Search

This study investigates an axiomatic approach to in-kind assignment problems with a single-unit demand such as triage. We consider multiple ethical criteria regarding which agents should be assigned that conflict with one another. To make compromises between criteria, we introduce two methods for configuring social choice rules that map from various problems to agents who are assigned slots: the method of procedure and the method of aggregation. From inter-problem regularities, we demonstrate characterization results, implying that the method of procedure emphasizes consistent respect for individual criteria across problems, whereas the method of aggregation emphasizes consistent respect for individual agents across problems. These methods are incompatible because only ethical dictatorships are induced by both methods. We show that the method of aggregation is superior when we can utilize detailed information about ethical concerns such as cardinality and comparability, while the method of procedure is superior when there are severe informational limitations.

This paper characterizes incomplete preferences with optimism and pessimism (IPOP) over Anscombe-Aumann acts, a class of preference orders that may fail axioms that require the decision-maker to think contingently. The main result axiomatizes preferences that compare any pair of distinct acts in such a way that an act is ranked higher than another act if and only if the minimal expected utility from the former is still greater than the maximal expected utility from the latter. This representation has a natural interpretation as conservative attitudes of the decision-maker under contingencies. The representation reduces to the standard SEU preferences when belief sets are minimal, while it encapsulates obvious dominance, the decision criterion proposed by Li (2017), as the polar case of when belief sets are maximal.

To organize all knowledge in biology in a coherent axiomatic system like mathematics or physics has been a dream for every scientist. This paper investigates the question how to formulate a set of axioms or fundamental laws governing all biological phenomena. We are able to identify a broad class of phenomena in biology including human society cannot be explained or forecasted by the existing fundamental laws of physics. However, the combination of existing fundamental laws of physics with laws in the recently-created Choice Axiomatic System in physics seems to be able to cover all known biological phenomena. This result enables this paper to propose a complete set of fundamental laws of biology for the first time in the history. Establishing a complete set of fundamental laws of biology provides a solid foundation for theoretical biology, and points to new directions of future biophysics research. We conclude that biology should not have any fundamental law of its own, all fundamental laws of biology are simply a subset of fundamental laws of physics, and identifying this complete set of fundamental laws of biology opens the door for an axiomatization of biology, social science, and humanities.

Empirical evidence shows that non-instrumental information attitudes are generally prior-dependent. However, Eliaz and Spiegler (2006) show that that such an anomalous information attitude cannot be captured by “expected utility-based models” and a potential way to fix this problem is replacing them by prior-dependent utility. This paper provides a systematic analysis of the prior-dependent utility approach as the explanation of prior-dependent information attitudes. First, the axiomatic system of this type of utility functions is studied, and I show that the representation theorem can be derived from extending the lottery-dependent utility theory (Schmidt, 2001) to the setting of temporal lotteries. Second, an alternative way to prior-dependent utility maximization is provided, where the decision maker chooses the prior belief and the temporal structure of information in a separate and sequential manner. Based on this interpretation, an anticipatory emotion-based explanation to the “ostrich effect”, one of the most common pattern of prior-dependent information attitude, is introduced.

Physicists have pursued the Theory of Everything (TOE) for centuries. Not much credible progress has been made towards the final theory so far. By extending the computability theory in mathematics, this paper proves a fundamental theorem of theoretical physics, which implies 21 structural features that TOE should have. The main result of this paper is that existing quantum gravity theories are not TOE; a unification theory of physics and social sciences/humanities, called “Choice Axiomatic System”, can be established even when the problem of unifying general relativity and quantum mechanics still remains unsolved; a prototype of TOE, which covers all existing human knowledge about the observable universe, can be created by the unification of physics and social science/humanities with a potential quantum gravity theory as an important component; unlike quantum gravity theories, Choice Axiomatic System has many important practical applications and its predictions can be tested with empirical data; Choice Axiomatic System can substantially narrow down the search for potential quantum gravity theories. This paper should be interesting to researchers working on the foundation of physics, social science, and humanities.

