The coalitional approach to core theory

The Core-Walras Equivalence is examined in a finite or infinite economy in which the competitive gap is bounded by the size of the atoms in the economy. The economy is represented by a Boolean algebra of coalitions, and coalitions rather than individual agents are taken as a primitive concept. Coalition arbitrage plays the central role in our analysis.     

On Vind’s theorem for an economy with atoms and infinitely many commodities

We extend Vind’s classical theorem on the measure of blocking coalitions valid in finite dimensional atomless economies (see Vind (1972)), to include the possibility of infinitely many commodities as well as the presence of atoms. The commodity space is assumed to be an ordered Banach space which has possibly the empty positive cone. The lack of interior points is compensated by an additional assumption of a cone of arbitrage that allows us to use Lyapunov’s convexity theorem in its weak form. The measure space of agents involves both negligible and non negligible traders. The extension is proved in the general class of Aubin coalitions for which a suitable version of Grodal’s result (Grodal (1972)) is also formulated. Our results wish to point out the relevance of cone conditions dealing with blocking coalitions of arbitrary measure or weight.     

A further note on arrow's impossibility theorem

For arbitrary measure spaces of agents we investigate the existence of social welfare functions which fulfill a suitable non-dictatorship axiom; it turns out that there is an essential difference between finite and σ-finite but infinite measure spaces. Furthermore the condition of universal domain of social welfare functions is weakened.     

On the existence of a probability measure compatible with a total preorder on a Boolean algebra

If an economic agent's beliefs about the relative likelihood of events are characterized by a total preorder ? on the algebra $\text{A}$ of events, the problem arises to know under which conditions, ? is representable by a probability measure. Here we show that there exists a probability measure compatible with a total preorder on a Boolean algebra, if and only if, the Boolean algebra is well bounded, weakly Archimedean, and perfectly separable, this last condition substituting for Villegas' monotone condition used in Chateauneuf and Jaffray (1984); if σ-additivity is required. Villegas' monotone condition, must merely be added.     

Judgment aggregators and Boolean algebra homomorphisms

The theory of Boolean algebras can be fruitfully applied to judgment aggregation: assuming universality, systematicity and a sufficiently rich agenda, there is a correspondence between (i) non-trivial deductively closed judgment aggregators and (ii) Boolean algebra homomorphisms defined on the power-set algebra of the electorate. Furthermore, there is a correspondence between (i) consistent complete judgment aggregators and (ii) 2-valued Boolean algebra homomorphisms defined on the power-set algebra of the electorate.     

Limiting Dictatorial rules

We consider the preference aggregation problem in infinite societies. In our model, there are arbitrarily many agents and alternatives, and admissible coalitions may be restricted to lie in an algebra. In this framework (which includes the standard one), we characterize, in terms of Strict Neutrality, the Ultrafilter Property of preference aggregation rules. Based on this property, we define the concept of Limiting Dictatorial rules, which are characterized by the existence of arbitrarily small decisive coalitions. We show that, in infinite societies which can be well approximated by finite ones, any Arrovian rule is limiting.     

Finitely additive exchange economies

It is shown that the core and the set of Walras allocations of a non-atomic exchange economy are equal, if the set A of agents is either countable or a continuum, and even if all subsets of A are admitted as coalitions. The set of Walras allocations is shown to be not empty. These results are obtained by use of finitely additive measures defined on the algebra of all subsets of A.     

Measuring the set of blocking coalitions in infinite dimensional economies

The classical core-Walras equivalence is investigated via the measurement of the set of blocking coalitions. In the framework of continuum economies with an infinite dimensional space of commodities, we find the measure of the set of coalitions that block a non-competitive Pareto optimal allocation. Then, from the relation between coalitions of a continuum economy with a finite number of types and fuzzy coalitions of an economy with finitely many agents, the previous results are translated as results on the measure of blocking fuzzy coalitions. Both results imply classically formulated core-Walras equivalence theorems. Finally, the measure of blocking "social communication structures" is determined.     

