Claude Ponsard (1927–1990): A biographical essay

Fuzzy Sets and Systems 49 (1992) 3-8 North-Holland

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Claude Ponsard (1927-1990): A biographical essay Antoine Billot Universit~ de Paris 2, France

Jacques-Francois Thisse CORE and Universit~ de Paris 1, France

Received January 1991

It is always extremely difficult to sum up the life of a man one encountered at a particular moment in one's own existence and in whose excitements and disappointments one shared, outstripping the relationship of master to student with that chemistry that is so special and so delicate that it would be presumptuous to set about explaining it here. There is nevertheless an objective, raw fact: the view we are going to take of the man and the work is not devoid of all feeling. We admired the mind, the tenacity, the scientific rigour of someone whose humanity and warmth we were fond of. The difficulty of the task lies in constructing a biography that does not overstate the qualities at the risk of discrediting their telling and one which does not lessen the defects at the risk of thinning down the portrait to the point where it pales. Before going into detail as to the dates and the chronology of the shaping of his scientific thought and the development of his work, we should describe in a few swift strokes both the man and the professor that he was at one and the same time. All his former students, and in particular his Ph.D. students, remember first how he came across as being so demanding. H e was a forthright, rigorous man who occasionally let drop a remark filled with enthusiasm in which one could perceive not just the pleasure of the researcher but of the teacher too. H e loved to win people over through intellect, for intellect's Correspondence to: Dr. A. Biliot, Dept. of Economics, University of Paris 2, 92 rue d'Assas, 75006 Paris, France.

sake. His forthrightness was so cruel that it is legendary and those of his colleagues and students who suffered from it were also those who, when they received encouragements or congratulations, knew to value them at their true worth. He did not mind being criticized, but he did insist that the criticism be solid, as solid as his own conviction. That was the style of discussions we had, sometimes harsh, always invigorating. A few of us experienced those afternoon work sessions in his study at his home, in Vincennes, when we discussed an assumption, an equation or an interpretation for hours. He enjoyed above all that emulation, that privileged relationship that grew little by little between him and his students. He enjoyed it when we successfully defended our point of view, he who did not look on his work as a researcher and teacher as a social function, but as a duty.

Some biographical landmarks: the university aspect Claude Ponsard was born on November 2nd 1927 in Dijon. This town was his hideout (he managed to draw both of us to it for several months) and above all the fixed point of his university career, attached as he was to his University and to the Department of Economics whose scientific reputation he helped to enhance over twenty seven years. From 1950 to 1958, he was 'charg6 de mission' at the I N S E E and spent four years (1950-1954) at the CNRS as a research assistant before becoming a part-time lecturer at the University of Nancy. In 1953, he presented his doctoral thesis in economics at the University of Dijon under the supervision of Henri Guitton. The thesis, awarded the Prix Vouters in 1954, concerned the integration of the spatial factor in

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A. Billot, J.-F. Thisse / Claude Ponsard

economic analysis and m a r k e d the beginning of his contribution to economic theory. In 1958, he passed the Economics Agrdgation and left for Lyon, where he was to remain for five years. In 1963, he took up a position as Professor at the University of Dijon, and a year later, as Professor at the Ecole Nationale

not understood, or at least that he was out of step with the rest of the scientific community. H e liked to say that he had had to write his History of Spatial Economic Theory so that people would at long last take the trouble to read his

Sup~rieure du P~trole et des Moteurs (Institut Fran~ais du P~trole). H e was still teaching there

also thought that his pioneering work in fuzzy economics would only meet with success a good while after he had been in the firing line of criticism. He was incontestably a forerunner; one of those in w h o m intuition comes first. With hindsight it is easy to m a k e out the two fundamental theoretical fields on which he built his research and which crop up constantly throughout his publications, either interleaved or separately: for the sake of convenience or efficiency (that is what the debate comes down to), traditional theory disregards a certain n u m b e r of real p h e n o m e n a . Denying them might be fertile for producing stylized results. Such is the case of the spaceless 1 economic model, or the crisp 2 economic theory. Nevertheless, if it is possible to formally integrate the real p h e n o m ena that the standard theory denies, the new theory will be superior. This conviction underlies the two canonical steps in the work of Claude Ponsard: integration of the spatial factor (1953-1974) and integration of imprecision in behaviour (1975-1990) 3.