Incompleteness specifically refers to the fact that given any system of symbols, there will always be questions that can be formulated in that system that cannot be answered using just the symbols of that system. An example would be that if a person had a box of objects that person was holding, and an interrogator asked to show the objects in the box which cannot be shown. That would be a paradoxical question with no possible answer. Those sorts of questions can always be formulated, and this shows that there are some propositions that will be unresolvable no matter what the premises are of a system. So, if one wanted to judge an axiomatic system — as David Hilbert did at the turn of the last century — by whether it could have an answer for any question one could ask of it, then one will not be able to make that judgement of some system being more thoroughly 'complete' (able to answer questions asked of it) relative to another. Can, this, then can be applied to law and moral judgements? If one perceives law or morality as a propositional system then, yes, it would be applicable to moral judgements. Many pragmatists do not perceive law as such a propositional system, though. Some of the quotes I have collected refer to such pragmatists with that different approach. Morality cannot be approved and everything is subjective intent including law. So, in the same way that in the early 1900s Bertrand Russell’s attempts with mathematics were approved futile in Principia Mathematica. Are the philosophical foundations of law proved futile? How is Godel's incompleteness theorem as being a problem for morals? Nobody has "true" premises to go from? Therefore — it can be said — all our conclusions are subjective. Is this accurate?

We examine the river sharing problem with a novel focus on implementing efficient outcomes. We introduce a class of two-stage games in which agents first announce desired levels of consumption and then bargain over monetary compensations. An outside observer with partial information connects the two stages by conditioning agents’ recognition probabilities in the second stage on the allocation realized in the first stage. We identify ways of setting recognition probabilities that give agents incentives to choose the efficient allocation of water all the while ensuring that the surplus obtained from efficient water usage ends up being shared in a fair way. In particular, we take an axiomatic approach to determine three new and implementable solutions.

We discuss the notion of a state of the world in axiomatic decision theory, and argue that it should be viewed as an "eventuality" that is implicitly assumed to be independent of the process by which prefer- ences are observed. The distinction between states, which are assumed to resolve all uncertainty, and eventualities suggests certain limitations on the axiomatic approach for defining and measuring mental concepts (such as belief ) by observed choices

The neoclassical synthesis has been defined as a bridge between Keynesian theory and Walrasian general equilibrium theory. The aim of this article is to show that founders of the neoclassical synthesis were not homogenous in their appraisal of the importance of Walrasian theory. To do so, we focus on Robert Solow’s contributions as a case study and examine the history of his lifelong criticism of what he called “axiomatics.” According to Solow, the axiomatic approach aims at founding economics on one general and complex model based on first principles or axioms. In contrast, Solow advocated the use of a diversity of simple and partial models, which have practical utility, are realistic in their crucial assumptions, consider institutions and the evolving nature of the economy, and rely on common sense microfoundations. We conclude by suggesting that Solow can be characterized as Cournotian.

This paper analyzes bankruptcy problems with nontransferable utility as a generalization of bankruptcy problems with monetary estate and claims. Following the classical axiomatic theory of bankruptcy, we formulate some appropriate properties for NTU-bankruptcy rules and study their implications. We explore duality of bankruptcy rules and we derive several characterizations of the generalized proportional rule and the constrained relative equal awards rule.

In this paper, we study the problem of non-Bayesian learning over social networks by taking an axiomatic approach. As our main behavioral assumption, we postulate that agents follow social learning rules that satisfy imperfect recall, according to which they treat the current beliefs of their neighbors as sufficient statistics for all the information available to them. We establish that as long as imperfect recall represents the only point of departure from Bayesian rationality, agents’ social learning rules take a log-linear form. Our approach also enables us to provide a taxonomy of behavioral assumptions that underpin various non-Bayesian models of learning, including the canonical model of DeGroot. We then show that for a fairly large class of learning rules, the form of bounded rationality represented by imperfect recall is not an impediment to asymptotic learning, as long as agents assign weights of equal orders of magnitude to every independent piece of information. Finally, we show how the dispersion of information among different individuals in the social network determines the rate of learning.

