Zhan B Nurgaliyev

ALTERNATIVE UNDERSTANDING OF GRAVITY AS RESULT OF MOVEMENT OF MASSES IN FOUR-DIMENSIONAL SPACE

An alternative approach to understanding gravitation is proposed and its possible technological application is described. A confirmation of the proposed approach is shown basing on observations of interacting spiral galaxies and positive results of experiments with Airbus company. The proposed idea is based on the assumption that movement of masses along the fourth coordinate causes a gravitational attraction similar to the attraction of electric currents flowing in the same direction. A new form of gravity force equation is proposed. The principle of the gravity induction is described as well as its possible application for gravitational propulsion.

INTRODUCTION

I started to look for alternative ways to describe gravity in search for possible technical applications that can arise from a new approach. The research has led me to certain ideas that do not contradict the facts and at the same time predict interesting phenomena under certain conditions.

Briefly speaking, the basic idea evolved from a comparison of gravity to a magnetic attraction of parallel electric currents. If the currents are oriented perpendicular to our three-dimensional space, then gravity would be similar to the magnetic field caused by the electric currents flowing in the same direction. The inverse-square law for the gravity force follows from that the gravity interaction takes place through a threedimensional space. The beauty of the idea is that the movement of mass itself causes gravity interaction just like a movement of an electric charge causes a magnetic field. Since all the masses move in the same direction along the fourth coordinate at a very high constant speed, under ordinary conditions we see only gravity attraction of masses that do not seem to be fast moving in our frame of reference. However, in special cases described below certain interesting phenomena are expected to be found, including gravity induction that can be used for propulsion.

INTERACTION OF PARALLEL ELECTRIC CONDUCTORS

Let us consider the following example from electromagnetism, illustrating the Ampere's force. There are two infinite parallel conductors in vacuum at the distance 𝑟 from each other. The currents 𝐼 1 and 𝐼 2 of the conductors are flowing in the same direction (see Pic 1).

Pic. 1.

According to the Biot-Savart law, a conductor creates the following magnetic field at distance 𝑟:

𝐵 1 (𝑟) = 𝜇 0 2𝜋 𝐼 1 𝑟 (1)
where 𝐵 1 is the magnetic field of the first conductor, 𝜇 0 is the magnetic constant, I 1 is the current of the first conductor, 𝑟 is the distance separating the conductors.

As it follows from the Ampere's force law, the first conductor acts on the second one with following force:

𝑑𝑭 ⃗ ⃗ 1-2 = 𝐼 2 𝑑𝒍 × 𝑩 ⃗⃗ 1 (𝑟) (2)
According to the right-hand rule, the force 𝑑𝑭 ⃗ ⃗ 1-2 is directed to the first conductor, meaning that the conductors are attracting. The previous formula can also be written in the following way:

𝑭 ⃗ ⃗ 1-2 = 𝑰 2 × 𝑩 ⃗⃗ 1 (𝑟) (3)
This law is a three-dimensional prototype of the basic equation of the proposed description of gravity.

GRAVITY FIELD VECTOR

The gravity field G generated by a single particle m in four dimensions can be shown as follows:

I1 I2 F1 F2 B1 B2 r Pic. 2.
where the square plane represents the threedimensional space 𝑮 is the gravity field vector, an analogue of vector 𝑩 in electromagnetism, that shows the direction and the magnitude of the gravitational field at a certain point, 𝑴 is the mass current, generated by movement of mass 𝑚 along the fourth coordinate, and analogue of 𝑰 in electromagnetism, 𝑟 is the distance from the mass to the point, at which the vector 𝑮 is located.

We use the same "right hand" rule from electromagnetism to find the direction of the vector 𝑮 in a 4D diagram. The previous diagram is an analogue of the following diagram from electromagnetism:

Pic. 3.
where 𝑩 is the magnetic field vector, 𝑰 is the current generated by movement of a charge 𝑞, 𝑟 is the distance.

The question is how to depict the 𝑮 vector in a 3D space. An ordinary vector cannot be used here, because the vector 𝑮 must be perpendicular to the radius 𝑟 and at the same time must be represented in the same form at any point on a 3D sphere formed by the radius 𝑟:

Pic. 4.
We need another geometrical object to represent the vector 𝑮 -a bivector.

USAGE OF BIVECTORS

A bivector is a quantity in geometric algebra or exterior algebra that generalizes the idea of a vector. Geometrically, a simple bivector can be interpreted as an oriented plane segment, much as vectors can be thought of as directed line segments. For the bivector a ^ b, its magnitude is the area of the parallelogram with edges a and b. The Pic. 6.

In our case, the gravity field bivector 𝑮 is represented by two vectors 𝒈 1 ^𝒈2 . And its magnitude is equal to the magnitude of the cross product of 𝒈 1 and 𝒈 2 :

|𝑮| = |𝒈 1 × 𝒈 2 | (5)
We can draw the vector 𝑮 in the following way in 3D space: Pic. 7.

FOUR-DIMENSIONAL CROSS PRODUCT

To obtain the gravitational field equation we need to write down the equation from electromagnetism

𝑭 ⃗ ⃗ 1-2 = 𝑰 2 × 𝑩 ⃗⃗ 1 (𝑟) (6) in the following form 𝑭 ⃗ ⃗ 1-2 = 𝑴 ⃗⃗⃗ 2 × 𝑮 ⃗⃗ 1 (𝑟) (7)
but here the vector 𝑮 ⃗⃗ 1 is a bivector that can be represented by two orthogonal components 𝒈 ⃗⃗ 1 1 and 𝒈 ⃗⃗ 1 2 .

𝑭 ⃗ ⃗ 1-2 = 𝑴 ⃗⃗⃗ 2 × 𝑮 ⃗⃗ 1 = 𝑴 ⃗⃗⃗ 2 × 𝒈 ⃗⃗ 1 1 × 𝒈 ⃗⃗ 1 2 (8)
A cross product of three vectors is not defined in 3 dimensions, but it exists in 4 dimensions.

Let us take three 4-dimensional vectors: 𝒖 = (𝑢 1, 𝑢 2, 𝑢 3, 𝑢 4 ), 𝒗 = (𝑣 1, 𝑣 2, 𝑣 3, 𝑣 4 ) and 𝒘 = (𝑤 1, 𝑤 2, 𝑤 3, 𝑤 4 ). The vector 𝒖 × 𝒗 × 𝒘 is orthogonal to 𝒖, 𝒗, 𝒘 and changes by sign if any two of the vectors are switched. The length of 𝒖 × 𝒗 × 𝒘 is the volume of the parallelepiped with edges 𝒖, 𝒗, 𝒘. The 4D cross product can be written in terms of coordinates in the following way:

𝒖 × 𝒗 × 𝒘 = det [ 𝒊 𝒋 𝒌 𝒍 𝑢 1 𝑢 2 𝑢 3 𝑢 4 𝑣 1 𝑣 2 𝑣 3 𝑣 4 𝑤 1 𝑤 2 𝑤 3 𝑤 4 ] (9)
The determinant of the matrix is

𝒖 × 𝒗 × 𝒘 = 𝒊 | 𝑢 2 𝑢 3 𝑢 4 𝑣 2 𝑣 3 𝑣 4 𝑤 2 𝑤 3 𝑤 4 | -𝒋 | 𝑢 1 𝑢 3 𝑢 4 𝑣 1 𝑣 3 𝑣 4 𝑤 1 𝑤 3 𝑤 4 | + + 𝒌 | 𝑢 1 𝑢 2 𝑢 4 𝑣 1 𝑣 2 𝑣 4 𝑤 1 𝑤 2 𝑤 4 | -𝒍 | 𝑢 1 𝑢 2 𝑢 3 𝑣 1 𝑣 2 𝑣 3 𝑤 1 𝑤 2 𝑤 3 | (10)

INVERSE-SQUARE LAW

In the case of parallel currents from electromagnetism, the vector B is in inverse ratio to distance r:

𝐵 1 (𝑟) = 𝜇 0 2𝜋 𝐼 1 𝑟 (11)
In case of 4-dimensional currents, there will be a 1/𝑟 2 -dependence of the gravitational field vector G on distance:

𝐺 1 = 𝐾 𝑀 1 𝑟 2 (12)
where K is a constant coefficient. The 1/𝑟 2dependence exists in this case because here the inverse-square law must be applied. The inversesquare law is generally applied when some force, energy, or other conserved quantity is radiated outward radially in a three-dimensional space from a point source. Since the surface area of a sphere (which is 4𝜋𝑟 2 ) is proportional to the square of the radius, as the emitted radiation gets farther from the source, it is spread out over an area that is increasing in proportion to the square of the distance from the source.

