The Valuation of Aesthetic Preferences and Consequences for Urban Transport Infrastructures

Abstract

The importance of transport infrastructure for individual well-being and regional economic development and growth, but also its adverse side-effects, make a comprehensive assessment of the general appropriateness of new construction and rebuild indispensable. Assessments, however, often lack certain issues. For instance, aesthetic aspects are usually not part of the (economic) evaluation of large infrastructure projects, albeit individuals may be (positively or negatively) affected by the aesthetic ‘value’ of infrastructures. This paper proposes the aesthetic index developed by Birkhoff as a method to quantify the aesthetic impact of buildings/facilities in urban areas. To test the basic applicability of the index for transport infrastructure facilities, we apply it at first to airport terminals in Germany. We also test the suitability of the index to derive the willingness to pay for aesthetic exterior design—since market prices are easy to obtain with respect to hotel room rates—using hotel architecture as the first example. Regression results of a hedonic price model indicate a significant relationship, suggesting the basic suitability of the index to uncover consumers’ willingness to pay for an aesthetic outward appearance. We suggest further research to test the suitability of Birkhoff’s index for general urban transport infrastructures in order to derive utility-based welfare measures toward aesthetic issues. For highly controversial urban (overground) infrastructures, we propose the inclusion of an aesthetic component in cost–benefit analysis.

1. Introduction

As mobility needs in society increase, so too does the need for new and modern transport infrastructure utilities. The importance of transport infrastructure for individual well-being, regional economic development and growth, but also its adverse side-effects, make a comprehensive assessment of the general appropriateness of new construction and rebuild indispensable. In most cases, project assessment takes place by means of cost–benefit analysis, in which all relevant costs and benefits of a project are evaluated and aggregated to a single (monetary) unit. Such assessments, however, often lack certain issues [1]. For instance, aesthetic aspects are usually not part of the (economic) evaluation of large infrastructure projects, albeit individuals may be (positively or negatively) affected by the aesthetic ‘value’ of infrastructures.

Importantly, despite the manifold potential benefits associated with new infrastructures (e.g., travel time savings, better accessibility), they often evoke opposition along with a lack of acceptance by citizens [2]. Recent examples of new infrastructure construction plans, such as the new railway connection between Torino and Lyon (Susa Valley—Italy), the new railway station in Stuttgart (Germany) show how sensible citizens oppose such plans. A prominent example is a relatively new road bridge in Dresden, Germany (the so-called Waldschlösschen bridge). Construction plans led to severe opposition, protests, court hearings and finally to a referendum. The result of the referendum was (albeit narrow) in favor of the construction, but, as a consequence of this, the city of Dresden ultimately lost its world cultural heritage status by the UNESCO in 2009. Obviously, aesthetic issues—an essential factor for the status—were not part of an initial project appraisal. However, they should be part of a comprehensive evaluation process, because side-effects of aesthetic issues, such as the loss of the cultural heritage status, may be closely related to economic losses through a reduction in tourism [3,4]. However, how can we measure aesthetics and do individuals attach some monetary value to aesthetic issues such that they can be part of an economic project appraisal?

The present study seeks to answer these questions. The paper proposes the aesthetic index developed by Birkhoff [5] as a method to quantify the aesthetic impact of buildings/facilities in urban areas. The index makes use of geometrical properties of the facility in question and, thus, is based upon objective criteria. To test the basic applicability of the index for transport infrastructure facilities, we firstly apply the index to airport terminals and, in addition, we test its suitability to derive the willingness to pay estimates (and thus the possibility to include such measurements in cost–benefit analyses) for hotel architecture since market prices are easy to obtain for hotel markets. The regression results of a hedonic price model indicate a significant relationship, suggesting that consumers are willing to pay higher prices for an aesthetic outward appearance. We suggest further research to test the suitability of Birkhoff’s index for further urban transport infrastructures in order to derive utility-based welfare measures for aesthetic issues. For highly controversial urban infrastructures, we propose the inclusion of an esthetic component in cost–benefit analysis.