Multiple causation is one of the most intricate issues in contemporary tort law. Sharing a loss suffered by a victim among multiple tortfeasors is indeed difficult and Courts do not always follow clear and consistent principles. Here, we argue that the axiomatic approach provided by the theory of cooperative games can be used to clarify that issue. We have considered the question from a purely game theoretic point of view in Dehez and Ferey (2013). Here we propose to analyze it in a legal perspective. We consider in particular the difficult case of successive causation to which we associate a general class of games called "sequential liability games". We show that our model rationalizes the two-step procedure proposed by the Restatement Third of Torts, apportionment by causation and apportionment by responsibility. More precisely, we show that the weighted Shapley value associated to a sequential liability game is the legal counterpart of this two-step procedure.

In the current FIFA penalty shootout mechanism, a coin toss decides which team will kick first. Empirical evidence suggests that the team taking the first kick has a higher probability to win a shootout. We design sequentially fair shootout mechanisms such that in all symmetric Markov-perfect equilibria each of the skill-balanced teams has exactly 50% chance to win whenever the score is tied at any round. Consistent with empirical evidence, we show that the current mechanism is not sequentially fair and characterize all sequentially fair mechanisms. Taking additional desirable properties into consideration, we propose and uniquely characterize a practical mechanism.

We study here the problem of evaluating whether the selection from a set is close to the ranking determined by a measurable criterion. We propose a number of natural axioms and show that an index exists that satisfies all these axioms. The paper ends with an application of the index to Italian academia.

We provide an axiomatic approach to a belief formation process in an informational environment characterized by limited, heterogenous and differently precise information. For a list of previously observed cases an agent needs to express her belief by assigning probabilities to possible outcomes. Different numbers of observations of a particular case give rise to varying precision levels associated to the pieces of information. Different precise information affects the cautiousness and confidence with which agents form estimations. We modify the Concatenation axiom introduced in Billot, Gilboa, Samet and Schmeidler (BGSS) (Econometrica, 2005) in a way to capture the impact of precision and its related perceptional effects, while still keeping its normative appealing spirit. We obtain a representation of a belief as a weighted sum of estimates induced by past cases. The estimates are affected by cautiousness and confidence considerations depending on the precision of the underlying observed information, which generalizes BGSS. The weights are determined by frequencies of the observed cases and their similarities with the problem under consideration.

The question of measuring and managing systemic risk - especially in view of the recent financial crises - became more and more important. We study systemic risk by taking the perspective of a financial regulator and considering the axiomatic approach originally introduced in Chen et al. (2013) and extended in Kromer et al. (2014). The aim of this paper is to generalize the static approach in Kromer et al. (2014) and analyze systemic risk measures in a dynamic setting. We work in the framework of Cheridito et al. (2006) who consider risk measures for bounded discrete-time processes. Apart from the possibility to consider the “evolution of financial values”, another important advantage of the dynamic approach is the possibility to incorporate information in the risk measurement and management process. In context of this dynamic setting we also discuss the arising question of time-consistency for our dynamic systemic risk measures.

The following analysis is meant to contribute to a history of rational choice theory. More specifically, I provide a multi-layered account of rational choice theory in terms of its biography as a scientific object. I argue that its axiomatic version, choice theory traveled between different research sites, became specified through different mathematical formalisms and occupied distinct epistemic functions; it was being applied to prescribe rules of proper behavior, as representation of behavioral hypotheses, and as measurement device to capture individual values. New modifications of what I call ‘axiomatic choice theory’ did not fully replace old versions of it, which prevents the reconstruction of its journey as a continuous process of progressive knowledge production and suggests a more nuanced account of axiomatic choice theory that acknowledges its different versions currently used in the social sciences. Furthermore, by revealing the diversity of its manifestations within the context of social networks and within particular research sites, the account of axiomatic choice theory developed here will ultimately contributes to an explanation of the disunity and confusion surrounding current debates about rational choice theory and allows for providing a more nuanced picture of its nature and scope. Jacob Marschak’s professional development is used as a guide through this history of axiomatic choice theory to illustrate its journey.

In view of the recent financial crisis systemic risk has become a very important research object. It is of significant importance to understand what can be done from a regulatory point of view to make the financial system more resilient to global crises. Systemic risk measures can provide more insight on this aspect. The study of systemic risk measures should support central banks and financial regulators with information that allows for better decision making and better risk man- agement. For this reason this paper studies systemic risk measures on locally convex-solid Riesz spaces. In our work we extend the axiomatic approach to systemic risk, as introduced in Chen et al. (2013), in different directions. One direction is the introduction of systemic risk measures that do not have to be positively homogeneous. The other direction is that we allow for a general measurable space whereas in Chen et al. (2013) only a finite probability space is considered. This extends the scope of possible loss distributions of the components of a financial system to a great extent and introduces more flexibility for the choice of suitable systemic risk measures.