Pic. 8. Hence, the intensity of radiation passing through any unit area (directly facing the point source) is inversely proportional to the square of the distance from the point source. Therefore, an application of the inverse-square law follows from the quantity of dimensions of the space through which the gravity field is propagated.

SPEED OF MASS ALONG THE FOURTH COORDINATE AND BIG BANG

The assumption of a motion of all masses in the same direction, perpendicular to the 3D space is in correspondence with the model of expanding Universe and the Big Bang theory. According to one of the common models, the space of our Universe has a positive curvature and can be thought of as an expanding 3D sphere, which is a surface of a 4D ball. Since the moment of the Big Bang the matter in the Universe is flying apart from a certain point in a 4D space (see Pic. 9). Pic. 9. Velocities of masses are equal in magnitude and oriented in the same direction due to an expansion of the Universe.

As for the speed of this motion, since at the early stages of the Universe it was filled only with light, with pure energy, we can assume that the expansion along the fourth coordinate is going on at the speed of light:

𝑣 4 = 𝑐 (13)
In electromagnetism there is the following formula for the electric current

𝐼 = ΔQ Δt (14)
That is an electric current is equal to the quantity of charges passing through a conductor in a period of time. In case of gravity, the mass current will be

𝑀 = Δ𝑚 Δt = 𝑚 ΔS 4 Δt = 𝑚𝑣 4 = 𝑚𝑐 (15)
where Δ𝑚 is the total quantity of mass passing in the period of time Δt, ΔS 4 is the distance passed by the mass 𝑚 along the fourth coordinate in time Δt, 𝑣 4 is the speed of mass along the fourth coordinate, 𝑐 is the speed of light.

GRAVITY FORCE EQUATION

Basing on the above-mentioned assumptions, the basic equation for the force of gravity can be The surface of the 4D expanding ball is our 3D Universe v1 v2

written using a four-dimensional cross product as follows:

𝑭 ⃗ ⃗ 1-2 = 𝑴 ⃗⃗⃗ 2 × 𝑮 ⃗⃗ 1 (𝑟)

(16) |𝑮 𝟏 (𝑟)| = 𝐾 𝑀 1 𝑟 2 (17)
where 𝑭 ⃗ ⃗ 1-2 is the force, with which the mass m1 affects the mass m2. 𝑀 1 is the value of the current generated by movement of mass m1, 𝑴 𝟐 is the vector of the current generated by movement of mass m2, 𝑮 ⃗⃗ 1 is the bivector representing the gravity field of mass m1 at the point of location of mass m2, 𝑟 is the distance from the mass to the point where the vector 𝑮 ⃗⃗ 1 is located, 𝐾 is a constant.

The following diagrams show the movement of masses, the orientation of gravity field vector and the gravity attraction force in 4 and 3 dimensions: Pic. 10. Pic. 11.

ORIENTATION OF INTERACTING SPIRAL GALAXIES

Since the speed of masses along the fourth coordinate is expected to be equal to the speed of light, noticeable effects can be observed when a significant amount of mass moves at a high speed in our 3D space or in case of relatively slow moving massive systems that are isolated from exterior influence for rather long periods of time. An example of such isolated systems are interacting spiral galaxies.

Interacting spiral galaxies are massive diskshaped rotating systems located close to each other. The galaxies are usually at the stage of approaching that usually results in a confluence. The fact that the galaxies interact only with gravity forces makes them an ideal natural laboratory for observing gravitational phenomena.

If the proposed understanding of gravity is true, then there must be a dependency of gravity force on the direction of moving masses. Particles moving in the same direction must experience a stronger gravity attraction than particles moving in opposite directions (see Pic. 12). Pic. 12. Attraction forces of two masses moving in the same (a) and opposite (b) directions.

Thus, according to the abovementioned assumptions, spiral galaxies must tend to acquire the following two mutual orientation while approaching:

Case A: rotation in the same direction in parallel planes above each other, Pic. 13. Case A. The phenomenon of a preferred mutual orientation of interacting spiral galaxies is also admitted by other researchers. For example, as stated in an article by Helou, G. [START_REF] Helou | Spin statistics in binary galaxies -Implications for formation and evolution[END_REF]: "A strong anticorrelation is found, whereby the spins of companion galaxies avoid being parallel and favor being antiparallel."

PROPULSION BASED ON GRAVITY INDUCTION PRINCIPLE

One of the interesting consequences of the proposed description of gravity is a prediction of a gravity induction phenomenon, which basically must resemble an electromagnetic induction.

According to the theory of electromagnetism, the Faraday's electromagnetic induction law defines an appearance of an electromotive force in case of an alternating magnetic field:

ℇ = - 𝑑Φ B 𝑑𝑡 (18)
where ℇ is the electromotive force, Φ B is the magnetic flux, 𝑡 is time.

The generated electric current can be found by the following formula:

I = ℇ R ⁄ ( 19
)
where R is resistance.

The induced electric current is proportional to the electromotive force. Therefore, a larger change (in magnitude and speed) in the magnetic field will result in a larger electromotive force in the conductor, which will cause an appearance of an induced electric current.

If we apply the same approach to gravity, we can expect that an alteration of the gravitation field G of certain configuration will cause a mass current M:

Pic. 24.
The mass current is a motion of mass. Thus, the field of the above configuration will cause an acceleration of mass in the 3D space. If the principle is true, the expected gravity induction phenomenon can be used for a construction of a gravity propulsion device.

EXPERIMENTS

To investigate and to prove the existence of the gravitation induction phenomenon, predicted by the theory, experiments should be performed. Therefore, Airbus, as a potential user of the theory, was approached in 2011. A presentation of the theory was given in 2012 in Ottobrunn, Germany. As a result, it was decided to conduct tests.

A test stand, based on a simplified concept, was developed and built. Two tests were performed in July 2015 and in January 2016 in Munich. The test stand (see Pic. 30) consisted of six aluminum wheels with a testing mass in the center in a plastic tube. The wheels with a mass of 5 kg were 36 cm in diameter and were accelerated by six powerful electric motors up to 3,000 RPM in 0.5 -1 second. A weighing sensor was used to measure a change in weight of the test mass. The test masses were an aluminum cylinder and a stone. The wheels were accelerated in forward and in opposite directions to test an expected decrease and an increase in weight.

Pic. 30.

Positive results of an average change in weight were observed in 80% of the measurements despite the presence of vibrations and oscillations. The magnitude of the effect was assessed at about 1.5 -3 grams per 1 kg. Due to oscillations the average weight per second changed by 0.02 -0.4 grams. Despite the positive indications, the magnitude of the effect was insufficient to be used as a propulsion method in practice at this stage. However, the goal of the experiment was reached, the predicted effect was observed. The author performed all the analysis of the experimental data and the conclusions are only the author's personal conclusions.

