Dutch books and agent rationality

According to the Dutch Book Argument (DBA), if an agent's subjective probabilities fail to satisfy the axioms of the probability calculus and so make the agent vulnerable to a Dutch Book, the agent's subjective probabilities are incoherent and the agent is therefore irrational. Critics of DBA have argued, however, that probabilistic incoherence is compatible with various kinds of rationality – logico-semantic, epistemic, instrumental and prudential. In this paper, I provide an interpretation of DBA on which it is true that probabilistic incoherence entails agent irrationality. Articulating this interpretation requires the specification of some of the connections among the varieties of rationality. Once this is done, it becomes possible to vindicate a modest version of DBA.     

On the evaluation of solution concepts

It is proposed that solution concepts for games should be evaluated in a way that is analogous to the way a logic is evaluated by a model theory for the language. A solution concept defines a set of strategy profiles, as a logic defines a set of theorems. A model theoretic analysis for a game defines a class of models, which are abstract representations of particular plays of the game. Given an appropriate definition of a model, one can show that various solution concepts are characterized by intuitively natural classes of models in the same sense that the set of theorems of a logic is characterized by a class of models of the language. Sketches of characterization results of this kind are given for rationalizability, Nash equilibrium, and for a refinement of rationalizability —strong rationalizability — that has some features of an equilibrium concept. It is shown that strong rationalizability is equivalent to Nash equilibrium in perfect information games. Extensions of the model theoretic framework that represent belief revision and that permit the characterization of other solution concepts are explored informally.     

On the logic of common belief and common knowledge

The paper surveys the currently available axiomatizations of common belief (CB) and common knowledge (CK) by means of modal propositional logics. (Throughout, knowledge — whether individual or common — is defined as true belief.) Section 1 introduces the formal method of axiomatization followed by epistemic logicians, especially the syntax-semantics distinction, and the notion of a soundness and completeness theorem. Section 2 explains the syntactical concepts, while briefly discussing their motivations. Two standard semantic constructions, Kripke structures and neighbourhood structures, are introduced in Sections 3 and 4, respectively. It is recalled that Aumann's partitional model of CK is a particular case of a definition in terms of Kripke structures. The paper also restates the well-known fact that Kripke structures can be regarded as particular cases of neighbourhood structures. Section 3 reviews the soundness and completeness theorems proved w.r.t. the former structures by Fagin, Halpern, Moses and Vardi, as well as related results by Lismont. Section 4 reviews the corresponding theorems derived w.r.t. the latter structures by Lismont and Mongin. A general conclusion of the paper is that the axiomatization of CB does not require as strong systems of individual belief as was originally thought — onlymonotonicity has thusfar proved indispensable. Section 5 explains another consequence of general relevance: despite the infinitary nature of CB, the axiom systems of this paper admit of effective decision procedures, i.e., they aredecidable in the logician's sense.     

Market uncertainty and the process of belief formation

Subjective or personal belief formation has been up to now grounded on axioms (e.g., the axioms of Savage) that can be described asintrospection axioms, for they bear only on judgments formed by the individual within himself (e.g., judgments on the ordering of the “acts” in Savage's contribution), excluding every reference to other, possibly external, sources of opinion formation. This current view, linked to the traditional concept ofinstrumental economic rationality, implicitly assumes cognitive capacities that are most of the time out of the reach of any individual. Therefore this view is little or improperly used in the practical world of economics and/or management. An alternative view of belief formation on a market is offered in this article, grounded on a much more modest demand of cognitive capacities from the individual and on a different concept of economic rationality known ascognitive rationality. The model introduces to this end the global concept of market psychology as well as the concept of regular revision of the sets of opinions. Belief formation then appears as a process of deliberation between the individual and the market, rationality emerging within this process as deeply intertwined with the way the individual revises his opinions during the process. The rational treatment of beliefs in view of reaching a decision can consequently be carefully distinguished from their rational formation process.     