A comprehensive dynamic model of the monetary economy that produces the key characteristics of a debt deflation has been presented recently by Steve Keen as an alternative to conventional approaches. His model is based on a double-entry bookkeeping methodology but lacks an acceptable profit theory. In this respect it is not different from familiar approaches. Clearly, a deficient profit theory prevents a proper understanding of how the real world economy works. The present paper takes an entirely different route and places the core of Fisher’s debt deflation theory into the context of the consistent structural axiomatic approach.

The main goal of this paper is presentation a modern axiomatic approach to financial arithmetic. At the first, the axiomatic financial arithmetic theory was proposed by Peccati who has introduced the axiomatic definition of the future value. This theory has been extensively developed in past years. Modern approach to financial arithmetic is based on the financial flow utility concept. This utility function is defined by linear extension of multicriteria comparison determined as product of the time preference and the capital preference. Then the present value is equal to given financial flow utility. Therefore, the law of diminishing marginal wealth utility has been considered as additional feature of the present value. The future value is defined as the inverse of utility function. This definition is a generalization of the Peccati’s one. The net present value is given as the unique additive extension of financial flow utility.Moreover, the synergy effect and the diversification effect will be discussed. At the end, the axiomatic present value definition will be specified in three ways.

We explore in this paper the implications of ethical and operational principles for the evaluation of population health. We formalize those principles as axioms for social preferences over distributions of health for a given population. We single out several focal population health evaluation functions, which represent social preferences, as a result of combinations of those axioms. Our results provide rationale for popular theories in health economics (such as the unweighted aggregation of QALYs or HYEs, and generalizations of the two, aimed to capture concerns for distributive justice) without resorting to controversial assumptions over individual preferences.

A crisis is but a crisis when the long run outlook is definitively positive. Then a lower turning point must exist. This implicates a vision or, in the ideal case, a formalized theory of the money economy’s possible end states. This theory has to provide an endogenous explanation of end states and crises. The equilibrium approach excludes endogenous causes in principle. Thus disturbances can only be explained by exogenous random shocks. The structural axiomatic approach, that is applied in the following, consistently defines the potential systemic crisis point and the conditions of an economic happy end.

Taking the water–diamond paradox as a time-honored challenge, at first the structural value theorem is derived from the set of structural axioms. This enables a reevaluation of classical and neoclassical conceptions. Ricardo realized that there are two entirely different kinds of markets but excluded the secondary markets by defining commodity in a restricted sense. Walras’s markets are secondary markets by construction. Primary markets thereby drop from sight. Since secondary markets presuppose primary markets the marginalistic approach is hanging in the air. The structural axiomatic approach demonstrates that the pricing in primary and secondary markets depends on different principles.

This paper discusses a new approach to validating risk-related expert systems. The paper builds on existing knowledgebase verification and software testing literature to propose that risk related expert systems check for pareto optimal trade-offs in rule conditions along with the checks for ensuring contiguous numeric risk state space is covered by rules to ensure to gap in logic occurs. The construct of pareto optimal rules is novel and shown to be an effective and tractable approach used in production systems. In addition the pareto optimal property is form of common sense which financial credit related expert systems, which abound in industry, can benefit from as evidenced by the recent credit crisis. Ensuring that all rules are contiguous and pareto optimal within rule contexts adds to the expert system verification literature and is an approach that can increase early detection of defects along with ensuring sound credit decisioning for industrial expert systems. Thus the work has theoretical and practical value.

