Core Rationalizability in Two-Agent Exchange Economies

We provide a characterization of selection correspondences in two-person exchange economies that can be core rationalized in the sense that there exists a preference profile with some standard properties that generates the observed choices as the set of core elements of the economy for any given initial endowment vector. The approach followed in this paper deviates from the standard rational choice model in that a rationalization in terms of a profile of individual orderings rather than in terms of a single individual or social preference relation is analyzed.

Fair Production and Allocation of an Excludable Nonrival Good

We study fairness in economies with one private good and one partially excludable nonrival good. A social ordering function determines for each profile of preferences an ordering of all conceivable allocations. We propose the following Free Lunch Aversion condition: if the private good contributions of two agents consuming the same quantity of the nonrival good have opposite signs, reducing that gap improves social welfare. This condition, combined with the more standard requirements of Unanimous Indifference and Responsiveness, delivers a form of welfare egalitarianism in which an agent's welfare at an allocation is measured by the quantity of the nonrival good that, consumed at no cost, would leave her indifferent to the bundle she is assigned.

On Demand Responsiveness in Additive Cost Sharing

We propose two new axioms of demand responsiveness for additive cost sharing with variable demands. Group Monotonicity requires that if a group of agents increase their demands, not all of them pay less. Solidarity says that if agent i demands more, j should not pay more if k pays less. Both axioms are compatible in the partial responsibility theory postulating Strong Ranking, i.e., the ranking of cost shares should never contradict that of demands. The combination of Strong Ranking , Solidarity and Monotonicity characterizes the quasi-proportional methods, under which cost shares are proportional to 'rescaled' demands. The alternative full responsibility theory is based on Separability, ruling out cross-subsidization when costs are additively separable. Neither the Aumann-Shapley nor the Shapley-Shubik method is group monotonic. On the otherhand, convex combinations of "nearby" fixed-path methods are group-monotonic: the subsidy-free serial method is the main example. No separable method meets Solidarity, yet restricting the axiom to submodular (or supermodular) cost functions leads to a characterization of the fixed-flow methods, containing the Shapley-Shubik and serial methods.

Sharing the cost of a public good under nonnegativity constraints

We study the construction of a social ordering function for the case of a public good financed by contributions from the population, and we extend the analysis of Maniquet and Sprumont (2004) to the case when contributions cannot be negative, i.e. agents cannot receive subsidies from the others.social ordering, public good, maximin

Welfare Egalitarianism in Non-Rival Environments

We study equity in economies where a set of agents commonly own a technology producing a non-rival good from their private contributions. A social ordering function associates to each economy a complete ranking of the allocations. We build social ordering functions satisfying the property that individual welfare levels exceeding a legitimate upper bound should be reduced. Combining that property with efficiency and robustness properties with respect to changes in the set of agents, we obtain a kind of welfare egalitarianism based on a constructed numerical representation of individual preferences.

Responsibility and Cross-Subsidization in Cost Sharing

We propose two axiomatic theories of cost sharing with the common premise that individual demands are comparable, though perhaps different, commodities, and that agents are responsible for their own demand. Under partial responsibility the agents are not responsible for the asymmetries of the cost function: two agents consuming the same amount of output always pay the same price; this holds true under full responsibility only if the cost function is symmetric in all individual demands. If the cost function is additively separable, each agent pays his/her stand alone cost under full responsibility; this holds true under partial responsibility only if, in addition, the cost function is symmetric. By generalizing Moulin and Shenker.s (1999) Distributivity axiom to cost- sharing methods for heterogeneous goods, we identify in each of our two theories a different serial method. The subsidy-free serial method (Moulin, 1995) is essentially the only distributive method meeting Ranking and Dummy. The cross-subsidizing serial method (Sprumont, 1998) is the only distributive method satisfying Separability and Strong Ranking. Finally, we propose an alternative characterization of the latter method based on a strengthening of Distributivity.