three months before his death. Claude Ponsard had great ambitions for his university. T o achieve them, he took on numerous administrative duties without detriment to his research work. F r o m 1966 to 1969, he was Chairman of the Economics Section, then from 1969 to 1972, he b e c a m e vice-Dean of the School of Economics and Management. In order to p r o m o t e research in (mathematical) quantitative economics, he set up the Institute de Math~matiques Economiques in 1969 which was given the C N R S seal of approval in 1974. This institute was to be a breeding ground for researchers and at the same time a privileged forum for scientific exchange. In 1982, the C N R S appointed Claude Ponsard Director of the L A T E C ( Laboratoire d'Analyse et de Techniques Economiques) which includes, among others, the I M E . Parallel to his activities in Burgundy, the renown of his work and his great rigour as a scientist led him to take on a certain n u m b e r of positions at the national level. In 1962, he was elected a m e m b e r of the C C U (Conseil Consultatif des Universit~s) and chaired the Economic Section between 1970 and 1978, at which date he was called on to chair the jury for the Economics Agrdgation. In the early eighties, he decided to devote himself entirely to research and gave up most of his official functions.

Some biographical landmarks: the scientific aspect Scientifically, he was first and foremost his own man: free in the choice of topics, he enthused about (space, fuzziness), free to exaggerate even. H e only liked tradition so as to escape from it, opening up new doors and bursting through without counting the cost, through conviction. Behind him, his students followed. H e often had the impression he was

Economie et Espace: Essai d'Int~gration du Facteur Spatial dans l'Analyse Economique. H e

Introducing the spatial factor into economic theory (1953-1974) It was in 1947 that Alain Piatier, then Director of Studies at the Ecole Pratique des Hautes Etudes de Paris, invited two young researchers An economic model is said to be spaceless, as opposed to spatial models, when it concentrates, by definition, the activities it describes (consumption, production, exchange) in one point and one alone, thus denying the economic influence of space. 2In a particularly novel article, Foundations of Soft Decision Theory, Claude Ponsard set the soft decision, i.e. imprecise, finely nuanced, possibly contradictory, against the crisp decision which corresponded to the standard theory. 3This division into two periods is necessarily artificial in that, during the second period, there is undeniably still a preoccupation with space; but one might still consider that the core of this research into fuzzy economics is not fundamentally influenced by the spatial factor but rather by behavioural patterns.

A. Billot, J.-F. Thisse / Claude Ponsard

to focus their theses, one (Claude Ponsard) on developing a synthesis of works involving space within economic theory and the other ( R a y m o n d Barre) along similar lines but with the focus on time. From the outset, the asymmetry in the careers that these two inquiring and brilliant minds were to lead came out even in the research topics. While time has been at the centre of fundamental debates on the theory of value, ever since economics developed as a scientific discipline, the spatial factor seems to have been neglected from economic thinking. And yet it is not for want of an eminent founder. In 1826, von Th/Jnen showed how differential land rent could be clearly and logically explained in the context of a spatial economy (unlike Ricardo who favoured differences in soil fertility). The work of von Thiinen is more abstract and more formal than those of his contemporaries; he also strove to confront his theory of concentric crop patterns with real data. Hence, von Thiinen may be considered without exaggeration as one of the founders of both pure economics and econometrics. In spite of, or perhaps because of, their many qualities, von Thtinen's work long remained little known outside Germany. However, in Germany, von Th/inen was to have numerous successors of whom the most prestigious were Launhardt, Weber, Christaller and above all L6sch. In the aftermath of war, i.e. at a time that was still not favourable to scientific exchanges, Claude Ponsard tackled the titanic work of providing French economists with a remarkable synthesis of works on spatial economic theory that, until then, had been scattered. 4 H e distinguished four major paradigms, namely the economic theory of land use in von Thiinen, the location of the firm in Weber, Hotelling's theory of spatial competition and that of central places by Christaller-L6sch. This same division governed the architecture of his History of Spatial Economic Theory 5 published in 1958. Thanks to Claude Ponsard, French economists 4Economie et Espace: Essai d'lnt(gration du Facteur Spatial darts l'Analyse Economique, Soci6t6 d'Edition de l'Enseignement Sup6rieur, Paris, 1955. 5 Histoire des Thdories Economiques Spatiales, A. Colin, Paris, 1958. English Translation: History of Spatial Economic Theory, Springer-Verlag, Berlin-New York, 1983.

