objective subjectivity”, where diverse perspectives are explicitly modelled in a probabilistic framework. SMAA is also flexible in aggregation. While the arithmetic mean is common, quasi-linear or geometric means can be applied. The geometric mean is less compensatory: weak performance in one dimension cannot be fully offset by strong performance in another. This property is crucial in sustainability assessments, where trade-offs, such as environmental loss versus economic gain, should not be assumed to cancel each other out. By integrating non-linear aggregation, SMAA strengthens robustness and accommodates different normative positions without altering its probabilistic foundation.

Formally, let A denote the set of n alternatives (e.g. regions), each evaluated across a set C of p criteria (sustainability indicators). The most common aggregation rule is the weighted sum, where each criterion c_j ∈ C (j = 1, …, p) is assigned a weight $wj∈R+p$ subject to the constraint w₁ + ⋯ + w_p = 1. The synthetic score of alternative a_i ∈ A (i = 1, …, n) is then defined as:

where w_j reflects the importance attributed to the j-th criterion and c_j(a_i) denotes the observed value for alternative a_i. Because the weights w may vary, the ranking of alternatives is not fixed but contingent on the chosen weighting scheme.

To formalise this variability, SMAA introduces a probability distribution over the weight space W, with density function f_W(w), and a probability distribution over the evaluation space χ (i.e. the feasible set of criterion values), with density function f_χ(ξ). In the absence of prior information, weights are assumed to follow a uniform distribution in W. For a given vector of weights w, the rank of an alternative a_i is defined as:

where ρ(false) = 0 and ρ(true) = 1. Thus, the rank of a_i under a given weight vector corresponds to one plus the number of alternatives performing better on the selected criteria.

The key innovation of SMAA is to consider the sets of favourable rank weights, defined as:

which represent the subsets of weight vectors for which alternative a_i obtains rank r. From these sets, the rank acceptability index (RAI) is computed as the expected measure of favourable weights:

The RAI $bir$ can be interpreted as the probability that alternative a_i achieves rank r, representing the proportion of weight vectors under which the alternative occupies that position in the ranking. This measure provides a nuanced, probabilistic picture of performance, showing not only whether an alternative is likely to be among the leaders or laggards, but also the degree of uncertainty about its position.

Beyond RAIs, SMAA produces several complementary indices that deepen the analysis. The central weight vector represents the barycentre of the weight configurations for which an alternative is ranked first, thereby identifying the “average” preference profile under which the alternative excels. Formally, if $Wi1(ξ)$ denotes the set of weight vectors for which a_i attains the first rank, the central weight vector is defined as:

where $bi1$ is the RAI of alternative a_i for the first rank. Intuitively, $wic$ captures the average set of preferences under which a_i emerges as the best alternative.

Associated with the central weight vector, the confidence factor quantifies the degree to which the alternative remains the best when evaluated with its own central weight vector, defined as:

where ρ[⋅] is the indicator function. The confidence factor $pic$ therefore represents the frequency with which a_i is the top-ranked option when assessed with its own central weight vector. This provides an interpretable measure of robustness: alternatives with a high confidence factor are not only occasionally first but are consistently supported by a stable weighting profile.

Overall, SMAA transforms the problem of constructing a synthetic sustainability index from one of fixed assumptions to one of probabilistic exploration. Rather than obscuring the diversity of stakeholder preferences, it explicitly models them, thereby producing results that are more credible, transparent, and useful for governance in contexts − such as tourism sustainability − where multidimensionality and contested priorities are inherent features.

Italy exemplifies the tensions between tourism-driven development and sustainability. As one of the world's most visited countries, it combines outstanding cultural assets, rich natural resources, and a strong tourism economy, yet faces overtourism, environmental stress, and socio-cultural pressures. Cities such as Venice, Florence, and Rome illustrate crowding, declining liveability, and ecological impacts, while coastal and mountain areas highlight the fragility of destinations. The COVID-19 pandemic briefly interrupted these dynamics, but recovery has revived concerns over resilience, governance, and equity. Policy debates at both the European and national levels emphasise the importance of robust monitoring frameworks to balance competitiveness with environmental protection and community well-being. Constructing a sustainability index thus requires careful operationalisation of multidimensionality. Variable selection was guided by three principles: regional comparability, reliance on official statistics, and alignment with international frameworks. Following the UNWTO's Statistical Framework for Measuring the Sustainability of Tourism (SF-MST), the European Commission's European Tourism Indicator System (ETIS), and the Global Sustainable Tourism Council (GSTC) Destination Criteria (UNWTO, 2024; European Commission, 2016; Global Sustainable Tourism Council, 2019), we adopted a triple-bottom-line logic. At the regional level ^[1], the 47 variables (Table 1) were grouped into environmental (17), economic (15), and social (15) pillars, ensuring conceptual continuity with established destination indicator systems (Antolini et al., 2024).