2. Theoretical Insights—Measuring the Aesthetic Value

The term esthetic was already known in the ancient world and originates from the Greek term “aisthētikos”, from “aisthēta” (perceptible things), from “aisthesthai” (perceive) [6]. The translation already indicates that the ancient philosophy just knew the term aesthetic in the sense of perception but not in the sense of theory concerned with beauty as it became popular some centuries later [7] (p. 14), [8] (p. 1).

In the 18th century, Alexander Gottlieb Baumgarten, a German philosopher, began to establish aesthetics as a philosophical science for the first time. In his work Esthetica (1750–1758) he established the new systematic and philosophical thinking about aesthetics and defined it as a philosophical explanation of beauty and art. Sesemann [8] (p. 2) points out that Baumgarten defined aesthetics as being “the act of consciousness that perceives an object, at the same time evaluates it and recognizes its aesthetic value”. For the first time, Baumgarten introduced terms such as sensation, feeling and taste in connection with beauty and aesthetic theory [9] (p. 255).

Many other well-known philosophers, e.g., Johann Gottfried Herder, David Hume, Immanuel Kant, and Friedrich Schiller mentioned the issue of aesthetics in their works in the following years. Nevertheless, their theories contradicted each other such that many different conceptions of beauty existed.

The contradictory views on taste development and sensual perception in connection with beauty become obvious when comparing two of the most famous philosophers of the 18th century: Immanuel Kant and David Hume.

Hume claims in his work ´Of the Standard of Taste’ (1757) that beauty is the expression of the subject’s aesthetic preference and not the result of an object’s characteristics. Beauty is exposed to subjectivism and always “lies in the eye of the beholder” [7] (pp. 13–14), [10]. At the same time, he explains that humans do not possess taste congenitally but that it is possible for everyone to acquire taste through experience, practice, and comparison. Following Hume’s notion, it is important to consider the opinion of experts when it comes to the judgment of aesthetics and beauty [11].

Kant countered Baumgarten’s and Hume’s theory with his work ‘Kritik der Urteilskraft [Critique of Judgment]’ (1790) in which he emphasized that humans generally possess an aesthetic power of judgment. Therefore, Kant’s notion “Beautiful is what is generally liked without definition” implies that beauty possesses a certain level of generality and, as a result, it is important to consider the average taste of people instead of looking at individuals [11].

Note that since we are interested in building architecture, we refrain from discussing product design literature (e.g., [12,13,14,15]), yet all these approaches have common elements with our approach in Section 3.

In economics, the measurement and valuation of aesthetics is rather underexplored [16]. The authors of [17] discuss the economist’s perspective for a sector, which is very close to the aesthetics, notably for the arts. Since, however, they deal with tradable goods (such as paintings) or art utilities, which are in general priced (e.g., museums, operas), we refrain from discussing this topic in more detail. The reason for this is that this paper centers on transport infrastructure utilities. Their aesthetical effects may be regarded an externality (positive of negative is not clear), for which there exists no market. We therefore need non-market goods valuation methods.

From the economist’s point of view, such methods are often used in transport economics. We therefore refer to a conventional approach when a method tries to find out whether individuals are willing to pay any money for a certain aesthetical view, thereby implying the existence of substitution (respectively, the existence of an indifference curve) between aesthetics and money.

Contingent valuation is a survey method in which individuals may directly express their monetary valuation for certain objects, or landscapes or buildings. Although this method is severely criticized [18,19,20], it enjoys (due to its simplicity) great popularity. With respect to the aesthetics of transport infrastructure utilities, the authors of [11] used this method to study the aesthetical effects of the controversially debated “Waldschlösschen” bridge in Dresden, where the bridge construction led to the loss of the UNESCO world heritage status for the city of Dresden. Their findings suggest that monetized aesthetical gains may be high enough to finance the cost difference for the construction of other infrastructure alternatives (such as tunnels) which do not intervene in the valley landscape and therefore may be regarded as more aesthetic.

In urban areas, a great variety of architecture can be recognized. Almost every building seems to have a different story and reflects the ideas and ideals of different periods of time as well as the views of the architects involved in the planning and construction process. At the same time, they have different levels of attraction for people. Especially historical buildings are often perceived as being highly aesthetic and beautiful and even worth travelling to and paying money for [21], thereby indicating a relationship between aesthetics and architecture [9,22].