Ordinally consistent tournament solutions

A set ranking method assigns to each tournament on a given set an ordering of the subsets of that set. Such a method is consistent if (i) the items in the set are ranked in the same order as the sets of items they beat and (ii) the ordering of the items fully determines the ordering of the sets of items. We describe two consistent set ranking methods

Maximal-Element Rationalizability

We examine the maximal-element rationalizability of choice functions with arbitrary domains. While rationality formulated in terms of the choice of greatest elements according to a rationalizing relation has been analyzed relatively thoroughly in the earlier literature, this is not the case for maximal-element rationalizability, except when it coincides with greatest-element rationalizability because of properties imposed on the rationalizing relation. We develop necessary and sufficient conditions for maximal-element rationalizability by itself, and for maximal-element rationalizability in conjunction with additional properties of a rationalizing relation such as reflexivity, completeness, P-acyclicity, quasitransitivity, consistency and transitivity.Choice Functions, Maximal-Element Rationalizability

Anatomical terms: towards development of terminologies (terminogenesis)

Anatomy is older than its name that means "cutting out" in Greek. The cut out parts must bear a name. This historical review is an attempt to investigate the evolution of the anatomical names from the prehistorical times when humans had no handwriting to record anatomy until the discovery of printing when anatomical names could become disseminated in printed books.Throughout indeterminately long times, the people who spoke anatomical terms were the embalmers who touched human bodies, the priests who read the future in the entrails of animals and the magicians who prepared healing charms from various human, animal or plant components. But we have no traces of their words.Having invented handwriting, early Egyptians and Mesopotamians were among those who began to give specific names to parts of the body. Yet it remains difficult to always understand them as they considered that each part of the body was inhabited by a specific god. Nevertheless, some of the names they used influenced the new language that unfolded in the South East corner of Europe, the unifying Greek language. Greek poets like Homer, philosophers like Aristotle and physicians like Hippocrates were using anatomical words that were later developed by anatomists like Herophilos, Erasistratos or Rufos to designate specific structures.Greek became the language of Western medicine by the 4th century BCE, but Latin later superseded it in terms of political and linguistic influence. This meant that translators, such as Celsus, played a major role during the first years of the Christian era.Nevertheless, it was still in Greek that Galen produced an immense medical literature in which anatomy was prominent. However, because Galen dissected animals, he unfortunately stamped in the minds of his successors errors that would last from his death (probably in 216 CE) until the Renaissance in the 15th century.Even as the world of Latin imploded, the language maintained its influence. In the West, Christianity spread, preserving Greek and Latin manuscripts in its abbeys and cathedrals. In the East, numerous Greek manuscripts had survived. After the advent of Islam in 622 CE, a "House of Wisdom" was created in Baghdad at the beginning of the 9th century CE. Under Hunayn ibn Ishak, a team of experts undertook to translate into Syriac or Arabic all the manuscripts collected by the armies of the Caliph. Thanks to them, Greek science, medicine and literature were studied and Arabic translations could be found throughout the expanding Islamic world. Avicenna could thus write amongst many books his most famous medical opus, the "Canon of Medicine", which influenced medicine, and anatomy, until well beyond the 16th century.On the Western side of the former Roman Empire, the organisation of medical practice had changed. It was linked to the abbeys and churches where healing monks and lay people (men and women) were instructed and entrusted with helping "the sick and the poor ones". In the 9th century, a medical school emerged in Salerno (Italy) and flourished there until the end of the 13th century, more or less independently from the Church.During the 11th century, Arabic manuscripts had found their way to Salerno and other healing institutions. A network of Latin translators from Arabic permitted the Western World to re-access the ancient literatures, the School of Toledo (Spain) becoming in the 12th and 13th centuries the most important European centre of translation. Anatomy also re-emerged in Italy at the same time thanks to two types of institutions: the School of Salerno and the universities gradually founded since 1088 (Bologna). Whereas barber-surgeons, surgeons and master-surgeons often came from Salerno, medical doctors came from such Universities as Padua, Bologna and Siena, Oxford, Paris or Salamanca. Trained surgeons attended Universities to deepen their knowledge.In 1315, Mondino de Liuzzi, Professor of Anatomy at the University of Bologna, inaugurated the teaching of human anatomy based upon the dissection of cadavers. The doors now opened to the re-discovery of anatomy, and especially of the internal organs. But Mondino still stuck to the doctrines of the “infallible” masters, although he had written (still in Latin) a book on dissection that remained a classic for two centuries.Some surgeons who had benefited from both an apprenticeship and a Humanist education wrote books in which they finally dared to contradict the old masters. The time was ripe for the arrival of Vesalius