The algebra of Bonferroni bounds: discrete tubes and extensions

Bonferroni, or inclusion-exclusion, bounds and identities have a rich history. They concern the indicator function, and hence the probability content, of the union of sets. In previous work, the authors defined a discrete tube which yields upper and lower bounds which are at least as tight as the standard bounds obtained by truncating inclusion-exclusion identities at particular depths. Here, some connections to other fields are made, based particularly on the algebra of indicator functions. These leads to the consideration of the complexity of more general Boolean statements.     

Concepts of similarity for utility functions

A generalization of the compact-open topology is defined for a space of utility functions with different choice sets. The space is a complete separable metric space. A continuous representation theorem of Levin (1983) gives a homeomorphism between this space and the space of preference relations, topologized by closed convergence. A map into the space is measurable with regard to the Borel algebra iff the choice set correspondence is measurable and the utility function is measurable on its graph. A coarser topology (that of subgraph convergence) is also studied. This topology is coarser than the compact-open topology when the utility functions are defined on the same choice set. However the demand correspondence is still upper-hemicontinuous. A homeomorphism is given between this space and the space of preference relations, with the latter given a certain topology coarser than closed convergence.     

Algebra for Enterprise Ontology: towards analysis and synthesis of enterprise models

Enterprise modeling methodologies have made enterprises more likely to be the object of systems engineering rather than craftsmanship. However, the current state of research in enterprise modeling methodologies lacks investigations of the mathematical background embedded in these methodologies. Abstract algebra, a broad subfield of mathematics, and the study of algebraic structures may provide interesting implications in both theory and practice. Therefore, this research gives an empirical challenge to establish an algebraic structure for one aspect model proposed in Design & Engineering Methodology for Organizations (DEMO), which is a major enterprise modeling methodology in the spotlight as a modeling principle to capture the skeleton of enterprises for developing enterprise information systems. The results show that the aspect model behaves well in the sense of algebraic operations and indeed constructs a Boolean algebra. This article also discusses comparisons with other modeling languages and suggests future work.     

Antibody tests: They are more important than we thought

Antibody testing is a non-pharmaceutical intervention – not recognized so far in the literature – to prevent COVID-19 contagion. I show this in a simple economic model of an epidemic in which agents choose social activity under health state uncertainty. In the model, susceptible and asymptomatic agents are more socially active when they think they might be immune. And this increased activity escalates infections, deaths, and welfare losses. Antibody testing, however, prevents this escalation by revealing that those agents are not immune. Through this mechanism, I find that antibody testing prevents about 12% of COVID-19 related deaths within 12 months.     

Cultural Values and Social Planning: A Control Theory Approach to Satisfying a Social Welfare Criterion

A bstract . A method of social planning is presented which can be used to fulfill a social welfare criterion with normative values. The purpose is to show how a social welfare model which includes cultural norms can be optimized using classical control theory. Current literature stresses the importance of incorporating social indicators in welfare economics. Given a social welfare function which actively includes a hierarchy of cultural values , control theory can be used to set social policy to reach social goals. The approach is to define a set of desired cultural norms at some future time and then determine the social policy necessary to reach this state. Control theory is used to find the social plan consistent with attaining the set of desired values.     

Nash and dominant strategy implementation in economic environments

When environments are ‘rich’, single-valued social choice functions which are implementable in Nash strategies are implementable in dominant strategies. Moreover the Gibbard–Satterthwaite impossibility theorem of implementation in dominant strategies has been extended to differential economic environments. Therefore it is important to study implementation for non-rich environments. We characterize for quasi-linear utility functions mechanisms which are implementable in dominant strategies (providing a generalization of the Groves–Clarke mechanisms) and in Nash strategies. This second type of mechanisms differ from the first only by the types of transfers they allow. Properties of these mechanisms such as balancedness, individual rationality and robustness with respect to coalitions are then studied.     

Optimal Social Design: Estimating a Social Welfare Function from Questionnaire Data

A social design x evokes a response y from a set of individuals. The value of the design is expressed in terms of a social welfare function which is derived from Arrow’s formulation of social choice. Making certain simplifying assumptions the social welfare function can be expressed in terms of individuals’ ideal designs. A method for estimating the social welfare function from quite limited empirical evidence is developed. The method is applied to an educational case study. There was considerable variation in individuals’ ideal designs. The components of the social welfare were estimated: the welfare ideal, the population sensitivity, the population variation, the deviation from the ideal and the welfare ceiling. Methodological problems are discussed.     