The advent of the hedonic pricing models (HPM) [23] brought a breakthrough for the consideration of architectural and aesthetic issues in economics. Assuming (among others) perfect information and no transaction cost, the hedonic approach treats the price $p$ of a differentiated good (such as houses or apartments) as a function of its attributes $z$, i.e., $p=p\left(z\right)$ where $z=z_1,z_2,\dots z_k$ denotes the attribute vector of the object (e.g., apartment) in question.

A view in the literature reveals that several hedonic approach contributions have empirically analyzed the impact of architecture in general and even to some extent the aesthetics of architecture, in particular on real estate prices (e.g., [24,25,26,27,28,29,30]). In-depth overviews are provided by [30,31]. All of these studies capture the aesthetic value of real estates in different ways. The authors of [28] used officially designated landmark and architectural award information in order to analyze office prices in downtown Chicago. The authors of [26,32] constructed indices out of expert’s surveys (architects) in order to analyze the impact of aesthetics on the prices of office buildings for Cambridge, Boston and Tel Aviv. The authors of [25,33] captured aesthetic effects in their studies by introducing parameters for the different architectonic styles in their hedonic price equations. A similar approach was also used in [25], where the authors analyzed the price effects of small historic buildings. The authors of [34] defined several different criteria for new urbanism to analyze its impact on house prices in Portland. The authors of [27] evaluated the impact of historic houses on real estate prices. Some studies have incorporated the aesthetic impact indirectly in their analyses. For instance, the analyses in [35,36] (both studies analyze the impact of noise on house prices) used variables for view, respectively, the construction period of the buildings to control for aesthetic effects.

Due to their microeconomic foundation, discrete choice models (see e.g., [37]) have become a common research instrument, especially in transport economics. Meanwhile, discrete choice models are used not only for mode, route or airport/airline choices but also in order to evaluate aesthetical preferences. An interesting choice experiment in this respect has been performed in Ireland [38,39], where the authors, by use of photographs in choice experiments, could derive spatially distributed willingness to pay measures for several landscape improvements.

In an experimental approach, [40] used bidding experiments and addressed the theoretical problems in the economic valuation of aesthetical preferences (mainly associated with divergences between the equivalent and the compensating variation and the aggregation of individual bids).

In addition to the economic perspective, landscape architecture provides some interesting approaches to measure the aesthetic value. Such methods result mainly in index numbers, i.e., different objects or landscapes are ordered according to their index value. Index approaches can be roughly subdivided into descriptive inventory methods and quantitative holistic models [41]. Such methods largely reflect Hume’s notion of standard taste mentioned before. This more or less implies that groups of experts or committees have the ability to judge aesthetic values better than individuals due to the experience and exercise of their members on aesthetic issues.

Descriptive inventory methods (e.g., bipolar semantic list or uniqueness ratio) define certain criteria for aesthetics and note their existence (or non-existence) for the objects to be evaluated. In some cases, they assign values to the beauty-relevant components. Finally, the (weighted) components may be aggregated to a single index value, which allows comparisons among various objects.

In quantitative holistic models (such as scenic beauty estimation or the law of the comparative judgment), the physical aesthetic criteria from descriptive inventory methods are combined with individual psychological cognitive criteria and are therefore extended by surveys.

3. The Birkhoff Index

An interesting alternative approach of measuring the aesthetic value of an object is provided by the American mathematician David George Birkhoff, who wrote four essays (1928–1932) about the problem of the perception of aesthetic objects such as works of art, spoken lyrics and musical compositions, and tried to find an empirical way to compare them [9] (p. 265). In the end, Birkhoff summarized his findings and presented a formula for the mathematical measurement of esthetics in his work ‘Esthetic Measure’ [3].