The Simplest Dynamic General-Equilibrium Model of an Open Economy

This paper presents the simplest possible general-equilibrium model of an open economy in which producer and consumer decisions are both intra- and intertemporally consistent. Consumers maximize the present value of the utility of consumption; producers maximize the present value of profits. The model solves for the set of intertemporally consistent prices. The parsimonious structure of the model is achieved by dividing the economy into two producing sectors—exports and domestic goods—and two consumed goods—imports and domestic goods. As a result, there is only one endogenous price per period to be solved for (the price of the domestic good), although “structural” questions, such as the evolution of the real exchange rate, can be posed with the model. Furthermore, with this structural breakdown, the model can be calibrated with national accounts data only. In the paper, we show how to calibrate such a model (including specification of an adjustment-cost function, to avoid “bang-bang” behavior) and use the model to examine various questions where intertemporal issues are important, including terms-of-trade shocks and tariff reform.     

A Model of Minimal Probabilistic Belief Revision

In the literature there are at least two models for probabilistic belief revision: Bayesian updating and imaging [Lewis, D. K. (1973), Counterfactuals, Blackwell, Oxford; Gärdenfors, P. (1988), Knowledge in flux: modeling the dynamics of epistemic states, MIT Press, Cambridge, MA]. In this paper we focus on imaging rules that can be described by the following procedure: (1) Identify every state with some real valued vector of characteristics, and accordingly identify every probabilistic belief with an expected vector of characteristics; (2) For every initial belief and every piece of information, choose the revised belief which is compatible with this information and for which the expected vector of characteristics has minimal Euclidean distance to the expected vector of characteristics of the initial belief. This class of rules thus satisfies an intuitive notion of minimal belief revision. The main result in this paper is to provide an axiomatic characterization of this class of imaging rules.     

Probability and logic in belief systems

This paper seeks to develop a formal (mathematical) model of belief systems based on the axioms of probability theory and propositional logic. By a belief system we mean a set of propositions along with an actor's objective probability assignments to (beliefs in) them, together with the relationships among and between propositions and beliefs. Belief systems are regarded as being comprised of interrelated elements.In the paper are developed measures of the distance between sets of beliefs; of the congruence, coherence, and consistency of belief systems; and of the degree of polarization of belief systems-which are derived from one basic operation, symmetric difference.We show that these measures possess a number of useful and powerful mathematical properties. Also, a model is set forth by which, from an actor's subjective probability assignment to propositions and pairwise conjunctions of propositions, we may then impute to the actor subjectively perceived truth functional relationships between proposition.The potential uses and practical difficulties with the approach taken in the paper are also discussed, and the assertion is made that the measures developed enable us to simply distinguish between certain notions (e.g., congruence, consistency, coherence) too often and easily confused, provide us with the possibility of interval (or at least, quasi-interval level) measurement of certain properties of individual belief systems, and also allows us to make comparisons between the structures of different actors' belief systems.An earlier version of this paper was delivered at the 1969 American Political-Science Association, Chicago.     

Implementing a social norms approach to reduce alcohol abuse on campus: Lessons learned in the shadow of ‘The World's Largest Six-Pack’

Many institutions of higher education are struggling with the problem of excessive alcohol consumption by students. Colleges and universities want to be ‘good neighbors’ in their communities and must limit legal and social risks that result from excessive alcohol consumption by students. At the same time, colleges and universities operate in an increasingly challenging marketplace where many prospective students seek out institutions with a ‘party school’ reputation. Thus, higher education institutions are finding it difficult to define and carry out alcohol reduction measures that satisfy all constituents. This article discusses the approach taken at the University of Wisconsin—La Crosse. UW-L is an institution that identified a serious alcohol consumption problem and had to address the problem in a community where high levels of alcohol consumption are socially and culturally condoned. The article profiles the UW-L community and discusses the campaign model and strategy chosen. Quantitative and qualitative measures of success are discussed, along with lingering issues of resistance. The article ends with a summary of current issues and future directions being taken by the campaign.     

A Reason to Believe: Examining the Factors that Determine Individual Views on Global Warming*

Objectives. In this article we examine the causes of both belief and disbelief in global warming among adult Americans. Methods. We use national‐ and state‐level telephone surveys to collect data on individual‐level beliefs regarding climate change and employ ordered logistical regression to measures the relative effect of various factors on those beliefs. Results. The study finds that U.S. views on climate change are being shaped by a combination of personal observations, meteorological events, and physical changes on the planet. The impact of various factors on one's belief in global warming are significantly determined by partisan affiliation, with Democrats and Republicans responding differently to assorted types of evidence. Conclusion. Beliefs regarding global warming are being shaped by individual experiences and weather phenomenon and the processing of such factors is substantially influenced by a person's partisan leanings.     