This article summarizes the theory of markets under uncertainty that Arrow and Debreu created, its achievements and the critical issues that it raises. It focuses on the way Arrow introduced securities: how he defined them and what were the most useful developments of this theory. It mentions the theory of insurance that Arrow pioneered together with Malinvaud and others, and Arrow’s theory of risk bearing that follows the axiomatic treatment of Von Neumann and Morgenstern, Milnor, Hernstein, De Groot, and Villegas. The classic expected utility theory embraces normal or frequent risks at the expense of neglecting rare events, even those with important consequences such as catastrophes, causing paradoxical experimental behavior as shown by the author. Kenneth Arrow encouraged the creation of an extension of classic axiomatic theory, and in the early 1990s the author proposed axioms that treat symmetrically frequent and rare events, leading to a new definition of rationality and a new form of choice under uncertainty that conforms better to the experimental evidence. Additionally, the introduction of markets with endogenous uncertainty in the early 1990s challenged the foundation of Arrow Debreu's theory of markets. Endogenous uncertainty is generated by the workings of the economy, and breaks down the equivalence between markets with and without uncertainty that prevails in Arrow Debreu's theory. This leads to a new world of uncertainty creation through financial innovation and regulation that is at the heart of the financial markets turmoil of 2008. In 1999 Arrow contributed to the theory of endogenous uncertainty in his work with Frank Hahn.

This article extends prospect theory, mental accounting, and the hedonic editing model by developing an axiomatic theory to explain the behavior of investors with extended value functions in segregating or integrating multiple outcomes when evaluating mental accounting.

Three axioms from decision theory select sets of Nash equilibria of signaling games in extensive form with generic payoffs. The axioms require undominated strategies (admissibility), inclusion of a sequential equilibrium (backward induction), and dependence only on the game's normal form even when embedded in a larger game with redundant strategies or irrelevant players(small worlds). The axioms are satisfied by a set that is stable (Mertens, 1989) and conversely the axioms imply that each selected set is stable and thus an essential component of admissible equilibria with the same outcome.

Reinforcement learning theory has produced important insights into economic behavior. Intriguingly, neuroscientists recently discovered a plausible mechanism through which reinforcement may be encoded in the brain. Yet their resulting "dopaminergic reward prediction error" hypothesis has not yet been incorporated into economics. We develop an axiomatic model that characterizes the empirical implications of this theory for an idealized data set comprising both neuroscientific measurements and choices. Our axiomatization removes the language barrier between economics and neuroscience. This will allow "neuroeconomic" experimental protocols to be developed appropriate to the questions motivating economic, as opposed to purely neuroscientific, interest in learning.

The most important economic measures are monetary. They have many different names, are derived in different theories and employ different formulas; yet, they all attempt to do the same thing: to separate a change in nominal value into a ‘real part’ due to the changes in quantities and an inflation due to the changes in prices. Examples are: real national product and its components, the GNP deflator, the CPI, various measures related to consumer surplus, as well as the large number of formulas for price and quantity indexes that have been proposed. The theories that have been developed to derive these measures are largely unsatisfactory. The axiomatic theory of indexes does not make clear which economic problem a particular formula can be used to solve. The economic theories are for the most part based on unrealistic assumptions. For example, the theory of the CPI is usually developed for a single consumer with homothetic preferences and then applied to a large aggregate of diverse consumers with non-homothetic preferences. In this paper I review both the general literature and my own past contributions in order to identify theories of measurement that are based on plausible economic assumptions. It turns out that all such theories lead to the Törnqvist price or quantity indexes. The paper also covers several related topics, particularly the presently unsatisfactory determination of the components of real GDP. I also propose a novel set of integrated accounts to measure changes in relative prices as well as the sectoral sources of inflation.

The paper reviews the theory of the measurement of poverty. The axiomatic theory is described and the axiomatic properties of poverty indexes are related to assumptions on the functional form of the poverty index function. The notion of poverty ordering is then introduced and followed by a review of the relations between the poverty orderings than can be defined from classes of poverty index functions with well-defined functional form properties and the notions of first order and second order stochastic dominance. The analysis applies the results used in the theory of economic inequality to study the relationship between welfare orderings and Lorenz dominance. The theory is used to analyze poverty patterns in Italy in 1997-2005.

