A Gate-and-Menu Theory of Collective Tourism Brand Value

Protecting the Anchors: Why Some Tourism Brands Collapse While Others Thrive

Tourism brands consist of two distinct parts. There is a "gate" of essential anchors—such as safety, infrastructure, or iconic landmarks. There is also a "menu" of many smaller, modular attractions. If a major anchor fails, the entire brand suffers a massive blow. However, if one small attraction in the menu fails, the impact on the overall destination is negligible. This distinction is critical. Destination managers often struggle to decide which assets require collective protection to prevent brand-wide decay.

A new study from Johan Fourie at Stellenbosch University proposes a formal mathematical framework to explain this asymmetry. The paper argues that treating a destination as a single, uniform bundle of assets fails. It ignores the structural reality of how tourists actually decide to visit a place. By separating the "participation" decision from the "itinerary" decision, the author provides a tool for identifying vital assets.

The failure of uniform bundling

Current approaches to tourism management often treat a destination as a single, aggregated bundle of goods. In these models, every attraction is treated with similar logic. This includes everything from a world-famous national park to a local village museum. If a model assumes all attractions contribute equally, it implies a minor museum could exert as much influence as an iconic monument.

The study demonstrates that this approach is fundamentally flawed. It ignores the different ways assets enter consumer demand. Most tourism brands operate under a "collective reputation" (a shared name used by many different owners). If a model treats all assets symmetrically, it cannot explain why a single security lapse can devastate an entire nation. Meanwhile, the closing of a single boutique cafe has almost no effect on national arrivals. As shown in, the relationship between quality and brand value is not linear.

It is shaped by the specific role an asset plays in the traveler's journey.

The gate-and-menu architecture

To resolve this, the paper introduces a multiplicative model. Destination value ($V$) is the product of a gate ($G$) and a menu ($A$). This reflects two stages of travel. The gate handles the decision to visit a country. The menu handles the decision of how to spend time once there.

The mechanism operates through two distinct mathematical aggregators:

1. The Gate (Weaker-Link Aggregator): The gate consists of essential inputs and non-reproducible "anchors." These are assets like a specific coastline or a national security regime. The authors model this using a "weaker-link" function. This is similar to the "O-ring" theory of economic development. In that theory, a single broken link in a complex process can cause the entire system to fail. Consequently, the gate is sensitive to its lowest-quality components. If a gate element degrades, its importance to the total value increases.
2. The Menu (Love-of-Variety Aggregator): The menu consists of modular, reproducible attractions. Examples include festivals, museums, or wine estates. These are combined using a "love-of-variety" function. This assumes that a wider range of options increases a destination's appeal. Unlike the gate, the menu is composed of many small items.

The structural asymmetry arises because the gate multiplies the menu. A shock to a gate element scales the marginal value of every item in the menu. Conversely, a shock to a menu item only affects the brand through a tiny, fractional share. This share effectively vanishes as the menu grows. illustrates this clearly. A 10% degradation in an iconic natural wonder causes a significant drop in total value. A similar degradation in a city museum results in a nearly invisible loss.

Measuring latent brand structures

Because "gate" and "menu" status are latent (meaning they cannot be observed directly in a database), the authors employ large language models (LLMs) as measurement instruments. Using Claude (Opus) and OpenAI’s Codex (gpt-5.5), the study processed public guide text from Wikivoyage and Wikipedia for 166 economies.

The researchers report high reliability in this automated classification. The two different LLM families showed a strong correlation ($r = 0.84$) in their assessments of brand homogeneity .

This correlation means the models reached highly consistent conclusions about how much a single theme dominates a country. Furthermore, the study performed an external check. Researchers matched the LLM-labeled "gate" attractions against the UNESCO World Heritage List. They found that the models correctly identified iconic, non-reproducible assets. Gate-labeled attractions appeared on the UNESCO list at 6.4 times the odds of menu attractions.

Beyond mere labeling, the paper uses Aumann–Shapley accounting. This is a method from cooperative game theory used to distribute the total value of a joint project among its contributors. The findings confirm the theoretical prediction. Binding gate anchors earn a non-vanishing share of the brand's value. Individual menu attractions earn only a minuscule portion.

Identifying the maintenance gap

A significant portion of the paper focuses on why these vital assets are often poorly maintained. The framework suggests that the gate behaves like a "commons." This is a shared resource prone to neglect because no single user owns it entirely.

In a decentralized system, the custodian of a gate asset captures only the local tourism revenue. This might be a local municipality managing an airport. However, the benefits of maintaining that asset spill over to every other region. Higher national reputation and arrival numbers benefit everyone. The authors prove that, under most standard conditions, a decentralized custodian will "weakly under-maintain" the physical quality of a gate asset. This happens because they do not capture the full social surplus (the total benefit to society) created by its upkeep.

This creates a "welfare wedge." This is the gap between the private benefit to the custodian and the social benefit to the nation. The paper suggests that destination managers should not look for the most "visible" site to fund. Instead, they should find the "binding" gate element. This is the element currently acting as the weakest link. Targeting this element maximizes the return on coordination efforts.

Limitations and practical application

The study is not without constraints. The authors note that the text-based homogeneity index is a descriptive proxy. It measures thematic concentration rather than a direct measurement of quality-conduct homogeneity. Additionally, the illustration involving French wine regions is based on a very small sample size ($n=4$). Therefore, the statistical power of that specific finding is limited. Finally, the model assumes the "gate" and "menu" distinction is driven by the margin on which an asset enters demand. This classification remains an empirical challenge for researchers to verify at scale.

For practitioners, the verdict is clear. Stop treating all tourism assets as equal. The research provides a specific decision protocol for destination management. Managers should first classify assets into gate or menu categories. Next, they must identify which gate element is currently the "weakest link." Finally, they should coordinate maintenance efforts specifically around those binding anchors. Relying on uniform branding or blanket tourism taxes may miss the mark. Instead, policy should target the specific custodians whose assets hold the entire brand's reputation in the balance.