CONCLUSION

The author believes that the research in the field must be continued, since there are positive indications that the theory can be valid -the experimental results and observations. The theory is simple in mathematical form and that is a good sign too, since all the basic laws of nature are simple. The measured forces were of low magnitude, but it was the simplest possible test carried out. Much larger effects are expected to be achieved since an acceleration of a vehicle is dependent not only on the speed of rotating masses, but also on their acceleration. The author will be glad to receive any opinion and feedback on these ideas from the scientific society.

  following parallel plane segments correspond to the same bivector a ^ b: Pic. 5. In three dimensions, all bivectors can be generated by the exterior product of two vectors. Exterior product of vectors is a generalization of a cross product. If the bivector B = a ^ b then the magnitude of B is |𝑩| = |𝒂||𝒃| sin 𝜃 (4) where θ is the angle between the vectors. The cross product 𝒂 × 𝒃 is orthogonal to the bivector a ^ b.

  Case B: rotation in opposite directions in the same plane side by side. Pic. 14. Case B. And vice versa, the following cases of mutual orientation must be rare: Case anti-A: rotation in opposite directions in parallel planes above each other, Case anti-B: rotation in the same direction in the same plane side by side. An analysis of the nine closest pairs of interacting spiral galaxies brought the following results concerning their mutual orientation:  Right (as expected, Cases A or B): 4 cases  Neutral (neither «right» nor «wrong»): 3 cases  Wrong (unexpected, Cases anti-A or anti-B): 0 cases  Undefined (correspondence cannot be determined): 2 cases. . Galaxies NGC 4567 & NGC 4568. Orientation: «Undefined». Pic. 23. Galaxies from Stephan's Quintet (NGC 7317). Orientation: «Right» (Case B).

A

  mass rotating along a circle will generate the following field G: Pic. 25. Let us consider a mass moving along a circular spiral (along a surface of a torus). It will generate a field G of the following configuration: Pic. 26. This is the exact field configuration that we need. If we put a mass in the center of the torus and accelerate masses along spiral (blue lines on Pic.26), an alternating gravity field of this type will cause an induced current M of mass m in our 3D space (see Pic. 27). Pic. 27. Therefore, there are two basic variants of trajectories T along which masses must be accelerated to cause an induced gravitational acceleration A of the central mass M (see Pic. 28 and 29 showing spiral and circular trajectories). Pic. 28. Pic. 29.


Pascal Bouvry
email: pascal.bouvry@uni.lu

Serge Chaumette
email: serge.chaumette@labri.fr

Grégoire Danoy
email: gregoire.danoy@uni.lu

Gilles Guerrini
email: gilles.guerrini@fr.thalesgroup.com

Gilles Jurquet
email: gilles.jurquet@fr.thalesgroup.com

Achim Kuwertz
email: achim.kuwertz@iosb.fraunhofer.de

Wilmuth Müller
email: wilmuth.mueller@iosb.fraunhofer.de

Martin Rosalie
email: martin.rosalie@uni.lu

Jennifer Sander
email: jennifer.sander@iosb.fraunhofer.de

Florian Segor
email: florian.segor@iosb.fraunhofer.de

ASIMUT project: Aid to SItuation Management based on MUltimodal, MUltiUAVs, MUltilevel acquisition Techniques

Keywords: multilevel UAV swarm, decisional autonomy, mobility management, automatic processing and detection, high level data fusion, smart mission management

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

The development and usage of UAVs has quickly increased in the last decades, mainly for military purposes. Nowadays, this type of technology is also used in non-military contexts, for instance for environment protection, by search and rescue teams, by fire fighters and police officers, for environmental scientific studies, etc. Although the technology for operating a single UAV is now mature, efforts are still necessary for using swarms of UAVs.

Even if UAV swarming has already stimulated a lot of research, many open issues must still be addressed, such as the use of multiple, multilevel cooperating autonomous swarms. This is the goal of the ASIMUT project, which results are described in this paper. It is a follow-up to [START_REF] Bouvry | Using heterogeneous multilevel swarms of uavs and high-level data fusion to support situation management in surveillance scenarios[END_REF], in which a detailed analysis of the current technologies and related works regarding ASIMUT was already provided.

The remainder of this article is structured as follows. Section 2 provides an overview of the ASIMUT project. Then the results obtained for each component is presented in section 3. Finally section 4 draws extensive conclusions to illustrate the capabilities of the ASIMUT system.

THE ASIMUT PROJECT

The ASIMUT project relies on the collaboration among swarms of UAVs evolving at different altitudes: e.g., fixedwing UAVs covering the area at a high altitude with coarse grain acquisition capabilities and low-altitude multi-rotor UAVs in charge of precise measurements.

The goal of this project is to address scenarios where a mission has to be achieved based on decisions made from data collected from different sensors in a number of UAVs that constitute swarms. High-altitude and low-altitude swarms are tasked based on the fusion of information coming from multiple sources. From an early warning process where data are provided by the UAV swarm payloads, the target localization, monitoring and classification processes are achieved using advanced techniques from the domains of artificial intelligence, machine learning, and statistics.

The objectives of the ASIMUT project are to design, implement and validate algorithms that will allow the efficient usage of autonomous swarms of UAVs for surveillance missions. To support situation management, the ASIMUT project focuses on:

• Providing automated assistance to human operators with regard to high level data fusion tasks. By doing so the project can significantly improve their capabilities for making efficient and effective decisions;

• Developing methods and algorithms to improve moving target detection in a video flow;

• Handling several swarms of UAVs including their communications, networking and positioning. This thus motivates the development of multilevel cooperation algorithms, which is an area that has not been widely explored, especially when autonomy is also a challenge. Thus, additional problematics appear, and it becomes necessary to focus on:

-Providing techniques to optimize communications within a swarm and between swarms (including multilevel swarms);

-Developing distributed and localized mobility management algorithms to cope with conflicting objectives, such as connectivity maintenance and geographical area coverage.

PROJECT RESULTS

The goal of the ASIMUT project was to provide a model combining detection, data fusion and mission management, including the use of new solutions such as UAV manoeuvrability and autonomy in swarms, to assist operators to better decide the course of actions when facing situation awareness. The Fig. 1 provides an overview of a mission as seen from the ASIMUT project perspective. Each step (from 1 to 6) is detailed in the following subsections. A video illustrating the simulation of the ASIMUT framework on a realistic scenario is also available online 1 .

Mission Management (1 & 2 in Fig. 1)

Using multilevel swarming reconnaissance assets requires completely different approaches (compared to standard single UAV approaches) in the domain of mission management. In order to keep the operators situational awareness focused on the relevant aspects of the current mission the developed ASIMUT smart mission management system has been abstracted from the classical single or multi UAV management system to achieve a target or objective oriented mission management system. Possible operator interactions combined with the reconnaissance assets are shifted to a macro level of control by introducing the doctrine of network centric multiple mission objectives management allowing the user to concentrate on the goals of active missions. Decisional autonomy within the reconnaissance assets combined with ergonomic human device interfaces and automation within 1 https://asimut.gforge.uni.lu/ downloads/asimut.mp4 the mission creation and management process is freeing capacities to raise the effectiveness and efficiency of the reconnaissance product creation cycle and making complex and parallel missions controllable.

Swarm Decisional Autonomy and Mobil-

ity Management (3 & 4 in Fig. 1)

The ASIMUT project requires cooperation within and between UAV swarms, the latter being an area that has not been widely explored, especially when autonomy is also a challenge. The management and the optimization of the interactions between the swarms that take part in the mission are provided. This permits to understand how the swarms local decisions and work impact the behaviour of the other swarms.

SnT and LaBRI developed a dedicated framework to manage the autonomy of UAVs that permits scalability over the number of swarms [START_REF] Rosalie | UAV Multilevel Swarms for Situation Management[END_REF]. Another contribution lies in the mobility management for both the High Level Coordination Swarm and Low Level Swarms which fulfil their objectives without any (predefined) flight plan. Novel distributed and online mobility models have been developed to enable efficient and unpredictable trajectories for UAVs. These rely on a chaotic behaviour and Ant Colony Optimization (ACO) method in order to handle conflicting objectives such as area coverage maximization and revisit time minimization [START_REF] Rosalie | From Random Process to Chaotic Behavior in Swarms of UAVs[END_REF].