At the beginning of his work, Birkhoff points out that aesthetics as a science is mainly concerned with aesthetic feeling and the aesthetic object leading to this feeling. Birkhoff at first divides aesthetic objects into two broad categories, notably natural objects and artificially created objects. Those belonging to the first category are usually created without intention and can be found in nature (e.g., landscape, sunsets), whereas objects from the second category are created with intention and, therefore, express the ideas and ideals of the creator (e.g., works of art, architecture) [3] (p. 3). Birkhoff’s measurement approach considers only objects of the second category and just looks at “the formal side of art”, i.e., the visible, exterior (mostly) geometric characteristics of an object (e.g., contour of a building, shape of an object) [3] (p. 13). Thus, this approach seems at first glance to fit well with the scope of our study. Transport infrastructure and buildings belong to the second group of objects as they represent the ideas of the architect and can be evaluated by looking not only at the functional but also at the visible and exterior attributes.

The functionality of the human brain is essential for aesthetic judgments. Birkhoff, therefore, defines a three-step process that takes place in the human brain when an esthetic experience is made [3] (p. 3). This process is illustrated in Figure 1.

The first stage comprises an initial effort of attention needed for the perception of an object, varying proportionally with the level of complexity (C) of an object. The higher the complexity (C), the higher the initial effort needed. In the next step, the brain rewards this effort with a “feeling of value”, which is expressed as aesthetic measure (M). Finally, “a realization that the object is characterized by a certain harmony, symmetry, or order (O)” takes place and represents the last stage within an aesthetic experience process [3] (p. 3f.).

For this reason, the aesthetic value (M) is composed of these two key elements: complexity (C), order (O). It is given by:

$$M=\frac{O}{C}$$

(1)

The complexity (C) refers to the effort of attention needed for the perception of an aesthetic object; it thus refers to the object’s composition. Every part of an object, i.e., every contour of the polygon, causes the eye to move and accordingly increases the effort involved. Consequently, Birkhoff defines C as being “the number of indefinitely extended straight lines which contain all the sides of the polygon” [3] (p. 34).

According to [3], “The property of an aesthetic object which corresponds to any association will be called an ‘element of order in the object’” (p. 9). This means that the order (O) results from the geometrical relationships between subcomponents of an object, which can be subdivided into the following elements of order:

• V = vertical symmetry;
• E = equilibrium;
• R = rotational symmetry;
• HV = relation to a horizontal-vertical network;
• T = characteristic tangents;
• S = similarity;
• F = unsatisfactory form.

Inserting these elements in Equation (1) yields:

$$M=\frac{V+E+R+HV+S+T-F}{C}$$

(2)

V takes the value 1 if the respective object possesses vertical symmetry and 0 if it does not. If an object has vertical symmetry, it is perceived as especially comfortable and favorable from the observer as he or she has the impression that it is in equilibrium.

This is why E equals 1 for objects that possess vertical symmetry (V = 1) or have a horizontal base and thus are in complete optical equilibrium. If a polygon is in ordinary mechanical equilibrium, it just takes the value 0, as it is less aesthetically appealing. For polygons without equilibrium, E equals −1.

The rotational symmetry (R) obtains the value 1 if the polygon possesses V = 1, and 0 if it has no symmetry. Generally, R is computed by q/2, where q denotes the number of partial symmetric polygons. R cannot be greater than 3 [3] (pp. 35–39).

If all sides of a polygon lie in a horizontal–vertical network, i.e., if the polygon has no diagonals but just vertical and horizontal lines, HV gets the value 2. HV equals 1 if there are some sides that do not fulfill this requirement or if there is a diagonal in the polygon. All other cases are evaluated with HV = 0 [3] (pp. 39–41).

The two order elements—similarity (S) and characteristic tangents (T)—find their application when it comes to, e.g., ornaments and curvilinear elements. As they can be found in the design of polygons such as buildings, which play an important role in this work, the two elements are added and considered in the evaluation. If a similarity of type exists, S receives the value 1; if there is more than one, it is assigned the value 2. In the case that there is no similarity, S equals 0. Design elements such as circles, curvatures, ellipses or parables are captured through their characteristic tangents (T). Their number equals the value of T with the exception that parallel tangents are only counted once. If the object does not contain curvilinear elements, T equals 0 [3] (pp. 57 ff.).