have had access to the key ideas of spatial analysis for over thirty years. Curiously enough, they hardly took any notice at the time. Some preferred the word wizardry of Francois Perroux to the rigour of Claude Ponsard. Others, the vast majority, only saw in the spatial factor another index to be added to the definition of commodity in the A r r o w - D e b r e u sense. In that case, why not leave this work to geographers; after all, space is their job! Claude Ponsard saw from very early on that the spatial factor did not simply call for existing theories to be generalized. On the contrary, the spatial factor is troublesome in that it forces us to invent new theories: wherever sellers and

buyers are separated in space, markets are no longer in perfect competition. As Sraffa had already noticed in 1926, spatial differentiation was enough to bring the assumption of a homogeneous commodity into question. From that point on, competition no longer involves a large number of agents but, rather, is among the few. Perhaps Claude Ponsard, in his eagerness to disseminate the theories of his great predecessors, did not put all the powers of persuasion that he indeed possessed into convincing his colleagues that space invited them to go beyond existing theories rather than to generalize them. Paradoxically for a man with such critical faculties, Claude Ponsard wanted to reconcile space and the theory of value. He was probably fascinated, as we all were, by the masterful elegance of G6rard Debreu's work. In private, though, he did not hesitate to defend the equation 'space = imperfect competition'. This point of view crops up again in the admiration he felt for L6sch 6 who may be considered as one of the chief founders of imperfect competition. Although he was only to further debate on this topic intermittently, 7 Claude Ponsard did exert a decisive influence in terms of space modelling. He retained from his readings a systematic, 6August L6sch: A famous but ignored economist, in Space, Structure, Economy: A Tribute to August L6sch, (R.H. Funks and A. Kuklinski, Eds.), Springer-Verlag, Berlin-New York, 1988. 7Quelques R6flexions sur la Th6orie Economique de l'Equilibre Spatial G6n6ral, in March~s, Capital et Incertitude: Essais en l'Honneur de Maurice Allais (M. Boiteux, T. de Montbrial and B. Munier, Eds.), Economica, Paris, 1986, 47-55.

A. Billot, J.-F. Thisse / Claude Ponsard overstated use of Euclidean geometry. H e criticized this hypothesis very early on. H e first integrated graph theory. 8 As he was to do later on when it came to fuzzy subsets theory, he took an interest in the mathematical tool for its own sake and glimpsed a wealth of applications. This was the start of a long line of works on the use of transfer graphs in the analysis of linear economic systems 9 (e.g. i n p u t - o u t p u t analysis). This was a rich vein and many a student developed and applied his ideas. In a second phase, in the early seventies, Claude Ponsard realized that Euclidean geometry like graphs are only particular structures. It was the full potential of metric, normed or topological spaces 1° which were available to spatial economists. With the generosity that typified the man, he gave up his ideas to his students, each of them forming the starting point of a thesis or of several articles. H e was happy to see his insights developed by others, when many people would have kept them jealously for themselves. Just when he was in a position to put forward his own synthesis of spatial economic analysis, Claude Ponsard to some extent abandoned the love of his youth: he had just discovered the existence of fuzzy subsets theory.

Introducing imprecise behaviour into economic theory (1975-1990) In August 1974, Claude Ponsard was walking along the boulevard Saint-Michel when he saw Kaufmann's manual on the fuzzy subsets theory in the shop window of the Presses Universitaires de France. H e went into the bookshop, bought the four volumes and headed off home, intrigued by the odd couple formed by the term f u z z y alongside set. The adjective f u z z y literally evokes what is imprecise, vague, ill-defined: everything which by definiton cannot be 8 Une application de ia th6orie de graphes ~t I'analyse de l'espace economique: un module de localisation de l'unit6 de production dans une structure de concurrence, Cahiers T.E.M. 4, 1966, 1-21. 9 Un ModUle Topologique d'Equilibre Economique Interr~gional, Dunod, Paris, 1969 and "Graphes de Transfert et Analyse Economique", special issue of the Revue d'Economie Politique, 1972. 10Economie urbaine et espaces m6triques, Sistemi Urbani 1, 1979, 123-135.