Moving Target Detection in a Video (3 &

5 in Fig. 1)

In order to significantly reduce the operator workload during a surveillance mission, a ground moving vehicle detection algorithm has been developed. The Low Level UAVs are mainly equipped with electro-optical/infrared cameras which video flow is sent to the ground station by the High Level Coordination Swarm. These dynamic data coming from all the UAVs of the Low Level Swarms coupled with the geolocation of the UAVs are automatically analysed in real time, without any human intervention. A major innovation is the possibility to detect small moving targets, with a size under five pixels in the video. For each detected vehicle, an alert is displayed on the Human Machine Interface, and the operator identifies the target emphasised on the video. Then, data concerning the targets is sent to the Intelligence Center which will classify the vehicle. (1, 5 & 6 in Fig. 1)

High Level Data Fusion

In ASIMUT, high level data fusion (HLDF) is applied in the Intelligence Center to support human operators. There are several tasks in the ASIMUT scenario which are supported by HLDF. The first task concerns the initialization of the scenario, where a request for information (RFI) is created (step 1), which in turn causes the creation of a mission (step 2). In the Intelligence Center, information is extracted (with the help of natural language processing) from intelligence reports and provided to an information integration and management system, called the Object-Oriented World Model [START_REF] Kuwertz | Extending adaptive world modeling by identifying and handling insufficient knowledge models[END_REF] (OOWM), which integrates this information with prior knowledge from an intelligence database. As a result, HLDF using first-order probabilistic reasoning can derive a critical event, being a possible assault with a certain vehicle, from the integrated information and the RFI is created to search for the vehicle. The second task (steps 5 & 6) is to process surveillance data on vehicles provided by the UAVs and the video target detection. This data is again passed to the OOWM, which applies HLDF in order to integrate the data with previous information stored in the OOWM. Here, the task is to identify the vehicle being searched for in the surveillance data (by associating it to the vehicle description known from the intelligence database).

The third task concerns performing a behavior analysis on vehicles observed by the UAVs in order to identify suspicious behaviors. The results of this analysis are then combined using HLDF with the results of the two previous tasks and provided to the OOWM (step 6). Finally, these integrated results, containing an estimate of the threat posed by each observed vehicle, are presented to the mission commander in an operational picture.

CONCLUSIONS

The ASIMUT project proposed, developed and validated beyond state-of-the-art technological building blocks for the enhancement of the autonomy of surveillance missions based on multilevel UAV swarms. We proposed new algorithmic approaches to address the different components of the functional chain of the underlying distributed system. The swarm decisional autonomy and mobility management took profit of past expertise of the consortium members on swarms of UAVs and of new technologies for the application to multilevel swarms. Automatic processing of the detection of (even small) moving vehicles from real-time video acquisition by an electro-optical payload looks promising to decrease the operator workload. By providing automated assistance for human operators with regard to high level data fusion tasks, ASIMUT significantly improves the capabilities of new algorithms for making efficient and effective decisions. Solutions for smart mission management and operator support have been developed. Information coming from the swarms can now be used to display the Common Operational Picture and other results within the ground control station and to compare the current situation with the planned one.

The most promising approaches implemented in the different algorithms that we have designed have been combined in a single demonstration framework and evaluated via state-of-the-art simulations. After testing all the interfaces, the different components (each implementing an innovative technology), have been integrated in a global single system. Therefore, we consider that IRL (Integration Readiness Level) level 3 has been reached and demonstrated. After the evaluation done in a simulation environment, the individual TRL (Technology Readiness Level) of each component reaches, by definition, level 3. The SRL (System Readiness Level) is therefore evaluated to be at level 2 (see [START_REF] Sauser | From TRL to SRL: The concept of systems readiness levels[END_REF] for details about TRL and SRL). In terms of swarming, we have been able to setup a multilevel configuration with UAVs that play different roles in the mission and that support resilience (regarding loss of UAVs) while on the field. The cooperation between the C2 (Command & Control), the High Level Coordination Swarm and the Low Level Swarms has shown that the situation management process has been improved and leads to a decrease of pressure on the C2 operator. The simulations have demonstrated that there are a number of parameters that impact the efficiency of the mission (coverage time, revisit time, etc.). Still, the covering based on the new mobility model that has been introduced has proven very efficient. Nevertheless, in order to further improve the efficiency of the area coverage and reduce the revisit time, all the UAVs in the swarms must be able to share their future trajectory plan. Regarding future work on the swarming issues, the following directions should be studied: resilience to messages loss, load and decision sharing between the UAVs of the low level swarms, the high level UAV swarm and the C2. The simulation results gave direction to define additional tests that need to be run.

Considering the video flow, the ASIMUT project deals with a lot of data. This work permitted to have a global idea of new problematics rose by such an amount of data for real time processing. The tools developed in the ASIMUT project permit to handle this data flow and especially the workload of the operators. In the future, it will be interesting to work on load balancing between the elements of the system (drones, GCS, etc.).

Considering high level data fusion for supporting intelligence analysts and decision making, both the approach used for fusion of observed video track data with intelligencebased prior information and the approach for analyzing the dynamic behavior of vehicles, are ready for evaluation (and subsequent refinement of parameters) in more complex realworld scenarios (more vehicles, real-world driving behaviors, real-world ground truth data). In such scenarios, the level of support to analysts (i.e., the reduction of workload and information overflow) and decision makers should be evaluated in more detail in order to acquire directions for further improvements of high level data fusion.

From the Mission Management perspective the human to device interfaces have been tested and their capabilities have been proven. Due to the automation of the mission creation process and the operator support by simple and intuitive interfaces the workload on the operator could be reduced leading to a shortened reaction time for commanding the swarm. To push this development further the automation of mission control has to be enriched with additional artificial intelligence to react based on the situation and the results coming from the reconnaissance assets following the dogma of "management by objective". In combination with a more complex real-world scenario the intelligent mission management could be evaluated in more details to identify the gaps and the strength of the system.

The objective to evaluate the benefits and relevance of the developments made went successful and provided fruitful results which are relevant for further steps towards a future demonstration of the system in a real configuration representative of an operational environment. Additionally, running a real world demonstrator would make thus possible to identify additional issues that can only be seen at runtime and to prove the concepts that we have developed really make sense on the field in the presence of real potential threats.

Figure 1 :

 1 Figure 1: ASIMUT components where swarms of UAVs (High Level Coordination Swarm & Low Level Swarms) collect data and send them to the GCS (Ground Control Station) to be handled by the Intelligence Center.

Acknowledgments

The authors acknowledge the support of the ASIMUT project A-1341-RT-GP, which is coordinated by the European Defence Agency (EDA) and partially funded by eight contributing Members (Austria, France, Germany, Italy, Luxembourg, The Netherlands, Poland and Sweden) in the framework of the Joint Investment Programme on Innovative Concepts and Emerging Technologies 2.


Pierre Salmon
email: pierresalmon@compuserve.com

Assigning powers in the European Union in the light of yardstick competition among governments by

Keywords: TFT, Classification: D72, H73

Intergovernmental yardstick competition is based on voters comparing the performance of their own elected government with what obtains in other jurisdictions. This mechanism can produce results that are favourable to voters but it may also be the case that it has consequences that are not favourable. Both cases are given some attention in the essay. Some of their implications for the assignment of powers in the European Union are then derived.

I. Introduction

II. Intergovernmental yardstick competition: the basic mechanism

The mechanism is exposed in an informal way, albeit in some detail, in SALMON [1987].1 Formal models have been proposed since then, the most influential being the one proposed and tested in B e s le y a n d C ase [1995], But there may be some advantage, in terms of robustness and versatility, in starting our reflection here from the informal account.