The unsatisfactory form (F) is an element of order that can have a negative influence on the aesthetic measure (M). If all of the above conditions are fulfilled, F equals 0 and has no negative influence on M. If one condition is not met, F equals 1, and if more than one condition is missed, F equals 2 [3] (pp. 41–42).

The maximum of the aesthetic value M can be reached if the order (O) reaches its highest positive value, whereas the complexity (C) approaches its possible minimum value: $M^{max}=\frac{O^{max}}{C^{min}}$. The relation $DU=\frac{M}{M^{max}}$ thereby gives the degree of utilization of the aesthetic potential.

One main advantage of Birkhoff’s approach is that all geometric features contributing to the aesthetic value of an object are combined to a single index. In addition, recent contributions from neuroaesthetics seem to confirm the significance of the geometrical dimensions used by Birkhoff. The authors of [42] (pp. 276–285) conducted an experiment in which they analyzed how the characteristics of an object (e.g., symmetry, complexity, geometrical shapes, order) affect the brain activities during the aesthetic experience of people looking at and judging about this object. Their findings support that the aesthetic judgment is mainly ruled by symmetry and order. In addition, this study identified complexity as being also a characteristic of aesthetic but not as important as symmetry and order. In general, a series of studies in neuroscience and psychology identify the importance of symmetry, order and complexity for aesthetic judgment [43,44,45,46]. Another advantage is that the index measures aesthetic objectively, thereby avoiding biased evaluations stemming from behavioral anomalies which have been found to distort the decisions of economic agents, even with respect to transport-related decisions [47,48].

These findings support the use of Birkhoff’s approach in our paper. Birkhoff assumes that symmetry as an element of order is very important for the aesthetic value of an object and that, in particular, vertical symmetry is perceived as especially comfortable by the beholder. This is in line with the neurological findings.

On the other hand, it should be noted that in Birkhoff’s approach, materials (e.g., glass, steel etc.) or colors are not part of the aesthetic value. We thus keep in mind that Birkhoff’s formula may not capture all possible factors, which contribute to the aesthetic value of an object. In addition, it seems that Birkhoff’s formula underestimates the uniqueness or even the reputation of the creator of the object in question. Take, for instance, a painting by a famous artist, for which potential buyers are willing to pay a lot of money in an auction, or for which the public is willing to pay a certain entrance fee to a museum. A (very good) copy of this painting by another unknown artist would certainly achieve a much lower price in an auction, or people would be willing to pay much lower entrance fees to a museum in order to be able to enjoy the copy. The aesthetic value assigned by the Birkhoff approach would, however, be the same for the copy and the original painting. Furthermore, the surrounding area is not considered in the formula but may play an important role in the process of aesthetic perception. It influences the beholder to a great extent according to the architect Richard Neutra (as cited in [9] (p. 109)). Moreover, buildings are often very complex objects, especially older ones. With increasing complexity, it becomes more and more difficult and time-consuming to capture all geometric elements and to define the components in a reliable and correct way. If there is a very high level of complexity, every indefinitely extended straight line and diagonal needs to be counted, which bears a great potential for errors. With rapidly increasing complexity, the aesthetic value automatically decreases as well, which might be misleading when considering the results of the neurological findings mentioned above that suggest that complexity is not always automatically perceived as unaesthetic by the beholder.

Accounting for the advantages and keeping the disadvantages in mind, in the empirical part, we will proceed with the calculation of Birkhoff’s index, using German airport terminals as an example.

4. Empirical Implementation: Birkhoff’s Aesthetical Value for German Airport Terminals

We now empirically calculate the Birkhoff index for nine German airport terminals. Airport terminals are typical transport infrastructure utilities in urban areas. In addition, they seem to fit with the main idea of this paper relating architecture to an aesthetical value. Furthermore, airport capacity expansion seems, in many cases, to lack acceptability (mostly due to noise-related issues). The (new) Munich airport, for instance, reached a total construction time of 28 years, where most of this time was court hearings. We thus conclude that the consideration of airport terminals is a good example for the scope of this paper. In total, we have considered the following cases:

• Berlin Brandenburg “Willy Brandt” Airport;
• Cologne/Bonn Airport
• Dresden International Airport;
• Erfurt-Weimar Airport;
• Frankfurt Airport;
• Hamburg Airport;
• Hannover-Langenhagen Airport;
• Leipzig/Halle Airport;
• Munich “Franz Josef Strauß” Airport.