We survey some recent research results in the field of dynamic cooperative differential games with non-transferable utilities. Problems which fit into this framework occur for instance if a person has more than one objective he likes to optimize or if several persons decide to combine efforts in trying to realize their individual goals. We assume that all persons act in a dynamic environment and that no side-payments take place. For these kind of problems the notion of Pareto efficiency plays a fundamental role. In economic terms, an allocation in which no one can be made better-off without someone else becoming worseoff is called Pareto efficient. In this paper we present as well necessary as sufficient conditions for existence of a Pareto optimum for general non-convex games. These results are elaborated for the special case that the environment can be modeled by a set of linear differential equations and the objectives can be modeled as functions containing just affine quadratic terms. Furthermore we will consider for these games the convex case. In general there exists a continuum of Pareto solutions and the question arises which of these solutions will be chosen by the participating persons. We will flash some ideas from the axiomatic theory of bargaining, which was initiated by Nash [16, 17], to predict the compromise the persons will reach.

The measurement and the allocation of risk are fundamental problems of portfolio management. Coherent measures of risk provide an axiomatic approach to the former problem. In an environment given by a coherent measure of risk and the various portfolios’ realization vectors, risk allocation games aim at solving the second problem: How to distribute the diversification benefits of the various portfolios? Understanding these cooperative games helps us to find stable, efficient, and fair allocations of risk. We show that the class of risk allocation and totally balanced games coincide hence a stable allocation of risk is always possible. When the aggregate portfolio is riskless: risk is limited to subportfolios, the class of risk allocation games coincides with the class of exact games. As in exact games any subcoalition may be subject to marginalization even in core allocations, our result further emphasizes the responsibility in allocating risk.

In Ellsberg paradox, decision makers that are partially informed about the actual probability distribution violate the expected utility paradigm. This paper develops a theory of decision making with a partially specified probability. The paper takes an axiomatic approach using Anscombe-Aumann's (1963) setting, and is based on a concave integral for capacities (see Lehrer, 2005). The partially-specified decision making is then carried on to games in order to introduce partially-specified equilibrium.

Most, if not at all, practitioners of welfare economics and social choice theory are presumed to be welfaristic in their conviction. Indeed, they evaluate the goodness of an economic policy and/or economic system in terms of the welfare that people receive at the culmination outcomes thereby generated. Recent years have witnessed a substantial upsurge of interest in the non-welfaristic bases, or even the non-consequentialist bases, of welfare economics and social choice theory. Capitalizing on the axiomatic approach which we explored in the recent past, we try to provide a coherent analysis of consequentialism vis-a-vis non-consequentialism. To begin with, we develop an abstract framework in which the primitive of our analysis is a preference ordering held by an evaluator over the pairs of culmination outcomes and opportunity sets from which those culmination outcomes are chosen. As a partial test to see how much relevance can be claimed of the axiomatized concepts of consequentialism and non-consequentialism, two simple applications of this abstract framework are worked out. The first application is to the Arrovian social choice theory and the second application is to the analysis of ultimatum games.

Born out of the conscious effort to imitate mechanical physics, neoclassical economics ended up in the mid 20th century embracing a purely mathematical notion of rigor as embodied by the axiomatic method. This lecture tries to explain how this could happen, or, why and when the economists' role model became the mathematician rather than the physicist. According to the standard interpretation, the triumph of axiomatics in modern neoclassical economics can be explained in terms of the discipline's increasing awareness of its lack of good experimental and observational data, and thus of its intrinsic inability to fully abide by the paradigm of mechanics. Yet this story fails to properly account for the transformation that the word rigor itself underwent first and foremost in mathematics as well as for the existence of a specific motivation behind the economists' decision to pursue the axiomatic route. While the full argument is developed in Giocoli 2003, these pages offer a taste of a (partially) alternative story which begins with the so-called formalist revolution in mathematics, then crosses the economists' almost innate urge to bring their discipline to the highest possible level of generality and conceptual integrity, and ends with the advent and consolidation of that very core set of methods, tools and ideas that constitute the contemporary image of economics.

We show in this paper how a tax law can be formulated which (i) does not distort economic incentives of individuals and firms, (ii) is based on low information requirements, and (iii) which does not violate important behavioral facts such as fairness in taxation of the subjects. That for, a social norm approach is used which replaces the individuals' utility functions in optimal taxation theory initiated by Vickrey (1945) and Diamond and Mirrless (1971). Based on axioms representing the social norms, we prove that a unique class of tax functionals exists. Furthermore, the tax functionals can be explicitly constructed and possess a concrete integral representation. This class of admissible tax functionals which are compatible with the given axioms allows to determine a tax functional which optimizes an externally given objective function. We also compare the theory to the actual Swiss tax law. In doing so, we find that all but one axiom are violated. More specifically, tax functional induced by the current law is neither monotone, nor continuous, nor additive nor time invariant. Finally, the tax law also violates the economic incentive compatibility axiom.