The past performance of politicians in power has some influence on the probability of their re-election and, therefore, on their incentives while in office. In a world in which there are many disturbances and change, as well as uncertainty, it is difficult, however, for voter X, located in jurisdiction A, to decide, given circumstances that X does not know, whether and to what extent the performance of the government of A is good or bad. Observing what obtains in some other jurisdictions may help X to form an opinion on that question. This follows from disturbances not being wholly idiosyncratic to the jurisdiction but, to a sufficient degree, common to -or correlated across -different jurisdictions. If the performance of the government of A, in domains of interest to X, is perceived by X to be superior to that observed in some other jurisdiction(s) that X considers as comparable in a relevant way, this may increase the probability that X will vote for the incumbents in A at the next election.

Conversely, if the performance of the government in A is seen by X as inferior, this may decrease somewhat the probability that X will vote for the incumbents. Office-holders in A do not know exactly what are the domains which X, or any other voter, will be mostly interested in, nor with which other jurisdictions will X be the most inclined to compare what obtains in A. However, they know that exerting themselves as much and in as many areas as possible enhances the chance that their performance will be judged comparatively good by the voters of their own jurisdiction, and thus increases the probability that they will win the next 1 In S a lm o n [1987], the exposition was inspired by the then recent literature on contests and tournaments, in particular L a z e a r a n d R o se n [1981], The mechanism was referred to as "rank-order" competition. "Yardstick competition" was mentioned only incidentally in the article. It became widely referred to, in the literature on organisations and incentives especially, under the influence of S h le if e r [1985). For our purpose, the difference between tournaments and yardstick competition does not matter very much. For convenience, I choose the latter term.

election. Because winning the next election is an essential objective of incumbents, this generates among them an incentive toward good performance, and moreover performance of a kind that tends to be aligned with the way voters themselves perceive their interests. Does the mechanism find some support in empirical work or, more generally, is it plausible? In the informal formulation of the mechanism used above, it has not been necessary to specify exactly what were the variables about which comparisons by voters were made across jurisdictions. Some voters may be concerned only with policies of support to music or to sports, others, or the same, with the rate of unemployment. Somewhat in the spirit of the probabilistic theory of voting, politicians being uncertain about that is an essential part of the mechanism which induces them to do their best overall, or on as many issues as possible.

Modelling and empirical testing, though, require more precision. In SALMON [1991],

[1997], the main variables are mostly of a macroeconomic kind (unemployment, inflation, and, especially, rates of growth). For the purpose of empirical testing, especially at the sub national level of government, taxation is a particularly obvious or convenient variable -see B e s le y a n d C ase [1995], A sh w o r th a n d H e y n d e ls [1997], R e v e lli [2002]; F e ld , J o s se lin AND R o c a b o y [forthcoming]. However, inasmuch as public spending is related to taxation and gives citizens some utility they are aware of, considering only taxation may lead to underestimate the empirical relevance of the mechanism. Solutions that are likely to be more difficult to make operational but are much more intellectually satisfactory take into account the connection between benefits and taxes, as in B r e to n [1996], [2002] and B r e to n ANDURSPRUNG [2002], In any case, formal testing of the yardstick competition mechanism is clearly difficult. In addition to the problem of finding variables that are both measurable and satisfactory with regard to theory or common sense, there is the usual problem of the existence of other possible hypotheses accounting for the same observations. It is thus quite remarkable that the very ingenious work done to overcome these difficulties has on the whole provided some empirical support -hardly striking, albeit significant -to the hypothesis.2 A quasi-philosophical problem which is not often mentioned in this context but which nonetheless underlies many of the difficulties of testing is that, in the actual, non-experimental world which is by necessity considered exclusively in the empirical studies, there is not enough variation of performance for the mechanism and its effects to really come to the fore. This is not purely accidental. An ontological reason is that the mechanism works at a deeper level of reality than the one observable empirically (except if one could observe politicians' reasoning, so to say, directly). In many settings, yardstick competition, if effective, will have even a tendency to cause its own disappearance from the universe of manifest phenomena. At the limit, if the mechanism worked perfectly, all the observed differences in outcomes would be related not to differences in the variables (such as effort) which are the targets of the mechanism, but to chance, compensations, or variables which the observers neglected but had some importance for voters. Thus, to assess the empirical relevance of the mechanism, it seems inevitable to have recourse also to other, much less formal means, such as casual historical information or thought experiments and counterfactual reasoning. Would the Communist regimes have survived if they had not been submitted by the people they ruled to performance comparisons with what was obtaining in the West? How would voters assess government in a one-government world submitted to historical change? Would the United States have developed all these checks and balances if it had been from the beginning a society intensely open to international comparisons of performance? III. Three particularly important characteristics of the mechanism existing arrangements. For that reason or for more general ones, the policies and institutions used by governments to address problems that are in part similar are, at any point in time, very varied. Even when some forces, yardstick competition in particular, are operating to make them converge, the incessant occurrence of new experiments and innovations disrupts such tendencies and ensures that heterogeneity persists. As a consequence, the task of comparing performance is more difficult, both for voters and for specialised observers. This would constitute a serious objection to the yardstick mechanism only if we had not made from the start uncertainty, both among voters and among politicians, one of its essential features.4

Variable strength

The second feature is a high degree of variability in the strength of the mechanism. For a given jurisdiction, that strength is a function of two things: the degree of competitiveness of the political system of that jurisdiction and the informational openness of the jurisdiction (SALMON [1997]). To start with the first, for a given set of comparative assessments made by the voters of a jurisdiction, the influence of these assessments on the incentives of office holders is related to the nature and intensity of electoral competition within that jurisdiction.

When the political regime is such that electoral competition is very strong, with incumbents and the opposition having more or less the same probability of winning, each voter (or category of voters) will tend to count. Thus, the slightest chance of inducing a change in the probability that a voter will support the incumbents will be an object of attention by the latter, and will tend to be taken into account in the process of policy-making. Conversely, if incumbents face an electoral constraint which is weak -because of some feature of the electoral system, clientélisme, the fragmentation of the opposition, a structural bias in the distribution of votes (following some ethnic or religious divide, for instance), and many other 4 There are many other sources of difficulties for making comparisons across jurisdictions. An important source is the absence of transparency in the financial relations between a central government and sub-central ones, see B r o s io [2002], Problems of another kind stem from the existence of political parties that straddle jurisdictions; see W re d e [2001] for a very interesting analysis of different situations that can emerge then.

possible reasons -exactly the same assessments by voters may have a much smaller effect on incentives. Then, political yardstick competition will be less effective.

This will not deprive it of its actual or potential relevance, however. Whereas under the first, highly competitive, political regime, a small level of potential discontent may have a very significant effect on incentives, to get the same effect under the second regime will require a higher level of potential discontent. In the second case, office-holders may feel free to remain unconcerned with the satisfaction of a part of the population but there is a limit to this freedom -as history documents abundantly (even in the case of undemocratic regimes).

As noted, one must also consider the informational openness of the jurisdiction. Here the relation whose strength matters is that between objective variations in comparative performance and the variations in subjective assessments that do or do not follow. Material or technical barriers to information may constitute one cause of weakness in that relation: the performance of a country is, say, pretty bad, but voters do not have access to the information.

The willingness of voters (or absence thereof) to take into account comparative performance constitutes perhaps an even more important factor. For various reasons -for instance, permanent superiority of the jurisdiction in the relevant area, or the feeling thereof, or sheer complacency -voters in some jurisdictions may be inclined to disregard what happens elsewhere. In other jurisdictions, voters prove extremely attentive to the same type of information. This means that the same level of objective performance gap can lead to almost no discontent in one jurisdiction and to considerable discontent in another. Important differences in the effectiveness of yardstick competition ensue. In jurisdictions in which voters are prevented from making or unwilling to make comparisons, office-holders will not feel very much constrained, even though, there also, there will be a limit to the discretion they enjoy.

By considering together the two dimensions, we get a typology, with cases in which their characteristics tend to compensate each other, so that their overall impact (positive or negative) on the effectiveness of yardstick competition is not very significant, and cases in which the impact is significant because the characteristics along the two dimensions add up.5 That discussion does not address the question of what happens when informational openness is different across policy areas. This interesting topic will be taken up in the next section.