The calculations consider only the respective airport terminal. For airports with more than one terminal, two separate calculations have been performed and the arithmetic mean of all terminals is computed. All results are rounded to two decimal places.

Color photos are the basis for the evaluation, which show the airport terminals in front view. During the selection of the pictures, it is important that all buildings have the same perspective (front view) and that the terminals are completely pictured to make them comparable.

In the following, in order to save space, we present computations for “Dresden International Airport”. The airport started its operations in 1935. In 1998, the terminal was rebuilt within three years. Since 2001, the terminal building has been located in a former hangar of the GDR aircraft industry. The exterior view shows contemporary architecture with glass front sides, metal lamination and brick-red ceramic tiles. Based on Figure 2,

Table 1. Birkhoff values for Dresden International Airport. Source: own calculations.

C	V	E	R	HV	S	T	F
12	1	1	1	1	1	0	1

presents all numerical values of several relevant variables:

The red lines in Figure 1 represent complexity C. This variable is defined as the number of infinitely extended lines that contain all sides of the polygon, as described above. Therefore, C takes the value of 12. The vertical symmetry axis is marked as a green straight line in the photography. Therefore, V = 1, the terminal building is in equilibrium and E is assigned the value 1. The rotational symmetry R received the value 1 because of the central symmetry of the terminal. HV = 1, because not all sides of the building would fit into a horizontal–vertical network. The parts of the building that are on the right and left side are similar to each other, so S = 1. T an F are both 0, because the front view of the terminal does not include characteristic tangents (T) and there is no unsatisfactory shape (F).

Plugging these values in Equation (2) gives the aesthetic result for “Dresden International Airport”:

$$M_{DRS}=\frac{1+1+1+1+1+0-1}{12}\approx 0.33$$

(3)

For the calculation of the maximum aesthetic utilization of the terminal (Equation (3)), we consider the maximum sum of the order O. $O^{max}$ is the result of the addition of the highest values of several components, which are defined as the order O. As already mentioned, $O^{max}$ takes the value of 9. C has the same value as in the calculation above (C = 12) and Equation (3) becomes:

$$M^{max}=\frac{O^{max}}{C}\approx 0.75$$

(4)

The ratio of $M$ and $M^{max}$ gives the utilization of aesthetic potential, which is in our case 0.44 or 44 percent.

Table 2. Total results of the Birkhoff approach. Source: own calculations.

Airport	M	Mmax	Utilization (in %)
Frankfurt	0.86	1.30	67
2. Erfurt/Weimar	0.75	1.13	67
3. Hamburg	0.67	1.00	67
4. Munich “Franz Josef Strauß”	0.65	1.13	61
5. Hannover-Langenhagen	0.63	1.14	56
6. Berlin Brandenburg “Willy Brandt”	0.45	0.82	56
7. Dresden International	0.33	0.75	44
8. Leipzig/Halle	0.25	0.52	49
9. Cologne/Bonn	0.066	0.14	48

summarizes the results of all considered airport terminals. The airports are ranked according to the aesthetic measure M.

Table 2 shows that Frankfurt Airport is the most aesthetical (rank 1) airport among the considered airport terminals according to the Birkhoff approach. By contrast, Cologne/Bonn Airport terminal has the lowest aesthetical value (rank 9).

In addition, Frankfurt (together with Erfurt/Weimar and Hamburg) mostly utilizes its aesthetical potential, whereas, Cologne/Bonn Airport has the lowest utilization of aesthetic potential. An interesting result was found for Erfurt/Weimar airport, a rather small sized airport located in East Germany. According to our measurements, this airport takes rank two and therefore has the second most aesthetic airport terminal in Germany. Besides, the new Berlin Brandenburg Airport performs rather below average.