‘‘With the greatest respect and fidelity:’ a Cherokee vision of the ‘Trust’ doctrine”

The trust relationship is the conceptual/philosophical framework against which all relations between the federal government and indigenous groups are conducted. Yet despite the centrality of this concept, federal policymakers have no consistent or agreed upon definition of what the trust relationship actually entails (Wilkins, 1997). And, more importantly, indigenous conceptions of trust have rarely been assessed. This article analyzes and advances one tribe's—the Cherokee—perspective on trust. In focusing on how the Cherokee perceive trust, this section emphasizes that from an indigenous viewpoint the trust relationship embodies a complex and sophisticated understanding that both the tribe and the United States have reciprocal responsibilities to maintain positive relations towards one another. The leaders of the Cherokee people—one of the more diverse indigenous groups— understood in the federal government's actions, whether these were expressed in treaties, policy statements, congressional laws, or court decisions, that the federal government was pledged to protect Cherokee property and sovereignty, would act with utmost integrity in its legal and political dealings with the people, and would insure that the United States political and judicial representatives would act in a moral manner regarding the tribe's rights. Notwithstanding the federal government's tremendous variety of treaty and trust violations, the Cherokee conception of trust is regenerative from generation to generation. This breathes new life into a seasoned concept and offers hope for the often difficult political/legal relations between the federal, state, and tribal governments. And here we beg leave to ask of our father that, in future transactions of a public nature between the United States and our nation, the American Government will not require of our nation any thing which, as our protectors and guardians, they will not, after due deliberation, advise us to comply with; and having no doubt of the magnanimity and benignity of the Government, we shall return home satisfied, and report to our nation the result of our mission to this. With the greatest respect and fidelity, we subscribe our names (Going Snake, et al., 1817, p. 147)     

Economics of (oil) price politics: Penalizing price changes

This article studies intertemporal monopolistic pricing strategies when demand is dynamic and when price volatility may harm other producer objectives, e.g. the political good will for an international cartel. The major implications from this framework are that the introduction of a penalty for price changes may actually change an otherwise (at least locally) monotonic policy into a (transiently) oscillatory strategy; on the other hand, penalizing price changes smooths the price policy when demand is convex and the optimal strategy would otherwise be extremely volatile. But, then, all various types of solutions—cyclical and even unstable solutions—may occur.     

Expected utility with lower probabilities

An uncertain and not just risky situation may be modeled using so-called belief functions assigning lower probabilities to subsets of outcomes. In this article we extend the von Neumann-Morgenstern expected utility theory from probability measures to belief functions. We use this theory to characterize uncertainty neutrality and different degrees of uncertainty aversion.We are grateful to Birgit Grodal, Salvatore Modica, David Schmeidler, and an anonymous referee for comments, help, and encouragement. Financial support from the Danish Social Sciences Research Council is acknowledged.     

A Unified Bayesian Decision Theory

This paper provides new foundations for Bayesian Decision Theory based on a representation theorem for preferences defined on a set of prospects containing both factual and conditional possibilities. This use of a rich set of prospects not only provides a framework within which the main theoretical claims of Savage, Ramsey, Jeffrey and others can be stated and compared, but also allows for the postulation of an extended Bayesian model of rational belief and desire from which they can be derived as special cases. The main theorem of the paper establishes the existence of a such a Bayesian representation of preferences over conditional prospects, i.e. the existence of a pair of real-valued functions respectively measuring the agent’s degrees of belief and desire and which satisfy the postulated rationality conditions on partial belief and desire. The representation of partial belief is shown to be unique and that of partial desire, unique up to a linear transformation.     

Economics of public policy in health care systems

Externality arises when the private economy lacks incentives to set up a potential market in some commodity and when the nonexistence of this market results in a Pareto-suboptimal allocation. How can this idea be modified in the setting of the public benefits model of health care? This article argues that the equilibrium level of expenditure on health care is likely to vary markedly, depending on the institutional arrangements for its provision—public, mixed private-public, or purely private—but in none of these is the level of expenditure necessarily Pareto-optimal.     