Vertical competition

Let us turn now to the third feature stressed because of its importance. Yardstick competition among governments is easier to understand and analyse when that competition takes place on the same level of jurisdiction -say, among national governments, or regional ones, or municipalities. However, competition between governments situated on different levels, that is vertical competition, can also take the form of yardstick competition (it can also take other forms, such as competition for the same tax base, or the same source of grants) 6

For instance, voters in Saarland may compare the performance of the government of that Land, not only with what they perceive of the performance of the government of, say, Bavaria (horizontal competition), but also with what they gather from the performance of the federal government (and vice versa).

Vertical yardstick competition is important (B reto n [1996]). It raises a number of issues though. Above all perhaps, there is, again but in a different setting, the question of what is compared. The traditional literature on federalism or decentralisation suggests a relatively strict division of responsibilities among tiers -both as a description of what is, and even more often, as a prescription for what ought to be. This might seem to be an obstacle to comparing governmental performance across levels. In fact, governments on different levels typically operate to some degree in the same policy areas (security, social policies, support to cultural activities, etc.). They are able to do this because they officially share some powers or responsibiliti es, because the assignment of powers is ambiguous, or because they use different powers to intervene in the same policy area. Moreover, potential entry across levels in a policy area is enough to generate incentives. Suppose the government of jurisdiction A is the only one in the jurisdiction to deal with some important issues in policy area X. Now, the office-holder s in jurisdiction B (situated either on a higher or on a lower level) may think that they could do better than the people in power in A to deal with the said issues (as they arise in A). If the office-holder s in A think that the danger of invasion is serious, that the invaders would be efficient, and that voters of A would notice the difference in performance , their concern with the probability to win the next election would generate among them an incentive to improve their own performance , and this even if in fact the invasion does not take place.

The foregoing argument refers to comparisons of services offered by different levels of government in the same policy areas. There is another possibility. Comparative assessments may be possible also as a consequence of voters being concerned with indicators of the degree of connection between benefits from public services and tax prices (B r e to n [2002], BRETON AND URSPRUNG [2002]). If some voters feel that this connection is tighter in other jurisdictions (whatever the levels on which they are situated) than it is in their own jurisdiction, this might reduce the probability that they will vote for the incumbents at the next election. A variant of that is when voters compare simply some general characteristi cssuch as speed, reliability or courtesyof the way services are provided by government services situated at different levels.

Another issue is the effect of vertical competition on horizontal competition. Because governments on different levels o f jurisdiction intervene in the same areas, horizontal comparisons may be more difficult, especially if the higher-level government engages, as claimed by B r e to n [1996], [2002] in policies that are not uniform across lower-level jurisdictions (see B r o sio [2002]). As noted earlier, however, uncertainty is not only tolerated by the comparison mechanism but central to it.

A very important question is that of the entrenchment of the rights of the different governments. Vertical relations between levels of jurisdiction are typically asymmetric and unequal. Thus, if the central government does not want the lower-level governments to look more efficient than it does itself in the eyes of voters, and if there is no entrenchment of the rights of these lower-level governments, the central government can change the law or reduce the funds available at their level so that they will not win the race. In systems that are not merely decentralised but really federal, level-2 governments enjoy some constitutional or quasi-constitutional protection against the deeds of the central government. This makes vertical competition easier to figure out in federations than in unitary states (but see [START_REF] Salmon | Vertical competition in a unitary state[END_REF].

IV. Negative effects of intergovernmental yardstick competition

Recent theoretical objections to the virtues of the mechanism

Several recent papers (B e lle fla m m e and H in drick s [2001], B e sle y a n d Sm art [2001],

BORDIGNON, C e r n ig lia an d R e v e lli [2002]) raise objections to the presumption that yardstick competition (or, more generally, performance comparison) is generally favourable to citizens or voters. It is not the place here to engage in a detailed examination and discussion of this very recent work. Let me tentatively say, as a first impression, that, even though it seems clear that there are circumstances in which the presumption should be of negative effects rather than of positive ones, I am not sure that the causes leading to that should be sought mainly in the direction followed in this recent work. One reason is that the context in which this work assumes the voters to be placed is that of a need to select, among politicians, "good" types when there are also "bad types" around -the difference between the two, moreover, not being about competenc e but about something like morality. This is certainly a very relevant question at some level of generality and under some institutiona l arrangeme nts. But I am not sure that either of the conditions is satisfied herewhere, more or less implicitly, our underlying assumption s, inspired by tournamen t theory, are that all politicians are the same (that is, in a sense, all equally "good" or "bad") and must be induced to provide more attention and effort to the needs expressed by voters. In other words, our problem is one of moral hazard, not selection.

Dynamic incentives, also referred to in this literature, are another matter. In M eyer a n d V ick ers [1997] implicit incentives in a dynamic setting have an influence on behaviour which may be the opposite of the incentives produced by performanc e compariso ns in a static framework . The overall effects appear thus to be ambiguous . The idea underlying the precise argument seems quite general and might have a lot of relevance for our purpose. It remains to be seen, however, whether it will yield the same ambiguity when applied to a political setting in which the principals are voters, instead of regulators and their relations with politicians (not firms) necessarily pursued under incomplete contracting . An important considerati on, in this context, might be whether politicians who lose an election are assumed to be eliminated forever or may be candidates again in the following elections (see W rede [2001]).

Perverse mimicking

Yardstick competitio n will lead to convergenc e. No governmen t can afford to do less well than others. But there might be multiple equilibria. Even without collusion among the governmen ts concerned, it may be the case, especially when there is a small number of jurisdiction s that can be compared, that convergenc e and equilibrium obtain at a level which is not the most efficient from the perspective of voters but which the governmen ts involved may find preferable. In an equilibrium of that kind, governmen ts make less effort or, by the way of increased taxation or of reduced spending on objectives voters share, manage to use resources for their own ends.

More casually, we can observe that comparisons are often asymmetric. In a number of jurisdictions, voters compare the performance of their own jurisdiction mainly with what obtains in one jurisdiction, A, singled out among several possibilities. Country A, say, is used as a kind of benchmark by voters and public opinion in several other countries. Now, if A under-perform s, this may reduce very much the political stakes involved in yardstick competition for the governments of the other jurisdictions. They feel free to relax, and thus the whole group under-perform s compared with jurisdictions outside the group. Again, there is an equilibrium of low performance (see SALMON [1991], [1997]).

Multi-task jobs

An equally or even more important problem for yardstick competition, and, at the same time, one which is also particularly likely to suggest interesting propositions for the allocation of powers across levels, originates in the fact that comparative assessments are much easier in some policy areas, or for some aspects of policies, than they are in other areas or for other aspects. As a consequence, an incentive is generated for governments to devote more attention and effort to the policies, or aspects thereof, whose assessments are easier. If yardstick competition is very intense and successful in the areas in which assessments are easy, other policies, or other aspects, may as a result get completely sacrificed. For instance if governments compete intensely in terms of growth, they may neglect income distribution or other social considerations (S a lm o n [1997]). This is clearly very much related to the work done, in the literature of labour economics or the economics of organisations, on the problem of multi-task jobs (H o lm stro m a n d M ilg ro m [1991], D e w a tr ip o n t, J e w itt a n d T ir o le [2000], S e a b r ig h t [2000])except that this work compares the measurabili ty of performanc e across tasks and analyses its effects on the allocation of effort but does not introduce yardstick competition . Combining the two ideas seems feasible though. The solution proposed by Holmstrom and Milgrom is to design jobs in view of limiting the bias toward the most easily measurable tasks. One way to achieve this is to separate the tasks that are subject to easy assessment s from those in which measureme nt is difficultthat is, to create different, more homogeneo us, jobs. L a z e a r [1995, p. 87] accepts the validity of the idea in principle, but does not believe it to be very relevant in practice because, according to him, jobs are based first of all on technical complemen tarities. When the separation of tasks is impossible or too costly, then, Holmstrom and Milgrom's solution to avoid the bias is to remain content with low-powere d incentives.