1. Environmental pillars (C1–C17) - Water-use intensity (C1) and the efficiency of wastewater treatment (C2) are retained because freshwater availability is repeatedly identified as a critical carrying-capacity constraint for tourism regions worldwide (Gössling et al., 2012). Waste generation (C3) and source-separation rates (C4) reflect the circular-economy focus embedded in the ETIS core indicators. In contrast, transport-generated PM_2.5 (C5) and the renewable share in electricity (C6) operationalise decarbonisation pathways consistent with the Paris Agreement. Climate-exposure proxies − consecutive dry days (C7) and heating/cooling degree-days (C8–C9) − translate climate-driver metrics into destination-scale risk indicators (IPCC, 2023). Spatial conservation (C10–C12), voluntary eco-certification (C13), and environment-related attitudes (C14–C17) mirror sustainable development goal (SDG) targets on biodiversity, pollution and behavioural change (UN, 2015).

2. Economic pillars (C18–C32) - Market-diversity (C18), the domestic/foreign mix (C19) and seasonality (C20) follow OECD guidance on resilience and demand dispersion (OECD, 2025). Capacity-use measures (C21, C23) track productivity. In contrast, seasonal employment (C22) and labour-quality variables (C28–C31) reflect the decent-work agenda of SDG 8. Density (C24) and the suite of expenditure, fiscal return and public-spending ratios (C25–C27, C32) position tourism yield to host-economy size, as advocated by the SF-MST.

3. Social pillars (C33–C47) - Resident-visitor ratios (C33–C36) operationalise social carrying capacity, a key determinant of community support for tourism (Deery et al., 2012). Satisfaction scores for entertainment, food and services (C37–C39) capture experiential quality and destination liveability, while average length of stay and guest-origin distance (C40–C41) link local benefit with travel-related carbon costs. Cultural-asset density (C42) embeds heritage stewardship, female-employment share (C43) addresses inclusive growth (SDG 5), and safety indicators (C44–C46) recognise that security perceptions strongly mediate resident well-being and visitor demand. Finally, the COVID-19 recovery index (C47) measures adaptive capacity to systemic shocks, an attribute emphasised in recent OECD tourism-resilience work (OECD, 2025).

The empirical analysis integrates multiple statistical sources at the regional level, following the open-data logic of the SF-MST to ensure replicability. Italian National Institute of Statistics (ISTAT) provides official demographic, social, economic, and environmental data. Italian Institute for Environmental Protection and Research contributes to environmental monitoring. EUROSTAT, the EU's statistical office, supplies harmonised cross-country indicators. Equitable and Sustainable Well-being, coordinated by ISTAT, tracks well-being and sustainability. INPS (Italian National Institute of Social Security) offers labour and employment statistics. BANKITALIA (Bank of Italy), the central bank, provides data on financial flows and tourist expenditure. Finally, CPT (Territorial Public Accounts) monitors regional public spending, including tourism. All variables were harmonised for comparability, with polarity assigned so that higher values consistently represent greater sustainability.

The descriptive statistics in Table 2 reveal marked territorial disparities across sustainability dimensions. Environmentally, Trentino-South Tyrol and Tuscany exhibit the highest pressures in terms of water use, waste, and emissions. In contrast, Molise reports the lowest values, primarily due to limited inflows rather than effective practices. Veneto and Aosta Valley emerge as benchmarks for waste separation, green space, and renewable energy. Economically, Sardinia and Lazio perform best in terms of tourist expenditure and added value, whereas Calabria exhibits structural fragilities characterised by high seasonality and low public spending. Socially, Abruzzo and Trentino-South Tyrol stand out for service satisfaction, while Molise, Liguria, and Lazio exhibit weaker performances, particularly in safety indicators. Overall, tourism drives regional development but also generates environmental and social risks, requiring careful governance to ensure long-term sustainability (Cegarra-Navarro et al., 2013).