Explaining third-party success in gubernatorial elections: The cases of Alaska, Connecticut, Maine and Minnesota

In the 1990s alone, four states elected third-party governors. Walter Hickel of Alaska and Lowell Weicker of Connecticut were elected in 1990. Maine elected Angus King in 1994. And Jesse Ventura was elected governor of Minnesota in 1998. In this article, I examine these four cases in an attempt to identify the factors that contribute to third-party electoral success. I apply two models to these cases. The first model, “alternative culture,” holds that certain voters—regardless of specific context—are predisposed to support alternative candidates. The second model, “institutional context,” looks at factors such as name recognition, resources, and access to media as explanations of third-party success. I find that except for the influence of “partisan independence,” there is little evidence to support the persistence of an alternative culture of third-party voting. Rather, these four cases are linked by a context particularly favorable to these alternative candidates.     

Ramsey's Foundations Extended to Desirabilities

In his Truth and Probability (1926), Frank Ramsey provides foundations for measures of degrees of belief in propositions and preferences for worlds. Nonquantitative conditions on preferences for worlds, and gambles for worlds and certain near-worlds, are formulated which he says insure that a subject's preferences for worlds are represented by numbers, world values. Numbers, for his degrees of belief in propositions, probabilities, are then defined in terms of his world values. Ramsey does not also propose definitions of desirabilities for propositions, though he is in a position to do this. Given his measures for probabilities of propositions and values of worlds, he can frame natural definitions for both evidential and causal desirabilities that would measure respectively the welcomeness of propositions as items of news, and as facts. His theory is neutral with respect to the evidential/causal division. In the present paper, as Ramsey's foundations are explained, several problems and limitations are noted. Their distinctive virtue – their evidential/causal neutrality – is demonstrated. Comparisons are made with other foundational schemes, and a perspective is recommended from which nonquantitative foundations are not the be all for quantitative theories of ideal preferences and credences.     

Amos Tversky and the Ascent of Behavioral Economics

Amos Tversky investigated and explained a wide range of phenomena that lead to anomalous human decisions. His two most significant contributions, both written with Daniel Kahneman, are the decision-making heuristics—representativeness, availability, and anchoring—and prospect theory. Tversky's concepts have broadly influenced the social sciences. In economics, they gave rise to the burgeoning field of behavioral economics. This field, skeptical of perfect rationality, emphasizes validation of modeling assumptions, integration of micro-level data on decisions (including experimental evidence), and adoption of lessons from psychology. Tversky's contributions are reviewed, assessed using citation analysis, and placed in historical context. Fertile areas for behavioral economics research are identified.     

Capacity Updating Rules and Rational Belief Change

Choquet expected utility substitutes capacities for subjective probabilities to explain uncertainty aversion and related phenomena. This paper studies capacities as models of belief. The notions of inner and outer acceptance context are defined. These are shown to be the natural acceptance contexts when belief expansion is described by naïve Bayesian and Dempster–Shafer updating of capacities respectively. We also show that Eichberger and Kelsey's (1999b) use of Dempster–Shafer updating as a model of belief revision may lead to violations of the AGM axioms for rational belief change.     

Games of Incomplete Information Without Common Knowledge Priors

We relax the assumption that priors are common knowledge, in the standard model of games of incomplete information. We make the realistic assumption that the players are boundedly rational: they base their actions on finite-order belief hierarchies. When the different layers of beliefs are independent of each other, we can retain Harsányi's type-space, and we can define straightforward generalizations of Bayesian Nash Equilibrium (BNE) and Rationalizability in our context. Since neither of these concepts is quite satisfactory, we propose a hybrid concept, Mirage Equilibrium, providing us with a practical tool to work with inconsistent belief hierarchies. When the different layers of beliefs are correlated, we must enlarge the type-space to include the parametric beliefs. This presents us with the difficulty of the inherent openness of finite belief subspaces. Appealing to bounded rationality once more, we posit that the players believe that their opponent holds a belief hierarchy one layer shorter than they do and we provide alternative generalizations of BNE and Rationalizability. Finally, we show that, when beliefs are degenerate point beliefs, the definition of Mirage Equilibrium coincides with that of the generalized BNE. This revised version was published online in June 2006 with corrections to the Cover Date.     

Doxastic Conditions for Backward Induction

The problem of finding sufficient doxastic conditions for backward induction in games of perfect information is analyzed in a syntactic framework with subjunctive conditionals. This allows to describe the structure of the game by a logical formula and consequently to treat beliefs about this structure in the same way as beliefs about rationality. A backward induction and a non-Nash equilibrium result based on higher level belief in rationality and the structure of the game are derived.