We examine the problem of measuring influence based on the information contained in the data on the communications between scholarly publications, judicial decisions, patents, web pages, and other entities. The measurement of influence is useful to address several empirical questions such as reputation, prestige, aspects of the diffusion of knowledge, the markets for scientists and scientific publications, the dynamics of innovation, ranking algorithms of search engines in the World Wide Web, and others. In this paper we ask why any given methodology is reasonable and informative applying the axiomatic method. We find that a unique ranking method can be characterized by means of five axioms: Anonymity, invariance to citation intensity, weak homogeneity, weak consistency, and invariance to splitting of journals. This method is easily implementable and turns out to be different from those regularly used in social and natural sciences, arts and humanities, and computer science.

Building upon the works of Anscombe and Aumann (1963) and Karni and Schmeidler (1981), we develop a general axiomatic theory of quantifiable beliefs - a form of probabilistic sophistication that does not preclude state-dependent preferences and does not require the reduction of compound lotteries. The theory includes the state-dependent expected utility model of Karni and Schmeidler (1981) and the state-independent non-expected utility model of Machina and Schmeidler (1995) as special cases. The theory is flexible enough to admit recursivity in the decision-making process. One specific example of this recursive class is shown to be compatible with a quantifiable beliefs version of Schmeidler's (1989) Choquet expected utility maximizing model and thus capable of rationalizing Ellsberg-paradox type behavior.

Within a production theoretic framework, this paper considers an axiomatic approach to benchmark selection. It is shown that two simple and weak axioms: efficiency and comprehensive monotonicity characterize a natural family of benchmarks which typically becomes unique. Further axioms are added in order to obtain a unique selection.

We investigate various properties of the internal rate of return (IRR) metric for investment projects. It is known that this metric does not exist or is not uniquely defined for many projects. Therefore many suggestions for replacing it by some modified indexes with a wider domain of definition are known to exist. Such sugestions are considered in the paper with a general inference as to their inappropriateness. On a positive side, we offer a system of axioms reflecting the basic properties of IRR and present the structure of “return indexes” which would satisfy such axioms. It is demonstrated that as long as the projects with identical “return indexes” maintain affine transformation along the time axis, such indices would coincide (accurate to a monotonous smooth transformation) with the “usual” IRR. An issue of defining “profitability indices” for projects with random cash flows is considered as well. Note: The downloadable document is in Russian.

The adversarial provision of evidence is modeled as a game in which two parties engage in strategic sequential search. An axiomatic approach is used to characterize a court's decision based on the evidence provided. Although this process treats the evidence submissions in an unbiased way, the equilibrium outcome may still exhibit bias. Bias arises from differences in the cost of sampling or asymmetry in the sampling distribution. In a multistage model, a prodefendant bias arises in the first stage from a divergence between the parties' stakes. Finally, the adversarial process generates additional costs that screen out some otherwise meritorious cases. Copyright 2000 by Oxford University Press.

The paper proposes two axioms that capture the idea of sustainable development and derives the welfare criterion that they imply. The axioms require that neither the present nor the future should play a dictatorial role. Theorem 1 shows there exist sustainable preferences, which satisfy these axioms. They exhibit sensitivity to the present and to the long-run future, and specify trade-offs between them. It examines other welfare criteria which are generally utilized: discounted utility, lim inf. long run averages, overtaking and catching-up criteria, Ramsey's criterion, Rawlsian rules, and the criterion of satisfaction of basic needs, and finds that none satisfies the axioms for sustainability. Theorem 2 gives a characterization of all continuous independent sustainable preferences. Theorem 3 shows that in general sustainable growth paths cannot be approximated by paths which approximate discounted optima. Proposition 1 shows that paths which maximize the present value under a standard price system may fail to reach optimal sustainable welfare levels, and Example 4 that the two criteria can give rise to different value systems.