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The dimensions of accessibility: proximity, opportunities, values

This paper proposes a conceptual framework that redefines accessibility through three distinct dimensions—Proximity, Opportunity, and Value—to overcome the limitations of single-metric approaches and enable more nuanced, context-sensitive urban design and governance.

Original authors: Matteo Bruno, Bruno Campanelli, Hygor Piaget Monteiro Melo, Lavinia Rossi Mori, Vittorio Loreto

Published 2026-04-30

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CC BY 4.0

Original authors: Matteo Bruno, Bruno Campanelli, Hygor Piaget Monteiro Melo, Lavinia Rossi Mori, Vittorio Loreto

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to judge how "accessible" a city is for its residents. For a long time, experts tried to boil this complex idea down into a single number, like a score out of 10. But the authors of this paper argue that a single score is like trying to describe a delicious meal using only one word, such as "hot." It misses the flavor, the texture, and the ingredients.

Instead, they propose that accessibility is actually a three-dimensional concept, like a cube with three distinct sides. They call these dimensions Proximity, Opportunity, and Value.

Here is a simple breakdown of what they found, using everyday analogies:

1. The Three Dimensions

Proximity: The "Walkable Neighborhood"
Think of this as your immediate backyard. Proximity is about the things you can reach quickly by walking or a very short bike ride—like a grocery store, a pharmacy, or a local park.

The Metaphor: It's like having a well-stocked kitchen right next to your bed. You don't need a car or a bus; you just step out and grab what you need for your daily life.
The Point: You can have a great neighborhood full of local shops (high proximity) but still be stuck in a place where you can't easily get to the rest of the city.

Opportunity: The "City Explorer"
This is about reaching the big, exciting, or essential things that aren't in your immediate neighborhood. This includes major job markets, big universities, famous museums, or stadiums.

The Metaphor: This is like having a fast train or a highway that lets you leave your cozy kitchen and get to the "Grand Buffet" in the city center within an hour. Even if you don't live right next to the buffet, you can get there quickly and reliably.
The Point: You can have a fast train system that connects you to great jobs (high opportunity) but live in a lonely area with no local shops or community life (low proximity).

Value: The "Quality Check"
This is the trickiest part. It's not just about how far you have to go, but how good the things you reach actually are.

The Metaphor: Imagine you can walk to a restaurant in 5 minutes (great proximity). But if that restaurant serves bad food and is overpriced, your "access" isn't actually very good. Conversely, a high-quality job might be far away, but if it's the best job for you, it has high value.
The Point: Two neighborhoods might look the same on a map (same distance to shops), but one has a vibrant, high-quality community while the other has empty, low-quality buildings. Value is the "soul" of the destination.

2. The "Isolation" Trap

The authors use a diagram to show what happens when these dimensions don't match up. They identify two specific types of "isolation" that people might feel:

Spatial Isolation (The "Bubble"): You have a great local neighborhood with friends and shops (High Proximity), but you are cut off from the rest of the city. You can't get to a good job or a major event without a long, difficult commute. It's like living in a beautiful, self-contained village that is too far from the highway.
Social Isolation (The "Transit Hub"): You have a super-fast train station right outside your door that gets you to the best jobs in the city in 20 minutes (High Opportunity). However, your immediate neighborhood is empty, boring, and has no shops or parks. You can travel far, but you have nowhere to "land" or belong locally. It's like living in a hotel lobby: great for transit, but no home.

3. What They Did in the Study

The researchers didn't just talk about theory; they tested this on 18 real cities around the world (including New York, Paris, Rome, and Tokyo).

The Map: They created digital maps (using a honeycomb grid) to measure how many things people could reach by walking (Proximity) versus how many things they could reach by public transport (Opportunity).
The Findings: They found that while these two things often go together (dense cities usually have both), they don't always match.
- Example: In New York, Manhattan and Brooklyn are great at both. But the South Bronx has good local shops but poor connections to the rest of the city, while Staten Island has great connections but lacks local density.
The Simulation: They tested a "what-if" scenario in Rome. They simulated adding new subway lines. The result? The "Opportunity" score for the city went up by 8%, meaning more people could reach more distant, important places faster.

4. The Big Takeaway

The paper concludes that we shouldn't try to force all cities into one "perfect" model. A "one-size-fits-all" solution doesn't work because different people need different things.

Some people might prefer a quiet, isolated suburb (low opportunity, high space).
Others might need a bustling city center with everything nearby.

The authors argue that city planners need to stop looking for a single "magic number" to measure a city's success. Instead, they should look at the three dimensions separately. By understanding the trade-offs—like balancing a quiet local life with the ability to reach big opportunities—planners can make better decisions that actually help people live better lives, rather than just chasing a high score on a chart.

In short: Accessibility isn't just about being close to things; it's about being close to the right things, in the right way, with the right quality.

1. Problem Statement

Accessibility is a foundational concept in urban planning, geography, and social science, yet it remains difficult to define and measure effectively. Existing frameworks often attempt to reduce accessibility to a single universal metric (e.g., the "15-minute city" concept or gravity-based models). The authors argue that this reductionist approach fails to capture the complexity of human needs and the trade-offs inherent in different urban contexts.

Specifically, current metrics often conflate:

Local services (daily needs like groceries) with distant opportunities (jobs, major cultural venues).
Physical presence of amenities with their quality or value to the user.
Spatial isolation (lack of transport) with social isolation (lack of community).

The lack of a structured, multi-dimensional framework limits the ability of policymakers to design inclusive urban systems, leading to "one-size-fits-all" solutions that may be impractical or undesirable for diverse populations.