measured or quantified. In contrast, the word set refers to set theory, to topological structures which correspond to sophisticated mathematics in the Bourbaki style of which economists (for the most part) learnt of the existence by reading Arrow and above all D e b r e u and his Theory o f Value. Without any doubt, this book, more than any other, exerted considerable fascination over the generations of economists who were around at the time of its publication or who came after. Claude P o n s a r d - w e r e p e a t - w a s one of the former, and was convinced a priori that the fundamental theory of exchange required a powerful mathematical instrument (and hence one difficult to get to grips with), convinced above all that the foundation of the central concept of economic analysis - equilibrium - had to be conveyed through this sort of esthetic starkness which was not unrelated to its success. The main features of Theory o f Value, rigour and elegance, are also the criteria on which Claude Ponsard appraised any scientific work; reading his thesis reports, his critical reviews in the Revue d'Economie Politique or even his report for the Agr~gation des Professeurs examinations which he chaired in 1978, is enough to convince one of this. By the time he had finished reading the first volume of Kaufmann's manual, he already had the main insights that he developed later, year after year, article after article, with shear tenacity, despite the polite silence from French scientific circles, to the point where he finally defined a Fuzzy theory o f value. Integration of the spatial f a c t o r - the favoured target of his early research - was matched here by integration of behavioural imprecision. T h e r e was a fairly lively debate between him and some of his students as to the origin of this imprecision: for him, it stemmed straight from man himself, it was an intrinsic part of mankind and anything that described the economic agent as a perfectly rational being, making complete and entirely discriminate choices, amounted to the most obvious kind of reductionism. For others, imprecision was extrinsic and came only from the modeller. In line with this view, Claude Ponsard, first of all, focused on the fundamental concept of the theory of value, namely utility. In a paper

A. Billot, J.-F. Thisse / Claude Ponsard

presented at the 4th Annual Meeting of the Canadian Regional Science Association and the

Association de Science R~gionale de Langue Fran~aise, in 1980, in Montr6al, he presented the first version of what was to become the founding article of the fuzzy economics, published a year later in Fuzzy Sets and Systems, "An application of fuzzy subsets theory to the analysis of the consumer's spatial preferences". His thesis was straightforward enough: the new methods of fuzzy optimization make it possible to consider that the objective or the constraint (or both) are fuzzy and so account for either the imprecision of the utility function (and so the preferences) or the imprecision of budget constraint. Once this possibility has been introduced, the economist steps in to justify his modifications. The introduction of fuzzy preference relations with more flexible properties makes it possible to describe economic agents with less rational behaviour, who state their choices with greater discrimination. Certain axioms such as totality of preorder (in the fuzzy sense), are no longer indispensable and allow the technical constraints of the traditional model to be slackened. Then, on this foundation, he developed the symmetrical analysis of the producer H after introducing a profit utility function (highly debated) and fuzzifying the technological constraints, then the concept of fuzzy equilibrium of an economy ~ la Arrow-Debreu ~2 and finally that of Nash equilibrium. 13 The theorems of existence were based on the works of Dan Butnariu who generalized the concept of fixed point to fuzzy correspondences. In addition, the concept of a median agent whose behaviour made it possible to aggregate demand correspondences was brought in and founded indirectly the classical hypothesis of the representative agent. Claude Ponsard, thus, showed that confronted with imprecise behaviour, the l~Producer's spatial equilibria with fuzzy constraints, 1982, 302-313. 12A theory of spatial general equilibrium in a fuzzy economy, in Fuzzy Economics and Spatial Analysis (C. Ponsard and B. Fustier, Eds.), Librairie de I'Universit6, n°32, 1986, 1-27. 13Nash fuzzy equilibrium: Theory and application to spatial duopoly, European Journal of Operational Research 31, 1987, 376-384.