Universal Pareto dominance and welfare for plausible utility functions

We study Pareto efficiency in a setting that involves two kinds of uncertainty: Uncertainty over the possible outcomes is modeled using lotteries whereas uncertainty over the agents’ preferences over lotteries is modeled using sets of plausible utility functions. A lottery is universally Pareto undominated if there is no other lottery that Pareto dominates it for all plausible utility functions. We show that, under fairly general conditions, a lottery is universally Pareto undominated iff it is Pareto efficient for some vector of plausible utility functions, which in turn is equivalent to affine welfare maximization for this vector. In contrast to previous work on linear utility functions, we use the significantly more general framework of skew-symmetric bilinear (SSB) utility functions as introduced by Fishburn (1982). Our main theorem generalizes a theorem by Carroll (2010) and implies the ordinal efficiency welfare theorem. We discuss three natural classes of plausible utility functions, which lead to three notions of ordinal efficiency, including stochastic dominance efficiency, and conclude with a detailed investigation of the geometric and computational properties of these notions.     

Minimal manipulability: Unanimity and nondictatorship

This paper is concerned with the number of profiles at which a nondictatorial social choice function is manipulable. For three or more alternatives the lower bound is found for unanimous social choice functions. In the case of three alternatives the lower bound is found for surjective social choice functions. In both cases all social choice functions reaching the lower bound are characterized for more than two agents. In the case of two agents the characterized social choice functions form a subset of the set of all social choice functions reaching the minimum.     

国际环境合作的经济学分析

本文利用现代经济学理论与方法，构筑了一个分析国际环境合作问题的经济学框架。分析的中心是建立一个静态模型来寻求作为一个联盟形态的国际环境合作的内部和外部稳定性条件，主要结论是稳定的国际环境合作是由模型给定的参数内生地决定的。与当前大多数研究的一个重要不同是，我们的模型没有采用通常的减少污染排放这一分析参数，而是选用了更为直接的污染排放量这一指标。在运用联盟理论对两类情形即不合作和完全合作进行模型化处理的基础上，本文导出了联盟成员国与非成员国福利水平和污染排放量的若干命题，并建立起国际环境合作稳定性的条件。     

A review of integrated QCA and statistical analyses

Systematically combining quantitative and qualitative research approaches offers the potential for a more comprehensive and nuanced understanding of social scientific phenomena. With their strong opportunities for building, qualifying, and testing social scientific theories, methodological integrations thus enable researchers to make substantive contributions that would not have been possible with one method alone. In this article we demonstrate how the integration of Qualitative Comparative Analysis (QCA) and conventional statistical analysis offers researchers new opportunities for contributing to the social sciences. Whereas statistical analysis is variable-oriented and relies on correlational analysis to make comparisons across cases, QCA is based on set theory, is case oriented, and relies on Boolean algebra to make comparisons between cases. Drawing on the literature on the interdependency between theoretical contribution and methodology, we review studies that integrate QCA and statistical analysis to explain how the specific combination of these two approaches allows researchers to strengthen the theoretical contribution of their research. From our review we identify common challenges and provide solutions for integrating QCA and statistical analysis.     

Social interactions and the prophylaxis of SI epidemics on networks

We investigate the containment of epidemic spreading in networks from a normative point of view. We consider a susceptible/infected model in which agents can invest in order to reduce the contagiousness of network links. In this setting, we study the relationships between social efficiency, individual behaviours and network structure. First, we characterise individual and socially efficient behaviour using the notions of communicability and exponential centrality. Second we show, by computing the Price of Anarchy, that the level of inefficiency can scale up linearly with the number of agents. Third, we prove that policies of uniform reduction of interactions satisfy some optimality conditions in a vast range of networks. In setting where no central authority can enforce such stringent policies, we consider as a type of second-best policy the implementation of cooperation frameworks that allow agents to subsidise prophylactic investments in the global rather than in the local network. We then characterise the scope for Pareto improvement opened by such policies through a notion of Price of Autarky, measuring the ratio between social welfare at a global and a local equilibrium. Overall, our results show that individual behaviours can be extremely inefficient in the face of epidemic propagation but that policy can take advantage of the network structure to design welfare improving containment policies.