Following the SMAA framework (Section 3), we analysed 47 variables for 20 Italian regions to derive a synthetic ranking of tourism sustainability. All computational procedures and simulation routines were developed and implemented in the R environment. In constructing synthetic indicators, each variable has an intrinsic polarity, that is, the direction in which its increase contributes positively or negatively to the overall concept (Alaimo and Maggino, 2020). For instance, higher waste generation or energy intensity implies negative polarity, whereas greater resource efficiency or employment in sustainable tourism reflects positive polarity. Ensuring correct polarity alignment before normalisation is essential for meaningful synthesis and comparability across regions. Variables were normalised through a robust z-score transformation mapped to the unit interval [0,1], ensuring positive values for geometric aggregation and mitigating outlier effects (Greco et al., 2018). One million weight vectors, uniformly sampled from a Dirichlet distribution, represented alternative stakeholder preferences across the economic, social, and environmental pillars. For each configuration, scores were computed using the weighted geometric mean, which limits compensability among dimensions. The resulting simulations generated ranking distributions and associated probabilistic measures (Eqs. (4)–(6)). Sensitivity analyses reported in the Supplementary Material (Section A.3) verify that these results are stable under alternative normalisation and aggregation assumptions, confirming the internal consistency of the SMAA framework.

To help the interpretation of results, it is useful to recall that the RAI represents the probability that a region attains a given rank when legitimate stakeholder priorities vary across the weighting space. The expected rank and the top-three probability summarise the central tendency of performance and the likelihood of being among the leading regions. The central weight vector captures the “typical” preference profile under which a region excels. At the same time, the confidence factor quantifies how often that region remains best when assessed using its own central weights. From a managerial standpoint, these outputs serve as probabilistic “confidence maps” of sustainability performance, enabling regional authorities to determine whether leadership positions are structurally stable or contingent upon specific assumptions. A high top-three probability combined with a narrow rank distribution signals robust competitiveness, whereas a wide distribution indicates sensitivity to shifting priorities. Confidence factors translate this statistical robustness into strategic reliability: regions with high confidence values can prioritise consolidation strategies, while those with volatile profiles should focus on structural reforms. Overall, these measures bridge the technical robustness of the SMAA model with practical governance and policy priorities, guiding communication, investment, and risk management.

Figure 1 reports the RAI heatmap, as defined in Eq. (4). The graph displays, for each region, the probability of attaining a given rank across the one million simulated weighting schemes, thereby offering a probabilistic representation of the ranking distribution. Darker cells denote higher probabilities, providing an intuitive visualisation of the likelihood that each region occupies specific rank positions. The representation ensures a transparent assessment of how likely each region is to be placed at different levels in the ranking space, also identifying the weighting structures under which leadership positions remain most stable.

Table 3 summarises the outcomes of the SMAA simulations, showing the expected rank together with the probabilities of attaining the first and the top-three positions. These values are directly derived from the distribution of rankings obtained through the simulation procedure and correspond to the empirical estimates of the probabilities.

Finally, Figure 2 illustrates the global importance of the ten most influential criteria. The values are computed ex post as Spearman correlations between each criterion and the expected rank, thus capturing the strength and direction of association between individual indicators and the probabilistic outcomes of the SMAA analysis.

The results reveal substantial heterogeneity in tourism sustainability across Italian regions, as shown by the SMAA framework. As detailed in the robustness checks (Supplementary Material, Section A.3), the stochastic simulations yield stable rankings for top and bottom performers, while mid-range regions display higher variability. These diagnostic results contextualise the probabilistic patterns discussed below. Abruzzo and Veneto emerge as robust leaders, with high probabilities of top positions across weighting schemes, while Calabria, Sicily, and Trentino-South Tyrol display persistent fragility (Table 3). These findings address RQ1, on how probabilistic methods enrich sustainability assessments. Rather than a single deterministic score, SMAA shows how outcomes depend on alternative value structures, exposing the subjectivity of any ranking. The RAI heatmap (Figure 1) shows that Abruzzo and Veneto not only dominate but do so consistently across scenarios. In contrast, Umbria and Molise exhibit wider probability spreads, reflecting sensitivity to weighting assumptions and less robust results. This probabilistic perspective shifts attention from rank levels to rank stability, an often-overlooked dimension in synthetic indicator approaches.