European Journal of Operational Research 10,

system of market organization remained efficient. In 1987, the reformulation of a theory of value was complete. J. Eatwell, M. Milgate and P. Newman asked him to write an article ~4 in the New Palgrave, A Dictionary of Economics; he saw in this a first sign of recognition for his works in the field. Claude Ponsard did not stop reviewing his own findings for all that. From 1988 until he passed away, he tirelessly continued to improve his theory by introducing nuances and analyses, interpretations and mathematical refinements. In February 1988, he published his first reflections on what was to enable the concept of commodity15 to be fuzzified and in 1990, a few days before his death, he was still correcting the proofs for an article on the many forms of fuzzy transitivity that can be introduced into models of preference theory. 16 At the same time, he encouraged a great many projects: those of B. Mathieu-Nicot in decision making theory, those of B. Fustier in spatial and urban economics and those of several students of the lnstitut Franf~ais du Pdtrole. ~7 He made fruitful contacts with foreign researchers, L.A. Zadeh, H.-J. Zimmermann, R.R. Yager and J. Kacprzyk who received one of his most stimulating papers TM in 1985; he persuaded P. Nijkamp and M. Beckmann of the interest of this theory; 19 he debated it with his friend P. Balestra, as well as with F. Hahn, E. Malinvaud or G.L.S. Shackle; he invited all the scientific world's fuzzyists, from D. Dubois to M. Roubens, from M. Salles to P. Vincke, to the Annual Meeting of the IME. 14Fuzzy Sets, Entry in The New Palgrave, A Dictionary of Economics (J. Eatwell, M. Milgate and P. Newman, Eds.), MacMillan Press, London, 1987, 449-452. 15 Note on the ranking of fuzzy numbers, Document de Travail de I'IME, n°102, 1989. 16Some dissenting views on the transitivity of individual preference, Annals of Operational Research 23, 1990, 279-288. 17 In December 1989, he was planning on developing a research programme on fuzzy econometrics with IFP students. lS Fuzzy sets in economics: Foundations of soft decision theory, in Management Support Systems Using Fuzzy Sets and Possibility Theory (J. Kacprzyk and R.R. Yager, Eds.), Verlag TUV Rheinland, K61n, 1985, 25-37. 19Fuzzy data analysis in a spatial context, in Measuring the Unmeasurable (P. Nijkamp, H. Leitner and N. Wrigley, Eds.), Martinus Nijhoff, Dordrecht-Boston, 1985, 487-508.

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A. Billot, J.-F. Thisse / Claude Ponsard

This energy, focused wholly on promoting a fuzzy economic theory, found its full reward when, in April 1986, the Economics Academy of Poznan (Poland) awarded him the title of Doctor Honoris Causa and he seized this unique opportunity to express his philosophy of economics. 2° In an astonishing speech, he integrated space and imprecision in a common perspective assimilating the two poles of his work to show how fertile they are. In addition, for two years, he gathered the material for what was to be the 'fuzzy' equivalent of his essay on the integration of the spatial factor and that he had planned entitling

Fuzzy Economic Spaces: An Axiomatic Approach. This was on the way to taking its final shape: fuzzy preferences, fuzzy utility function, consumer's partial equilibrium, producer's partial equilibrium, fuzzy general equilibria and finally a chapter on imperfect competition where 20 See on this topic Claude Ponsard's other epistemological text, "L'homo oeconomicus et l'espace", in L ' H o m m e et l'Espace, CRDP, Dijon, 73-80.

Nash equilibria generalized to fuzzy games are presented. This book exists in manuscript form, partly unfinished. In it, Claude Ponsard sets out his theory in an homogeneous and rigourous manner. He planned on the work coming out to close the often rich but frequently polemical debate on how much of an innovation fuzzy subsets theory has actually been for economic analysis. He did not have enough time. At the end of this biographical homage, we have the strange feeling that the existence of a man captured in a few pages is merely a poor photograph, a rough portrait that lacks the essential feature which would lend it some sort of likeness. This feature is probably not a matter of science, but rather a collection of scattered and personal memories, of real life impressions and it is not for us to impose ours. Perhaps there are some who will not recognize Claude Ponsard in these lines; it is that they have other landmarks, other images. We have simply tried to describe the man we knew.