The foregoing reasoning can be coupled with differences in the feasibility of yardstick competition overall. In S a lm o n [1991], two groups of policies and two pure cases of feasibility of comparison s are considered together. They are, respectively , macroecono mic policies versus "transaction s with interest categories", and countries being "informatio nally open" versus countries being "informatio nally isolated or closed". The idea is that change in the easiness of yardstick competition will affect considerabl y the assessment of macroecono mic policies but not much that of transactions with interest categories. Therefore, when a country is information ally isolated, and thus when its policies are not easily submitted to comparison s with those of other countries, the assessment of performanc e with regard to transactions with interest categories is much easier than the assessment of performanc e with regard to macroecono mic policies. This creates a bias in the incentives of the governmen t, which does not devote enough attention or resources to macroecono mic outcomes and too much to interest categories. But when a country is very open to internationa l comparison s, this will affect macroecono mic variables more than it affects transaction s with interest categories. As a consequence the bias will consist now of paying too much attention to macroeconomic variables, and not enough to interest categories.

Another application of the multi-task idea is to leadership.8 Assume that there is an international public good subject to free riding on the part of nation-states. As argued forcefully, many years ago, by KiNDLEBERGER [1976], leadership by one country may be necessary for an international public good (such as peace, economic stability, freedom of navigation, free trade, etc.) to be produced. Assume that the production of the public good is in the long-term interest of voters in the country which could play the role of leader, but that voters are unaware of this. If yardstick competition is so intense that the government of the would-be leader country is constrained to devote all its resources to the production of the goods and services that are the objects of the comparative assessments of voters, nothing will be left for the leadership task, which therefore will not be fulfilled. In that case, less intense yardstick competition might well be beneficial to all.

V. Implications of yardstick competition for the governance of the EU

A large part of the implications of yardstick competition for the governance of the EU are implicit in the foregoing discussion provided we add some fairly well-known facts about the EU and its member countries. Implications are made explicit below in the form of six propositions. In each case, the proposition should be read with the more general argument, formulated in the earlier sections, in mind.

Proposition 1.

An effect of yardstick competition between the member countries of the EU is to make unlikely in the medium-term any substantial divergence in income per head.

The political regimes of member countries of the EU are very competitive in the sense that incumbents are far from feeling certain to be re-elected at the next election. This means that they will be attentive to the views of all sectors of opinion. Comparative assessments of macroeconomic performance are easy to make between these countries and, in fact, are the object of significant attention by the media and public opinion, or subsets thereof. Thus, with regard to macroeconomic performance, the two conditions noted earlier are met for yardstick competition to be effective. Casual evidence from the public debate confirms this. The observation of the convergence of income per head among EU member countries also provides support.

This convergence is striking but it could be caused by other factors. Hence the very cautious formulation of Proposition 1. Yardstick competition would create in a country strong political incentives to prevent it from falling behind in a substantial way in terms of macroeconomic performance. This does not apply of course to short term divergence. What one should have in mind here is the kind of evolution experienced by countries like Argentina or Spain, when their incomes per head were brought down from a level roughly comparable to that of France or Germany to the third or half of that (SALMON [1997]).

Proposition 2:

A major task of the EU institutions should be to provide (or to ensure that others provide) comparative information and analysis in all policy areas.

The rationale for this task is also fairly obvious. In areas other than macroeconomic performance, comparisons are difficult to make, with the difficulty increasing, as already noted, when competition or emulation takes the form of innovation or experimentation. At any moment in time, the policies or arrangements offered in the various countries will tend to be different. For instance, very different welfare systems or social policies have been put in place by EU member countries (B e r to la e t a l. [2001]). There are often compensations, however, so that completely different means may produce in the end results that are not so dissimilar. As a consequence, to provide citizens in the various countries with the kind of information they need to gauge the comparative performance of their government will require a lot of analysis and assessment. This feature of information supply increases the need for objective sources, as independent as possible from the governments whose policies are scrutinised.

It is probably difficult for the Commission or any other independent institution at the EU level to frame comparative information directly in term of rank-order assessments (that would make it too exciting). But the information produced should allow other agents or organisations (the media, universities, etc.) to do so. The objects of comparisons should be first of all the policies implemented by the member-states governments, but they could include, at lower levels of jurisdiction, those of the regional and municipal ones. The information should be supplied for free, and even some cost incurred to make it as widely available as possible. In addition, increased support should be devoted to programmes which have, among other effects, that of facilitating comparative assessments. Examples of such programmes are the spread of English as a common working language and the funding of studies abroad.

PROPOSITIONS:

For the sake o f yardstick competition, tolerance of some fragmentation of the EU market and of some distortions of competition should be maintained or increased.

This is also an implication of innovation-rich yardstick competition. Such competition necessarily fragments the economic space of the EU. Innovations, and more generally government decisions at a sub-central level, typically create additional transaction costs for private-sector activities that straddle jurisdictions and additional rents for those that do not. In the language of international trade theory, this means that innovative governments create non border, non-tariff barriers to trade. Since the Single Act, this fragmentation runs against a major undertaking of the EU, which is to eliminate all barriers to trade, including all non border, non-tariff barriers.

The capacity of the national and sub-national governments to innovate, or simply to act, is also constrained by another aspect of the single-market programme, which is to implement "fair competition" and a "level-playing field". Subsidies by governments to firms, often referred to in the literature as "state aids", may distort competition and thus are at least suspect and often banned under this aspect of the programme.9

If yardstick competition is of some value, then the implication is that a compromise is necessary between the objective of enhancing it and that of eliminating all barriers to trade and all distortions to competition. The observation of countries in which intergovernmental competition at the sub-national level is intense, such as Canada, the United States or Switzerland, shows that a more liberal interpretation of free internal trade and "fair competition", or of the establishment of a "level-playing field", are perfectly compatible with a high degree of political integration and market competition.10

P r o p o s itio n  perverse effect of yardstick competition may be that equilibrium growth in the EU is too low; to move it up, more power in the area of economic policy-making should be given the

Commission.

We saw earlier that a low-growth equilibrium can be the result of yardstick competition taking the form of "perverse mimicking", especially (but not necessarily) when comparisons are asymmetrical (citizens of A compare with what obtains in B but the reverse is not true or not to the same extent). It seems quite possible that this phenomenon is a cause of the present situation in Europe, as it was already in the first half of the 1980s. If we consider France and Germany, there is some empirical evidence that any differential in macroeconomic performance between these countries has a significant effect on votes in France but not in Germany (see L ew is-B eck e t a l. [2001]). If this can be generalised to other member countries, this means that special circumstances that generate relatively low growth in Germany will have the effect of making growth in the EU as a whole relatively low.

Things would be different if voters in the EU compared growth in the EU as a whole with growth elsewhere, in particular in the United States, but also in Asia, and if the rate of growth there was high. It is argued in SALMON [1991] that this kind of comparisons in the early 1980s may well have been at the root of the feelings about "Europessimism" and "Eurosclerosis", which in turn seem to have played a role in the adoption of the Single Act and the 1992 project.

If there is some truth in this hypothesis, then, ways to redirect the attention of voters to comparisons of performance in the area as a whole with what obtains elsewhere may help escape the low-growth equilibrium trap. To achieve this, more responsibilities with regard to the governance of the economy could be given to the Commission than seems justified on other, more conventional grounds. For instance, even if the utility of coordinating economic policies is denied on purely conventional economics grounds, as some economists do (e.g., T a r f t .t.int [2002]), there might still be some argument, related as indicated above to yardstick competition, in favour of assigning a coordinating task to the Commission.

PROPOSITIONS:

In the current state o f European integration, there is not much scope for vertical yardstick competition to be enhanced.