Albeit the weaknesses of the Birkhoff approach discussed in the previous section, we see clearly that it is basically possible to compute and evaluate the aesthetics of transport infrastructure. Nonetheless, the question remains of whether it is possible to attach an economic value to it, suitable for welfare analysis in the sense of cost–benefit analysis. For this reason, it is necessary to apply methods of non-market valuation. As transport infrastructure utilities have no market prices, a direct use of hedonic pricing for infrastructures is not possible, leaving choice modeling approaches as the only possibility to test the economic suitability of the Birkoff approach.

However, in order to gain a first impression, we made use of the hotel market. More specifically, we computed the Birkhoff value for several hotels around Bonn/Germany and fed these values into a hedonic pricing model. Hedonic pricing has been intensively applied in the past in the tourism industry. Related studies have utilized price information on package tours [49,50,51,52,53] or of room rates [54,55,56,57,58,59,60] in order to construct and estimate hedonic price equations, where vectors with room characteristics, hotel attributes, and locational attributes enter the analysis.

Although the evaluation of intangible aspects of tourism such as hotel brands has been gaining increasing attention in recent years and presents a foundation for the investigation of architectural influences [61] (p. 187), to the best of the authors knowledge, hotel architecture and its impact on room rates has not yet been analyzed in the literature.

The whole procedure, analysis and results are described in Appendix A. Therein, we found a positive and significant impact of the exterior design, respectively, hotel architecture (measured by the Birkhoff index) on hotel room rates. This indicates a basic applicability of the Birkhoff index in order to derive the willingness to pay for architecture.

5. Discussion and Conclusions

Motivated by a potentially increasing public acceptability of new transport infrastructure utilities via better aesthetic appearance, this paper presented and discussed a simple index—the Birkhoff index—for aesthetical measurement. Subsequently, we applied the Birkhoff index to airport terminals in Germany. We also tested the basic applicability of the Birkhoff index to derive the willingness to pay for exterior design of hotel buildings using market prices for hotel bookings. Our findings support the hypothesis that consumers may attach value to aesthetics. We were able to identify a significant relationship between esthetics and room rates.

Nonetheless, the conceptual construction of the Birkhoff index seems to have some shortcomings. First, it only takes into account the geometry of the building in question and ignores further factors that could be of importance for aesthetics, such as colors, materials and the surroundings. Consequently, not all possible aesthetic effects are captured by the approach. Second, the Birkhoff index ignores further dimensions of objects such as uniqueness or the reputation of the creator.

According to our findings, aesthetics should no longer be only a subject of philosophy but also one of practical significance for business and policy. Generalizing our results to all consumers, we can therefore conclude that in particular for highly contested new transport infrastructure projects a higher-valued aesthetic appearance will certainly increase individual utility and possibly also public acceptability. Unfortunately, current project appraisals (e.g., cost–benefit analysis) for public infrastructure usually does not include an aesthetic component. Such aesthetic components might, however, alter the results of cost–benefit analyses. Occasionally, economists suggested the consideration of an aesthetic component in project assessment methods, in particular for highly controversial infrastructure. For instance, [11] found that for the case of the “Waldschlösschenbrücke” in the city of Dresden (Germany), citizens may have a willingness to pay high enough to finance the difference of the current to a more aesthetic and also more expensive bridge appearance. Such smart policy is in our view in a position to enhance public acceptability.

As the Birkhoff formula offers an easy, understandable and objective way to assess aesthetics and to compare aesthetic values for different projects, we suggest its further use or even its extension in order to account for the unsettled factors mentioned above.

The hedonic approach for aesthetic valuation that we performed in our paper applies only for cases where market prices exist. Since for infrastructure market prices are usually not available, we carried out our calculations for hotel buildings as a first attempt to attach a monetary value to aesthetics, measured by the Birkhoff index. However, computing willingness to pay measures in the case of transport infrastructure requires the use of choice modelling approaches. As [38,39,62] show, it is possible to apply choice experiments in order to evaluate the aesthetic appearance of landscapes. We thus suggest the inclusion of the Birkhoff index in adequate choices experiments for urban transport infrastructure in order to derive utility-based welfare measures that can be part of cost–benefit analysis. Moreover, because aesthetic issues might also be a matter of concern for other transport facilities, e.g., public transport stations or even whole systems [63], dealing not only with buildings in the narrow sense could be appropriate as well.