This interpretation aligns with prior research highlighting the multidimensional and context-dependent nature of sustainability assessment. Punzo et al. (2022) showed with the SusTour-Index that Italian regional rankings are highly sensitive to weighting and aggregation, consistently placing Trentino-South Tyrol first. Our SMAA analysis reveals this dominance is not robust once preference uncertainty is introduced. Similarly, Blancas and Lozano-Oyola (2022) demonstrated that compensatory methods can mask weaknesses, whereas alternative formulations yield very different outcomes. By combining the geometric mean with SMAA, we limit compensability and uncover fragilities concealed by deterministic indices. More broadly, this reflects broader debates that methodological choices often drive results as much as the data itself (Torres-Delgado and Saarinen, 2014; Blancas et al., 2018). Antolini et al. (2024) reinforced these concerns, using multi-source data and the Mazziotta-Pareto index to argue that robust frameworks must capture both territorial disparities and multidimensionality, noting that regions like Trentino-South Tyrol may appear as leaders but conceal vulnerabilities. Our findings extend this by emphasising that robustness must also account for preference uncertainty. Complementary insights come from Alaimo and Finocchiaro (2022), whose fuzzy clustering distinguished two groups of regions, not by geography but by structural patterns of environmental pressure and infrastructure. Our results partly overlap: Abruzzo and Veneto, consistently stable in our rankings, show how diversification mitigates environmental pressures, while Calabria and Sicily align with weaker Cluster 2 performance. The intermediate case of Apulia aligns with our finding that mid-ranked regions are susceptible to weighting assumptions, underscoring the non-linear nature of sustainability outcomes.

Turning to the drivers of rankings, Figure 2 shows that environmental management and resource efficiency correlate most strongly with expected rank. This directly addresses RQ2, on the factors shaping regional sustainability in a probabilistic setting. Regions balancing ecological dimensions display resilience across scenarios, even when economic or social indicators are weaker. Thus, ecological sustainability functions as a stabiliser in the hierarchy, consistent with theories of territorial capital and resilience (Camagni and Capello, 2012; Martin et al., 2016). By contrast, short-term economic indicators do not guarantee robust results, as shown by Trentino-South Tyrol volatility.

Some results are unexpected. Trentino-South Tyrol, often ranked first in deterministic indices (Punzo et al., 2022; Antolini et al., 2024), performs weakly here, showing how probabilistic methods expose the instability of apparent leadership under varying preferences. Conversely, Abruzzo's strong performance challenges the assumption that peripheral or less developed regions are disadvantaged, supporting evidence that sustainability is not mechanically tied to gross domestic product or tourist volume (Harb and Bassil, 2021; Volgger et al., 2025). These insights underline the need for place-based strategies that reflect structural diversity rather than uniform prescriptions.

Theoretically, this work contributes to sustainability assessment by operationalising uncertainty. Traditional indices embed assumptions on weights and compensability but seldom make their implications explicit. SMAA instead converts these assumptions into probability distributions, offering a more faithful view of sustainability as a multidimensional and contested construct. This links with theories in regional economics, where diversity, institutional capacity, and resilience underpin long-term performance (Camagni and Capello, 2012; Martin et al., 2016). In this sense, our analysis addresses RQ1 by showing how probabilistic frameworks shift assessments from static rankings to dynamic evaluations of robustness and stability. Managerially, the combined evidence of Table 3, Figures 1 and 2 clarifies opportunities and risks in regional trajectories. Table 3 shows Abruzzo and Veneto not only lead but do so with high probabilities, signalling competitive advantages that support branding, investment, and policy prioritisation. The heatmap (Figure 1) confirms these stable positions, while regions such as Umbria and Molise show volatile distributions, reflecting exposure to preference shifts. The importance analysis (Figure 2) highlights environmental criteria as the most consistent drivers of sustainability. This answers RQ2, suggesting that ecological stability and resource efficiency are more reliable strategic levers than short-term economic gains. This implies that investments in water management, waste treatment, and renewable energy are more likely to secure resilience than strategies focused on arrivals/revenue growth.