2. Methodology

The authors propose a quantitative framework that decomposes accessibility into three distinct dimensions: Proximity, Opportunity, and Value. They apply this framework to 18 global cities using a rigorous data-driven approach.

Data Sources

Administrative Boundaries: Municipal open data portals.
Transport Networks: GTFS (General Transit Feed Specification) schedules collected in May 2025.
Points of Interest (POIs): Extracted from OpenStreetMap (used as proxies for opportunities).
Population Data: WorldPop (100m resolution density grids adjusted to UN estimates).

Computational Framework

The study utilizes the H3 geospatial indexing system (Resolution 9, ~200m hexagons) to discretize city spaces. Travel times are calculated using the Open Source Routing Machine (OSRM) for walking and the Connection Scan Algorithm for public transport.

The three dimensions are quantified as follows:

Proximity ( $A_{prox}$ ):
- Definition: Access to everyday local services (e.g., grocery, pharmacies) via walking.
- Metric: Calculated as the integral of POIs reachable within a time $t$ , weighted by a utility function $f_{foot}(t)$ that decays exponentially (representing diminishing value of distance).
- Formula: $A_{prox}^\lambda = \int_0^\infty dt \, \rho_{foot}^\lambda(t) f_{foot}(2t)$ , where $\tau = 60$ min.
Opportunity ( $A_{opp}$ ):
- Definition: Access to non-local, high-value resources (e.g., jobs, stadiums, universities) via public transport.
- Metric: Uses public transport reachable POIs ( $\rho_{pub}$ ) and a utility function $f_{pub}(t)$ derived from travel time probabilities. This function accounts for schedule variability by averaging over peak hours and days.
- Formula: $A_{opp}^\lambda = \langle \int_0^\infty dt \, \rho_{pub}^\lambda(t_0, t) f_{pub}(2t) \rangle_{t_0}$ .
Value:
- Definition: The qualitative aspect of accessibility, encompassing service quality, reputation, and alignment with user preferences.
- Treatment: While theorized as a critical third axis, it is not quantified in this specific study due to data heterogeneity and bias issues (e.g., crowd-sourced ratings skewing toward wealthier demographics). It is proposed as a future layer to be integrated via triangulation of data sources.

Isolation Analysis

The authors define four states based on the intersection of Proximity and Opportunity:

Total Isolation: Low Proximity, Low Opportunity.
Spatial Isolation: High Proximity, Low Opportunity (local community exists, but disconnected from broader city opportunities).
Social Isolation: Low Proximity, High Opportunity (connected to the city, but lacks local social fabric/services).
Inclusion: High Proximity, High Opportunity.

3. Key Contributions

Tri-Axial Framework: The paper introduces a conceptual shift from 1D or 2D metrics to a 3D framework (Proximity, Opportunity, Value), explicitly distinguishing between "place" (local density) and "node" (connectivity).
Decoupling Metrics: It demonstrates that Proximity and Opportunity are theoretically independent dimensions. A city can have high local walkability but poor regional connectivity, and vice versa.
Quantitative Isolation Typology: It provides a method to classify urban areas into specific isolation types (Spatial vs. Social), offering nuanced diagnostic tools for urban planners.
Policy Simulation: The framework is applied to simulate the impact of infrastructure changes (e.g., new metro lines in Rome), showing how specific interventions can shift Opportunity scores without necessarily altering Proximity.

4. Results

The study analyzed 18 cities, with detailed case studies on New York, Rome, and a comparative analysis of all 18.

Correlation: There is a positive correlation between Proximity and Opportunity across cities (Pearson's $R \approx 0.61$ for New York; $R^2 \approx 0.76$ across all cities). Denser cities generally score higher on both axes.
City-Level Variations:
- Paris showed the highest average scores in both dimensions.
- New York and Berlin showed significant deviations from the regression line, indicating unique structural characteristics not explained solely by population density.
- US Cities: Generally clustered in lower accessibility zones compared to European counterparts.
Spatial Patterns: Low-proximity/low-opportunity zones consistently concentrate in peripheral belts.
Case Study (Rome): Simulating the addition of Metro Line C1 and Line D increased the population-weighted Opportunity score by 8%. Notably, 20% of residents saw an increase of at least 1,000 opportunities, with specific neighborhoods (Magliana Nuova, Salario) gaining over 8,000.
Isolation Identification: The framework successfully identified areas like the South Bronx (high proximity, low opportunity) and Staten Island (low opportunity access compared to the rest of NYC), highlighting specific infrastructure deficits.

5. Significance and Implications

Beyond the "15-Minute City": The paper argues that the "15-minute city" concept primarily addresses Proximity but often neglects Opportunity (long-distance access). A truly inclusive city requires both.
Equity and Planning: By distinguishing between spatial and social isolation, the framework helps policymakers target interventions more precisely. For example, a suburb might need better local services (Proximity) rather than just faster trains (Opportunity), or vice versa.
The "Value" Dimension: The introduction of "Value" challenges the assumption that physical access equals utility. It highlights that "quality deserts" (areas with services but low quality) are a critical form of inequality that standard metrics miss.
Future Directions: The authors emphasize that while a single "perfect" metric is elusive, a multi-dimensional toolkit allows for adaptive planning. They call for the integration of diverse data streams (crowdsourced ratings, transaction data) to eventually quantify the "Value" axis, acknowledging the inherent biases in such data.

In conclusion, this work provides a robust, quantitative foundation for moving away from scalar accessibility metrics toward a multidimensional understanding of urban equity, enabling more systematic analysis and decision-making in complex urban environments.