We saw that vertical competition needs constitutional protection. It is tempting to apply that to the EU. Usually, the idea is that the most central government is the one to be protected against (there is a centralisation tendency in most existing federations). Thus it is tempting to argue that, for vertical competition to remain fair or stable, national governments should be protected against Brussels. In fact this reasoning is quite widespread (see, for instance, VAUBEL [1999]). But this line of reasoning runs against European being under construction, so to say. We are not at equilibrium and thus cannot apply rules now that make sense only at equilibrium. The European integration project, officially aiming at "ever closer union", is based on the dynamics of reallocating increasing powers or competences at the EU level and is thus not really compatible with the idea of a stable or fair vertical competition between the governments of the member countries and Brussels. Ironically, one may argue that if a level is to be constitutionally protected, this is the EU level -and in fact it is protected to some degree thanks to "ever closer union" being included in constitutional or quasi-constitutional documents, and thanks to the acquis communautaire principle.

Proposition 6 :

To protect some worthy tasks from a perverse effect of yardstick competition, one might want them to be removed from the national governments.

We saw that high-powered incentives such as those brought about by yardstick competition may lead, in the case of multi-task jobs, to a bias in favour of some of the tasks, the other being neglected. This has certainly very important potential implications for European governance, even though they will not be spelled out here. We noted that complementarities may be an argument against designing single-task instead of multiple-task jobs. Where complementarities are not too strong, the merits of single-task jobs might inspire a criterion for judging ex post the separation of tasks among levels. This point is related in an interesting way to one made by BERTOLA ET a l. [2001, p. 103]:

"A problem with shared decision-making is that a particular decision may never be important enough in any particular government tier, even if it should be implemented from an overall point of view. For example, spending on minimum social protection or on family support measures may be crowded out by policies receiving stronger support at each decision level, despite its desirability from an ex ante point of view. In such cases (as in the case of monetary policy delegated to an accountable and independent central bank), the government tier or institution with the highest degree of commitment should be identified at an equally ex ante constitutional stage and receive a clear mandate to target a specific problem." Yardstick competition may be the mechanism that explains why some concerns are crowded out, and to that extent our approach is convergent with that of B e r t o la ET AL.11 However, the question of complementarities cannot be glossed over in the context of the EU. As noted by P e r sso n , R o la n d a n d T a b e llin i [1997], it is central to the spillover strategy which has been followed until now for the purpose of integrating Europe (see also S a lm o n [2000b]).

The problem of finding tasks that can be separated and reallocated without weakening the drive toward a more integrated EU is thus worth addressing but necessarily complex.

Achieving such separation at a constitutional stage seems very problematic. Ex post assessments and discussions seem a more realistic alternative on this matter as on many others that are the objects of theoretical reasoning.

VI. Concluding remarks

When economists have felt qualified to contribute to the question of the assignment of responsibilities among levels of government in the EU, their main instrument has usually been the theory of fiscal federalism as exposed a long time ago by Richard Musgrave and Wallace Oates. In the context of the European Union, the theory is now fairly generally considered as of limited use (P e r sso n , R o la n d a n d T a b e llin i [1997]). It suggests centralisation in areas, such as foreign policy, defence, or income redistribution, in which there is little of it so far and in which having more in the near future proves extremely difficult. Even though this is not a fatal flaw in a theory which is mainly normative, this lack of influence suggests the 11 We saw earlier that another illustration of the possibility that yardstick competition could prevent governments to devote sufficient attention to certain tasks is when a country which could fulfil a role of leader, provided it devoted sufficient resources to it, is prevented to do so by the pressure of competitioa In S a lm o n [1992], this was applied to the role of Germany in the EU. For sufficient resources and attention to be devoted to some tasks in the field of foreign affairs it may thus be useful to escape the competitive pressure to which governments are submitted by transferring the tasks, or part of, to the Commission in Brussels, and this even if, on other grounds, such transfer does not seem very justified.

possibility that the theory misses some important considerations. Three such considerations (at least) can be found in the economic literature. First, many of the problems created by decentralised policy-making can be solved at the same level of jurisdiction by negotiation or coordination between some or all of the governments situated at that level. Whether this is more efficient and thus more likely to obtain than centralising the policies at a higher level depends on transaction costs of various kinds, as explained in detail by B r e t o n a n d S c o t t [1978],12 As I have stressed elsewhere, it is particularly noteworthy in the case of decision making in the EU that a large part of negotiations takes place under a perspective of repeatbusiness and -to borrow an expression coined or used by C o o t e r [2000, p. 120] -"splicing issues."13 A second consideration is the degree of heterogeneity of preferences on each issue across member entities or, in the EU context, countries. It is given a place in some recent work on the assignment of powers (see A le s in a , A n g e lo n i a n d S c h u k n e c h t [2001] and the references therein).

The third missing consideration is politics, and the way it can be analysed in economics -often referred to as "public choice". Decisions in the public sector are made by individual actors who have their own goals and make decisions under conditions of uncertainty, information asymmetry and incomplete contracting. Thus, even under a normative approach, one should reason in a world of second-best. More intuitively, it is in a messy world akin to the real one that genuinely convincing reasons for decentralisation and federalism can be found. And it is in such a world that intergovernmental competition appears no more as a force complicating or disrupting the otherwise efficient arrangements prescribed by normative theory, but, under a perspective of positive economics, as an essential ingredient in the explanation of how democratic governmental systems operate. Now, there are at least two forms of intergovernmental governmental competition, the most frequently studied and referred to being by far competition based on the mobility across jurisdictions of individuals, factors of production and business firms. If the government's policies in jurisdiction A do not please individual or firm X as much as would policies adopted in some other jurisdiction B, X might move to B, an event that the government of A will generally want to avoid. This paper has focussed on another other form of intergovernmental competition: yardstick competition. Even more clearly than mobility-based competition, its relevance stems from the existence of imperfections in the political process. Do the two forms of competition add up in favour of voters or does mobility erode the capacity of governments to act and thus in the end hinder yardstick competition? This important question is addressed a little, in the context of the EU, in Salmon [2002a] but a much more deliberate attempt at tackling it is needed.

  7 F e ld , J o s s e lin a n d R o c a b o y [forthcoming] argue that something of that kind has happened at the level of regional governments in France.

See in particular B esley and C ase[1995], Asworth and[START_REF] Heyndels | Politicians' preferences on local tax rates: an empirical analysis[END_REF],[START_REF] Revelli | Local taxes, national politics and spatial interactions in English district election results[END_REF], Bordignon, Ce r n ig l ia a n d[START_REF] Revelli | Local taxes, national politics and spatial interactions in English district election results[END_REF],

See Salmon [1991].

An illustration or application o f such a typology can be found in[START_REF] Raynauld | Democratic governments, economic growth, and income distribution[END_REF],

An interesting, albeit very particular, form of vertical yardstick competition is considered in B odenstein and U rspru n g[2001],

See S a l m o n [1992].

On all this, see B r e t o n a n d S a lm o n [2001] and S a lm o n [2002a], [2002b],

See M u e l l e r [2000] for a convincing criticism of the '"fair competition" argument against regional government subsidies to private firms. T a b e llin i [2002] acknowledges the existence of a trade-off or dilemma between the goal of decentralizing policy-making and that of eliminating all barriers to trade and distortions of competition but his position is that in each case when they conflict the first goal should be sacrificed.

See also.Inm an a n d R u b in f e ld [1997, pp. 96-101].

This has very important consequences, as argued in S a lm o n [2002a]. For instance, it explains that even under unanimity rule, decisions at the level of the EU are very far from being generally plagued by a tendency to adopt the lowest-common-denominator solution, as has often been unjustly claimed. Many policies have been adopted unanimously even though they displeased a majority of member countries.

* Without implicating their authors, I am extremely grateful for the very useful comments made on an earlier version of the paper by Jom Ratts0 and by the participants in the conference on European Governance organized by the Center of Law and Economics of the University of Saarbrücken, 10-12 October 2002.