Despite its contributions, this study has limitations. Indicator selection was constrained by data availability, leaving cultural and institutional aspects underexplored. While SMAA handles weighting uncertainty, other subjectivities, such as normalisation and indicator choice, remain inherent to synthetic indicators. These choices can influence comparative outcomes, particularly where indicators exhibit skewed distributions or unequal data quality, and should therefore be interpreted as one plausible representation of sustainability rather than a definitive ranking. A sensitivity extension comparing alternative normalisation and weighting rules would provide a more systematic measure of methodological uncertainty. The analysis was conducted at the NUTS-2 level because this scale ensures data availability and comparability across economic, social, and environmental dimensions. Although finer territorial disaggregation (NUTS-3 or municipal levels) could capture local heterogeneity, data coverage and consistency remain limited, particularly for social and environmental indicators. Future research should extend SMAA to longitudinal and cross-country settings, offering more profound insights into how structural and governance factors shape regional sustainability trajectories. Moreover, integrating subregional datasets or spatial microsimulation techniques to model intra-regional variation will enhance the spatial resolution of sustainability assessments and their policy relevance for local governance.

This paper set out to address the challenge of measuring tourism sustainability by integrating indicator-based approaches with SMAA. The central contribution lies in demonstrating that sustainability cannot be reduced to a single deterministic index but must instead be assessed through methods that recognise its multidimensionality and explicitly incorporate uncertainty in weighting schemes. In doing so, the study advances both the conceptual debate on sustainability measurement and the methodological toolbox available to scholars and practitioners. The findings provide clear answers to the two research questions. For RQ1, the results show that integrating economic, environmental, and social dimensions is both feasible and informative. Yet strong territorial heterogeneity persists: Abruzzo and Veneto emerge as robust leaders, while Calabria, Sicily, and Trentino-South Tyrol display enduring fragilities. This confirms that sustainability is not mechanically tied to economic size or tourism intensity but depends on structural and contextual conditions. Concerning RQ2, the analysis shows that probabilistic methods shift attention from ranking levels to ranking stability. The RAI heatmap and rank probabilities show which regions maintain stable positions across diverse value structures and which are vulnerable to changes in weighting. Finally, the importance analysis highlights environmental management and resource efficiency as key stabilisers, underscoring their centrality for long-term sustainability strategies. The supplementary analyses (Section A.3) confirm that the SMAA-based indicator is methodologically sound and not dominated by single variables or compensability assumptions. This reinforces the validity of the insights discussed here.

From a managerial and policy perspective, these results carry important implications. Destination managers should view sustainability not as a fixed score but as a range of possible scenarios, using probabilistic frameworks to design adaptive strategies. Policymakers can rely on benchmarking tools to clarify trade-offs among economic, social, and environmental goals, thereby supporting more transparent and inclusive governance. The finding that ecological sustainability is the most consistent driver of robust performance suggests that investments in water management, waste treatment, and renewable energy secure more resilient outcomes than strategies centred on short-term growth. Overall, sustainable tourism should be treated as a transversal objective embedded in regional development strategies rather than a niche policy domain. Building on these implications, and extending the managerial perspective to the policy level, the probabilistic results generated by SMAA could be incorporated into regional monitoring systems and sustainability dashboards, providing decision-makers with dynamic tools to visualise ranking stability and trade-offs among objectives. Such integration would enhance evidence-based policymaking by linking quantitative assessment with adaptive management, allowing regional authorities to update priorities as new information becomes available. This operational use of probabilistic rankings bridges methodological innovation with practical governance, fostering transparency, accountability, and policy learning.

In conclusion, this study highlights the importance of incorporating uncertainty into sustainability measurement. By combining indicator-based approaches with SMAA, it provides a more faithful representation of sustainability as a multidimensional and contested construct, moving beyond the illusion of definitive hierarchies. Future research could extend this work by incorporating participatory weighting processes, qualitative dimensions, and longitudinal analyses to capture temporal dynamics. Such developments would not only refine methodological robustness but also support inclusive governance practices, thereby guiding tourism systems toward resilience and sustainability in increasingly complex territorial contexts.

The supplementary material for this article can be found online.